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CHIGAN STATE UNIVERSITY RABIES

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3 1293 00901 0640

 

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—

 

 

 

 

 

 

 

 

 

 

 

 

 

This is to certify that the

thesis entitled

DIVERSE PLATFORM MODELING OF DYNAMICAL SYSTEMS

presented by

Robert Alex Mitchell

has been accepted towards fulfillment
of the requirements for

Master o_t_SLj_ence_degree in Mechanical. Engineering

   

Major professor

Date HAZ[4/
/ /

0-7639 MS U is an Affirmative Action/Equal Opportunity lnstitu lion

 

 

 

 

l LIBRARY
Michigan State
' University

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.

TO AVOID FINES return on or before due due.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An Affirmative ActionlEqual Opportunity Institution
cmma-ptt

DIVERSE PLATFORM MODELING OF DYNAMICAL SYSTEMS

By
Robert Alex Mitchell

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering
1991

 

A cunt
dynami
softwai
soluti01
propos
platfor
bond g
Systerr

aStan

6574767

ABSTRACT
DIVERSE PLATFORM MODELING OF DYNAMICAL SYSTEMS
BY
Robert Alex Mitchell

A current problem in engineering simulation is the difficulty with which the various
dynamical components of a system may be conveniently modeled using a single .
software platform. The Diverse Platform Modeling (DPM) technique proposes a
solution path for this modeling difficulty. Two general strategies for application of the
proposed technique, using the bond-graph modeling domain as a ”host" simulation
platform, are presented. A software utility has been created for ENPORT, an existing
bond graph modeling and simulation platform, that allows externally created dynamical
system models of a specified class to be injected into the ENPORT system graph using
a Standard Model Description (SMD) file.

during
invalu
at Ros

much a

a stude

eventuaj

Commen

the ph y

 

formidai

 

 

ACKNOWLEDGEMENTS

I would like to thank my advisor, Dr. Ronald Rosenberg, for his guidance
during the development of this thesis. I would also like to thank Dr. Rosenberg for the
invaluable skills I have attained in the area of software development under his direction
at Rosencode Associates Inc. The experience I have gained in this area has been as

much a part of my education as the course work.

I would like to thank my family for their support throughout my long carrier as
a student at Michigan State University. They have continually assured me that

eventually all the struggles and sacrifices would pay off.

Finally, I would like to thank my wife Robin for her suggestions and helpful
comments during the writing of this thesis. There is a bright carrier waiting for her in
the physieal sciences. Also, I would like to acknowledge her blossoming as a

formidable contender in the arena of miniature basketball.

iii

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES
NOMENCLATURE
Chapter
1. INTRODUCTION
2. THE DIVERSE PLATFORM MODELING TECHNIQUE
3. THE BOND GRAPH MODELING DOMAIN AS HOST FOR DPM
4. TOPOLOGICAL APPROACH TO DPM WITH ENPORT AS HOST
4.1 Multiport Configuration for Injected MCK Models
4.2 Modal Configuration for Injected MCK Models
5. SYSTEM EQUATION APPROACH TO DPM WITH ENPORT AS
HOST
5.1 The Macro Dynamic System as Applied to MCK Models
5.2 A Class Specific Macro Dynamic Node Type
6. EXAMPLE SYSTEM
6.1 The Finite Element Model
6.2 Multiport Expansion
6.3 Modal Expansion
6.4 MCK Macro Dynamic System
6.5 Numerical Results
7. SUMMARY AND RECOMMENDATIONS
7.1 Summary
7.2 Recommendations for Future Development
LIST OF REFERENCES

iv

Page

vii

viii

ocooo‘Jx

11
15

15
17
19
19
22
23
24
25
26
26
26
28

APPENDICES
A. USER DOCUMENTATION

A1. SAMPLE MCK STANDARD MODEL DESCRIPTION FILE
A2. USER ACCESS FROM ENPORT

. THE EXAMPLE SYSTEM

Bl. MCK FILE FOR THE EXAMPLE SYSTEM

132: ENPORT MODEL FILE FOR EXAMPLE PROBLEM
(MULTIPORT)

133. ENPORT MODEL FILE FOR EXAMPLE PROBLEM
(MODAL)

. ORGANIZATION OF THE FORTRAN SOURCE CODE

C1. SUBPROGRAM CALLING TREE

C2. SUBPROGRAM LIST

C3. FORTRAN SOURCE CODE LISTINGS

29
30
32

35
37

46
47
48
49

 

Table
Table
Table
Table
Table

 

 

Table B-1 .
Table B-2.
Table 3-3.
Table C-l .
Table C-2.

LIST OF TABLES

MCK file for the example system.
ENPORT model file for multiport example.
ENPORT model file for modal example.
The subprogram ealling tree.

The subprogram list and associated source files.

Page
35
37

47
48

Figure
Figure

Figure

 

 

 

Figure

Figure .

Figure A

Figure 4

Figure 4

Figure 5

 

Figure 6
Figure

Figure 6
Figure 6
Figum 6

Figure A

Figure A

Figure 1-1
Figure 2-1
Figure 3-1
Figure 3-2

Figure 4-1
Figure 4-2

Figure 4-3
Figure 4-4

Figure 5-1
Figure 6-1
Figure 6-2
Figure 6-3
Figure 6—4
Figure 6-5

Figure 6—6

Figure A-l

Figure A-2
Figure A-3

LIST OF FIGURES

Graphical representation of DPM.

Diagram of the Diverse Platform Modeling technique.
Topologieal expansion of SMDs with bond graph domain as host.
Direct equation generation from SMDs with bond graph domain as
host.

Multiport configuration for a MCK dynamical system model.
Multiport configuration for a MCK dynamical system model with
causality visible.

Modal configuration for a MCK dynamical system model.

Modal configuration for a MCK dynamical system with causality
visible.

The Macro Dynamic System for an n-dimensional MCK model.
Dynamical system employed in numerical study.

Schematic diagram of FE nodal degrees of freedom.

Example system modeled using multiport expansion.

Example system modeled using modal expansion.

Example system modeled using a MCK Macro Dynamic System
node.

Response of the momentum of the load mass vs. time for
sinusoidal forcing.

Sample MCK Standard Description File for two DOF System.
ENPORT directory path for MCK model injection utility.

Sample ENPORT dialog screen for MCK model injection.
vii

Page

\ION-hN

11

13
14

17
19
20
22
23
24

25

31

32
33

NOMENCLATURE

C damping matrix

C' modal damping matrix
translational displacement

E external effort vector
stiffness matrix

K' modal stiffness matrix

M mass matrix

M' modal mass matrix

V velocity state vector

X state vector

2 physical coordinate vector

Greek Symbols

¢ rotational displacement

77

modal coordinate vector

viii

 

 

simula.

compo
electro
simulat
system
mentio

subsys

Wmmi
Diverse
modelin
SUbSysu
The mo

of the S,

Chapter 1

INTRODUCTION

The practicing engineer has an arsenal of powerful software available for
simulating the behavior of dynamical system components. For example, Finite Element
(FE) software may be used to develop accurate dynamical models of intricate structural
components of a system. Similarly, circuit analysis software may be used for modeling
electronic components of a system. Thermal, hydraulic, and other domain-specific
simulation software is also available. It is typical, however, for large dynamical
systems to be composed of elements or subsystems from a variety of the previously
mentioned modeling domains as well as others. The interactions between these

subsystems define the dynamieal behavior of the conglomerate system.

A current problem in engineering simulation is the difficulty with which the
system as a whole may be conveniently modeled using a single software platform. The
Diverse Platform Modeling (DPM) technique proposes a solution path for this
modeling difficulty. Proper application of DPM will allow the behavior of each
subsystem to be modeled using the domain specific platform best suited for the task.
The models may then be placed into a common, or ”host”, platform for the simulation

of the system as a whole. This is represented graphically in Figure 1-1.

 

Elec

:\ T—l

( a»

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Electronic Circuit Finite Element Hydraulic
Domain Domain Domain
I—
DICE]:
Host Platform

 

 

 

 

 

Figure 1-1. Graphical representation of DPM.

The DPM concepts presented in this thesis are general and may be applied to a
broad spectrum of modeling problems. The software development effort, however, has
been focused on a single common class of dynamical system models. This thesis
documents the current state of the proposed modeling technique and provides guidance
for additional development. Illustrative examples, borrowed from existing modeling
technology, lend support to the feasibility of DPM.

Ti
abstract
the bond
first app
approach
DPM w
simulatio
platform.

presenter

 

The DPM technique is first presented as a system modeling alternative in
abstract form. Two general strategies for application of the proposed technique, using
the bond graph modeling domain as a host Simulation platform, are presented. The
first approach may be considered as a topological expansion technique. The second
approach may be considered as a system equation technique. A software realization of
DPM was created for use within ENPORT, an existing bond graph modeling and
simulation package [1]. An illustrative example of DPM, using ENPORT as the host
platform, is provided. Finally, a summary of the proposed modeling technique is

presented with recommendations for additional development effort.

 

provided
states anc

data state

 

dynaija
Dynamic;
pape, teci
Capable 0,

Chapter 2

THE DIVERSE PLATFORM MODELING TECHNIQUE

The general concepts of the DPM technique are illustrated by the diagram
provided in Figure 2-1. The blocks shown in the figure represent three distinct data
states and the arrows indieate a process by which data states are transformed. Each

data state indicated in Figure 2-1 is discussed briefly in the following paragraphs:

 

Dynamical System
Model (DSM)

 

 

     
   
 

Standard Model
Description
(SMD)

 

Host Platform
Model Realization

(HPMR)

 

Figure 2-1. Diagram of the Diverse Platform Modeling technique.

The ”Dynamical System Model” (DSM) is any reasonable representation of a
dynamical system. Two common forms for a DSM are graphical and numerical.
Dynamical models may be generated using diverse platforms ranging from pencil and
paper techniques to sophisticated software packages. Each modeling platform must be

capable of creating a standard model description to communicate modeling information.

 

 

A ”Standard Model Description“ (SMD) is a standardized format for
communicating parameters of a specific problem class. The development of SMDs is
essential for communieation between diverse modeling platforms and the host
simulation environment. Ideally, several classes of dynamical system models should be
expressible using SMDS. A communication medium, such as the data file, is required
for convenient transport of SMDs between modeling platforms. As a result of the
increasing popularity of windowing software, a standardized protocol for ”clipboard”

communieation would also prove useful as a medium for data exchange.

It is the responsibility of the host simulation platform to provide the necessary
utilities to convert SMDs into an internally useful format or a ”Host Platform Model
Realization” (HPMR). It is not necessary that the host simulation platform be eapable
of translating all classes of dynamical systems represented by SMDs. The host
platform capable of the greatest number of translations, however, is potentially the

most useful.

In summary, the DPM technique allows individual components of a dynamical
system to be modeled using the platform best suited for the task. The resulting models
may then be injected into a host platform through the use of SMDs. The host platform
has the responsibility of translating SMDs into a locally useful format or HPMR.
Interactions between the components of the dynamical system are achieved in a manner
prescribed by the host platform. Finally, numerical simulation of the system as a
whole may be performed.

Chapter 3

THE BOND GRAPH MODELING DOMAIN AS HOST FOR DPM

A feasibility study of DPM was conducted using the bond graph modeling
domain as the host environment. The term "system graph” will be used to indicate a
bond-graph/block-diagram representation of a dynamieal system. Two general
strategies for incorporating SMDs into a system graph were investigated. The first
strategy, illustrated in Figure 3-1, may be considered a topological expansion approach.
Using this approach, a complete system graph representation of the injected model is
generated and available for inspection. System equations are then generated from the

system graph using standard bond graph and block diagram modeling techniques [2].

 

Dynamical System
Model (DSM)

 

 

     
   
 

Standard Model
Description
(SMD)

 

System Graph

Representation

 

Figure 3-1 . Topological expansion of SMDs with bond graph domain as host.

The second model injection strategy, illustrated in Figure 3-2, may be considered a

system equation level approach. This method absorbs details of the injected model into

6

the equi
of gene
containe

system

Figure I

Fi
Classe3 ofi
The mp0]
imilkimem
0f DPM
Problem C

 

Chis saw

 

 

the equivalent of a new system graph node type. The new node type must be capable
of generating platform-specific system equations directly fiom the model information
contained in the SMD. In this approach, the topological details are reduced to a single
system node.

 

 

 

    

Standard Model
Description
(SMD)

 
   
 

 

Platform Specific

Equations

 

Figure 3-2. Direct equation generation from SMDs with bond graph domain as host.

Figure 3-1 and Figure 3-2 illustrate two general strategies for injecting various
classes of externally created dynamical system models into a bond graph host domain.
The topological expansion approach was employed in the development of a software
implementation of DPM using ENPORT as the host platform. Although the concepts
of DPM are not limited to a specific class of dynamical system models, a single
problem class was selected for the present software development effort. The problem
class selected is the topic of Chapter 4.

 

model
equation
techniqu

Equatio

In Equa

and stiffn
velocity,
vector. 1

common

followin g
Presented

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Chapter 4

TOPOLOGICAL APPROACH TO DPM WITH ENPORT AS HOST

The behavior, or local behavior, of many dynamical systems may be accurately
modeled using systems of second-order, linear, constant-coefficient, differential
equations. These equations may be generated using any of several analytical modeling
techniques or computer software platforms and are of the classical form provided in
Equation 4-1.

M2(t) + cam + Kz(t) = E'(t) (4-1)

In Equation (4-1), M , C , and K are (run) real, constant-coefficient mass, dissipation,
and stiffness matrices respectively; 2 , 2 , and z are (nxl) time-dependent acceleration,
velocity, and displacement vectors respectively, and E is a (nxl) time dependent effort
vector. For the purpose of the present investigation, dynamical system models of this
common class (MCK) will be injected into the ENPORT modeling domain. The
following articles discuss a software utility developed to achieve this result. The utility
presented uses the system graph expansion technique to create two topologically unique

but numerically equivalent representations of the injected MCK model.

4.1 Multiport Configuration for Injected MCK Models

The first of the of the two topological expansion techniques exploits multiport
concepts of bond graph modeling. Multiport nodes provide a convenient method for
organizing the energy of a system into lumped storage and dissipation fields. The

structure of Equation (4-1) suggests an organization of this type and lends itself

8

 

mmml

mbna

 

 

 

si'SIth':
mecm
C; and

naturally to the multiport configuration shown in Figure 4-1. The interested reader is

referred to reference [2] for a more complete coverage of multiport systems.

 

 

 

 

I:M'1 R:C C:K
I I
§
1 l 1 no... 1
I I I
21 22 2.3 Zn
SC SC SC on... se

 

 

 

Figure 4-1. Multiport configuration for a MCK dynamical system model.

The multiport I, R, and C nodes shown in Figure 4-1 represent the dynarnieal
system's dissipation, potential energy, and inertia fields respectively. Associated with
the C node is the stiffness matrix K; associated with the R node is the damping matrix
C; and associated with the I node is the inverse of the mass matrix M. The node
constitutive equations can be defined by the ENPORT function type ”MATRIX". A
software utility was created to facilitate automatic system graph generation of the form
indicated in Figure 4-1. The utility reads the MCK model description from a file of the
form provided in Appendix A1. A suitably-sized IRC bond graph is generated. The
matrix elements are placed into ENPORT as indicated in Figure 4-1 (:M'l, :C, :K).
The l-junctions shown in the figure mark the geometric coordinates and provide input

locations for external effort sources. Each l-j unction corresponds to a single degree of

 

 

10

freedom in the MCK model. The effort sources (Se) shown in the figure are provided
for illustrative purposes. In practice, effort inputs may be of the form indicated or may
be provided by connections to other nodes in the system graph. An 'Se" is needed

only if the input effort is different from zero or the velocity is of interest.

At this point it is important to address the issue of interfacing the injected
dynamical system models to other system components in the host simulation platform.
This issue is not unique to a specific problem class, to the host platform representation
of the problem class, or even to the host simulation platform selected. This issue is an
inherent component of dynamical system modeling. Inspection of Figure 4-2 reveals a
preferred causality at the interface ports (Se locations). The term ”preferred” refers to
the causal markings which result from application of the Standard Causality Assignment
Procedure (SCAP) [2]. From these markings, the causal requirements at the interface
nodes in Figure 4-2 are apparent. Although an alternative causality assignment at any
of these locations is physically reasonable, the equations for the system would become
implicit in that case. A suitable solver in the nonlinear case would require an implicit

integration method.

 

 

Figure

4.2 Mi

Equati
equatit
throug

ll

 

 

SC SC SC IIIII SC

 

 

 

Figure 4-2. Multiport configuration for a MCK dynamical system model with causality

visible.

4.2 Modal Configuration for Injected MCK Models

The second topological expansion technique requires that the MCK model of
Equation (4-1) be transformed into a set of n decoupled second-order differential
equations. This is accomplished using the transformations provided in Equations (4-2)
through (4-4).

M' = UTMU (4-2)
I _ T

c _ U cu (4-3)

x' = UTKU (44)

U is the run modal matrix composed of n column eigenvectors corresponding to the n
natural frequencies of the system. M ’, C’, and K’ are the (run) modal mass, damping,

and stiffness matrices respectively. It is important to note that the modal damping

 

matrix

. i

specral
|

softwatl

 

for this
defined

Equatio

 

 

Eqmtior
differan‘

found ir

ahermit

12

matrix will only be decoupled by the technique presented in Equation (4-3) for the
special but important case of a modally damped system. The current state of the
software utility developed for modal expansion of injected MCK models does not check
for this condition and should be used with caution. If the displacement vector is

defined as

z(t) = Un(t) (4-5)

Equation (4-1) may be written as:
M'mt) + C’ii(t) + K’n(t) = UTE“) (4-6)
Equation (4-6) is a decoupled system of linear, second-order, constant-coefficient

differential equations. More comprehensive coverage of modal decomposition may be

found in Reference [3] or any standard vibrations text.

The transformation of the MCK model into its modal form facilitates an

alternate bond graph representation as illustrated in Figure 4-3.

 

 

The n&

and has
defined ;

 

Values “
follows

intIOduc
rnOdel a1

bOIld gr;

locatiOns

Dons of

13

 

T C I C I

m. \1 fr, \1 f,

+ R T—‘1 o e o o e . R T—1 n
1/ . . . . \l

 

 

 

Figure 4-3. Modal configuration for a MCK dynamical system model.

The nib I, R, and C nodal grouping shown in Figure 4-3 represents a ”modal oscillator"
and has parameter values which correspond to the nib diagonal elements of the matrices
defined in Equation (4-6). The n transformers (TF) incident to the i9! O-junction have
values which correspond to the nib row of the modal transformation matrix (U). This
follows from Equation (4-6). The O-j unction nodes provide locations for the
introduction of external effort sources for each of the n degrees of freedom in the
model and for observation of the resulting motions. More detailed coverage of modal

bond graph representation is provided in references [4] and [5].

Inspection of Figure 4-4 reveals a preferred causality at the interface ports (Sc
locations). This observation is consistent with the discussion regarding the interface

ports of the multiport topology presented in article 4.1.

 

 

 

 

Figure

14

 

Coordinate
Transformation

Phyaioal
inputa

 

T c
es. T
+ A

I
ill
1 a o

TFa a aTF

1/

T2;

Se

“\f

T2:

Se

 

Figure 4-4. Modal configuration for a MCK dynamical system with causality visible.

 

 

 

equal

Chapter 5
SYSTEM EQUATION APPROACH TO DPM WITH ENPORT AS HOST

The system equation approach is presented as an alternative model injection
strategy to topological expansion. This approach builds platform-specific system
equations from a SMD. The resulting set of equations are represented with a single
multipOrt node in the system graph. Two system-equation level techniques for injecting
dynamieal system models into ENPORT are presented in the following articles. The
first technique, the ”Macro Dynamic System” or MDS, requires the creation of a
FORTRAN problem description module which must be compiled and linked with the
ENPORT software package. The second technique, the "Class Specific Macro
Dynamic Node Type" , involves creating a new ENPORT node type for each dynamical
system class of interest. Although both strategies may be applied to a broad class of
dynamical system models, the following articles concentrate on models of the form
indicated in Equation (4-1).

5.1 The Macro Dynamic System as Applied to MCK Models

The Macro Dynamic System (MDS) is an ENPORT utility currently under
development by Yan Ying Wang, a mechanical engineering doctoral student at
Michigan State University. This utility facilitates the creation of a "black box” node
type in which the relationship between an arbitrary number of input and output signals
is defined by a FORTRAN problem description of a specified format. The FORTRAN
code must be compiled and linked with the ENPORT software package. Creating a
MDS from a MCK model description requires the formulation of a set of state

equations which may be integrated by ENPORT. To this end, Equation (4-1) may be
15

 

transfo

Equati ‘

 

I
Equatic

 

 

 

The ap;

Equafii

Expreg

Equati
numet
m3ch

Vafiab

l6

transformed into a system of 2n state equations by introducing a state variable as in
Equation (5-1).

v a 2 (5-1)

Equation (4-1) may now be expressed as follows:

I} = -M"CV - M'JKZ + M'lE (5-2)

The appropriate state vector is provided below.

le
szr = [27:13] (5-3)

Equations (5-1) through (5-3) may be combined to form the compact state space
expression shown in Equation (54).

{71nd _ -M-1C -M'1K Var]. + M-1 0 Erin]
2,... -[ I . lizml . .[o <54)

Equation (5-4) defines 2n first-order differential equations which are required for
numerical integration within ENPORT. The inputs required for the MCK dynamic
macro are the applied forces, E. The output variables may be selected from the state

variable list. A graphical representation of the MDS is shown in Figure 5-1.

 

 

Ft

The stat
to the it
(54), 2
output -
an iter.

one tin

5.2 A

Piatlo
inton-
3550c.
moot
Thirc
MD:

CnCa,

Fina

l7

 

 

Rest of the
System Graph

 

 

MDS
Xlt) DX(t)

 

 

 

Figure 5-1. The Macro Dynamic System for an n-dimensional MCK model.

The state variables, X(t), and the effort variables, E(t), shown in Figure 5-1 are passed
to the MDS module. The derivatives of the state variables, DX(t), defined by Equation
(54), are ealculated by the MDS and returned to the ENPORT solver for storage. The
output variables, Y(t), are available for use by other nodes in the system graph. This is
an iterative process which serves to advance the state of the numerieal simulation by

one time step.

5.2 A Class Specific Macro Dynamic Node Type

The MDS utility presented in the preceding article provides an excellent test
platform for a variety of dynamical systems. Its generality, however, presents some
inconveniences. First, knowledge of the FORTRAN programming language and
associated computer skills are required. Second, compiling a problem description
module and linking it with the ENPORT software package is a time consuming process.
Third, development of problem description modules is prone to error. Fourth, the
MDS is a "black box" representation of a system. Thus, the dynamics of the
encapsulated systems must be known to assure proper numerical integration parameters.

Finally, supplying users with complete object code for a commercial software package

 

 

is not i
part, b
softwa

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applied
state 51
mod
equival

 

identic:
class 5]
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the Sys
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deSCIi;
exists

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may ta

18

is not wise as a business consideration. These difficulties may be overcome, at least in
part, by the inclusion of problem class specific MDS node types within the ENPORT
software package. The creation of a MCK specific node types is the topic of the

following discussion and is the recommended path for future DPM development effort.

Inspection of Equations (5-1) through (54) reveals an algorithm which may be
applied to an MCK model description for automatic formulation of ENPORT solvable
state space equations. The equations generated may be placed directly into the
ENPORT equation data base for integration. This development path creates the
equivalent of a new node type for ENPORT. The topology of the new node type is
identical to the MDS node and is functionally equivalent. The development of system
class specific node types for ENPORT has many benefits. For example, dynamical
system models could easily be injected into ENPORT using SMDs and represented in
the system graph as a single node. In addition, by developing system class specific
node types, equation generation is performed automatically and FORTRAN problem
description modules are not necessary. One example of this type of node that currently
exists in ENPORT is the transfer function node type. This node generates system
equations directly from polynomial coefficients supplied when defining parameters for
the system graph nodes. Further information regarding the transfer function node type

may be found in Reference [1].

 

 

 

 

DPM f

(FE

me
the

pn

 

Chapter 6

EXAMPLE SYSTEM

The dynamical system illustrated in Figure 6-1 will be used to demonstrate
DPM for the class of problems indicated in Equation (4-1).

 

 

 

 

 

 

 

 

 

 

Figure 6-1. Dynamieal system employed in numerical study.

The beam indieated in Figure 6-1 will be constructed using the Finite Element Method
(FEM). The resulting model will be injected into the ENPORT software platform by
means of a SMD. The damped spring mass oscillator will be modeled and attached to
the beam within ENPORT. The source of effort will be a simple sine wave also
provided within the ENPORT simulation platform.

6.1 The Finite Element Model

The three-element beam structure illustrated in Figure 6-1 will be used to

demonstrate DPM. Each node of the finite element mesh contains two degrees of

freedom (translational and rotational) as indicated in Figure 6-2.

19

20

 

d"

ad;

 

 

 

Figure 6-2. Schematic diagram of FE nodal degrees of freedom.

The elemental coefficient matrices are provided in Equations (6-1) and (6-2).

p

156 22L

pAL 22L 41.2

420 54 13L

_-13L -3L2

 

12 6L
6L 4L2
-12 -6L

__ 6L 21.2

E1
“6:?

 

54 —13L‘
13L -3r.2
156 -22L

-22L 4L2
—12 6L ‘
-6L 21:.2
12 —6L
-6L 4sz

 

 

(6-1)

(6-2)

M e is a consistent mass matrix, Re is the stiffness matrix, E is the material modulus of

elasticity, I is the moment of inertia, P is the material density, A is the cross-

sectional area, and L is the elemental length. The elemental mass and stiffness

matrices are combined using standard FE techniques to form the global system of

equations for the beam. The resulting (6x6) equation is of the following form,

MI'r-i-Kz:

E

(63)

The global M and K matrices indicated in Equation (6-3) are provided in Appendix B1

in the form of a SMD file and z is defined below.

 

dis
ye

CT

21

z = 2 (6‘4)

3

 

 

¢
d3
_¢

In Equation (6-4), d indicates translational displacement and ¢ indicates rotational
displacement. Superscripts indicate the node number (see Figure 6-2). The effort
vector provided in Equation (6-5) indieates the nodal coordinates which are stimulated
externally.

TEEN?)

E = (6-5)

 

 

The external effort sources indicated in Equation (6-5) are not necessarily defined
explicitly. As previously mentioned, E1(t) is defined as a simple sine wave for this
example. The effort applied to the fifth degree of freedom, E5 (t ), is the reaction
force generated by the damped spring mass oscillator and may not be assigned
explicitly. More detailed discussion regarding the formulation of FE models is
provided in References [6] and [7]. The SMD created for the FE model is provided in
Appendix B1. The following articles illustrate three unique yet numerically equivalent

system graph models of the dynamical system shown in Figure 6-1.

 

6.2 M

 

multip

graph i

 

Cairn

PTOpi

22

6.2 Multiport Expansion

The dynamieal system shown in Figure 6-1 was modeled in ENPORT using the
multiport expansion approach to represent the beam component. The resulting system
graph is shown in Figure 6—3.

 

 

 

 

 

Figure 6-3. Example system modeled using multiport expansion.

Careful inspection of the causal markings shown in Figure 6—3 indicates that integral
eausality has been maintained throughout the system graph. Thus, the model is
properly posed for the ENPORT solver.

6.3 M.

 

repres:

 

shown

As in

thrOUg]

 

23

6.3 Modal Expansion

The modal expansion approach was used to create a second system graph
representation of the model shown in Figure 6-1. The resulting system graph model is
shown in Figure 6-4.

 

C

iF—oi—éi

/
1 \
id" id's

L 9'3. L
A A A A A A

 

 

 

Figure 6-4. Example system modeled using modal expansion.

As in the multiport expansion approach, integral causality has been maintained
throughout the system graph.

 

6.4 M

medy

 

 

Figu

Asmd
i“Puts .
lhat w
reQuite
umfide

24

6.4 MCK Macro Dynamic System

The system graph shown in Figure 6-5 represents the hypothetieal appearance of
the dynamieal system as modeled using a MCK macro dynamic system node.

 

C

IIQoI-At/
1 ’\

Sf

MCK
5'3 mos

 

 

 

 

Figure 6-5. Example system modeled using a MCK Macro Dynamic System node.

As indicated in Figure 6-5, the MCK Macro Dynamic System node requires signals as
inputs and provides signals as outputs. There are, however, no fundamental difficulties
that would prevent this hypothetical dynamic node type from being developed to
require power bonds to communicate information. This design issue is left for the

consideration of future ENPORT developers.

25
6.5 Numerical Results

The numerical results obtained during the numerical simulation of the system
shown in Figure 6-1 were identical for the two system graph configurations tested (see
Figure 6-3 and Figure 6-4). Thus, a single figure, representative of both topologies, is
provided in Figure 6-6.

ENPORT/PC Plot Date: 11/84/91 Tine: 13:23:50

 

      
 

Responsaof
ModaIModel

   

I-..‘

a

9 a
a
a
a
o
a
a
O
a
a
a
u
a
a
o
a

I. o a .-

C a

e a

a a

I a

O o

a a

   

Response of -
iRC Model

 
 

  

 

 

 

.90 i A Iiiii.‘ A A 1.0

lionentun of the iiass
WISH; 0
1.601144
16013-04

Figure 6-6. Response of the momentum of the load mass vs. time for sinusoidal

forcing.

 

7.1 S

oftoo

develc

 

means
Inject:

other :

COmp]

7.2 R.

Chapter 7

SUMMARY AND RECOMMENDATIONS

7.1 Summary

The Diverse Platform Modeling Technique addresses the need for a coherent set
of tools when modeling dynamical systems. Specifically, two software utilities were
developed that facilitate the injection of MCK dynamical system models into the
ENPORT modeling platform. MCK system models are communicated to ENPORT by
means of a Standard Model Description file developed specifically for the task.
Injected MCK models are represented in the ENPORT system graph and interact with
other system nodes according to the standard rules of bond graph modeling.

The utilities created to facilitate DPM within ENPORT do not represent a
complete set of tools which will solve all modeling difficulties. The utilities, however,
do provide support for further development of the proposed modeling technique.

Recommendations for development are provided in the following article.

7.2 Recommendations for Future Development

Topological expansion of MCK dynamical system models provided useful
information pertaining to the development of system graph "macros" and model
injection strategies. First, the two topological representations of MCK dynamic
systems investigated (multiport and modal form) indicate a specific causality forced at
the input sites using the Standard Causality Assignment Procedure [2]. Thus, it is

recommended that future development include a method for enforcing or ”locking"
26

 

 

PW

simul

 

advan
cxperi
capabi
increa
that St

1011010]

27

proper causality at the input sites of macro nodes during the model building stage of the
simulation process. Second, the topological expansion of even small MCK models
produced unreasonably large system graph representations. There does not appear to
be any strong evidence that these visual representations are necessary or particularly
useful for the user. Thus, it is recommended that future development be focused on the
direct formulation of system equations from the SMDs. This approach has the
advantage of reducing topological details to a single node in the system graph. Finally,
experience suggests that the platform best suited for the exploitation of graphical macro
capabilities are windowing environments. This type of environment has become
increasingly popular among software users and developers. Thus, it is recommended
that software design and development of advanced ENPORT capabilities, such as

topological macros, be restricted to environments of this type.

LIST OF REFERENCES

28

LIST OF REFERENCES

1. Rosenberg, R. C., 'The ENPORT Reference Manual', Rosencode Associates Inc.,
Lansing, Michigan, 1990.

2. Rosenberg, R. C. and Kamopp, D. C., INTRODUCTION TO PHYSICAL
SYSTEM DYNAMICS, McGraw-I-Iill, New York, 1983.

3. Meirovitch, L., ANALYTICAL METHODS IN VIBRATIONS, Macmillian, New
York, 1967.

4. Margolis, D. L. and Young, G. E., 'Reduction of Models of Large Scale Lumped
Structures Using Normal Modes and Bond Graphs', J. Franklin Inst., Vol. 304, No. 1,
pp. 65-79, July 1977.

5. Margolis, D. L., 'A Survey of Bond Graph Modeling for Interacting Lumped and
Distributed Systems', J. Franklin Inst., Vol. 319, No. 1/2, pp. 125-135,
January/February 1985.

6. Reddy, 1. N., AN INTRODUCTION TO THE FINITE ELEMENT METHOD,
McGraw-Hill, New York, 1984.

7. Logan, D. L., A FIRST COURSE IN THE FINITE ELEMENT METHOD, PWS,
Boston, 1986.

8. Press, W. H. and Flannery, B. P. and Teukolsky, S. A. and Vetterling, W. T.,
NUMERICAL RECIPES - THE ART OF SCIENTIFIC COMPUTING, Cambridge
University Press, Cambridge, 1986.

9. Shigley, J. E. and Mitchell, L. D., MECHANICAL ENGINEERING DESIGN,
Fourth Edition, McGraw-Hill, New York, 1983.

APPENDICES

APPENDIX A
USER DOCUMENTATION
The information in this appendix pertains to the use of the MCK model injection
software utility created for ENPORT. A sample SMD file is presented in Appendix A1

with discussion regarding format requirements. An abbreviated ENPORT session is

included in Appendix A2 that demonstrates user access to the new utility.

29

APPENDIX A1

SAMPLE MCK STANDARD MODEL DESCRIPTION FILE

A sample SMD file for a two degree of freedom MCK model is shown in
Figure 11. Note that text may not be placed in the first column of the file. Data
entered in the "FILE", "NAME", ”TITLE", and "DESCRIPTION” fields is not used
internally by ENPORT. These fields are provided for user documentation and future
internal use. The dimension of the MCK model is placed in the ”DIMENSION" field.
The current maximum value for this parameter is ten. The ”FORCE
INFORMATION " field contains two columns for information. The first column must
be an integer value equal to zero or one. If a value of one is entered in this column, an
effort source is placed in the system graph with the value indicated in the second
column of the corresponding row. A value of zero in the first field prevents the
placement of an effort source in the system graph for the associated degree of freedom.
Thus, if a particular degree of freedom in the MCK model is of interest, a value of one
must be placed in the first column. The proper format for data entry into the ”MASS
MATRDI", 'STIFFNESS MATRIX", and "DAMPING MATRIX" fields is provided
in Figure A-l. A ”*" in the second column of the file indicates a comment line. The
delimiters for a matrix entry are '[" and "J”. The delimiter for a matrix row is ";".
These delimiters are required. The mass matrix and stiffness matrix are required. The
damping matrix, however, is not required. Blank lines are ignored by the processor.
Finally, the file is terminated with an "END-FILE" statement.

30

31

 

 

 

READING
FILE (Not uaed internally)
VIBSZ.MCK
NAME (Eight chare max - for future macro use)
V1382
TITLE (Not used internally)

MCK teat file.

DESCRIPTION (10 linea max - Not used internally)
Thia ia a Standard Model Description tile for a two degree of
freedom MCK ayatem.

DIMENSION (10 ie max for now)
0002

FORCE INFORMATION (0 s ignore, 1 - include)
i

1 1.00003+00
1 1.00003+00
l
MASS MATRIX (Required - Format in Sx,1p,313.4,1x....)

* bbax.xxxxE+xx bbax.xxxxE+xx bbex.xxxx£+xx bbex.xxxxE+xx bbex.xxxxE+xx

I
1.00008+00 0.00003+00;

0.0000!+00 1.00008+00)
] i

STIPPNESS MATRIX (Required - Format ie Sx,1p,313.4,1x....)

I
2.ooooe+oo -1.ooooe+oo; i

-1.00002+00 1.00003+00;
1

DAMPING MATRIX (Values optional - heading and [] required.)

I
l

END-FILE

Figure A-l. Sample MCK Standard Description File for two DOF System.

APPENDIX A2

USER ACCESS FROM ENPORT

Figure 12 indicates the menu path required to gain access to ENPORT's MCK
rmmklhwumbnufifign

 

 

 

  
 
 
 
  
   

    
  
   
   

Add Node

Delete Bond
Modify Signal
Zoom Mg;

 

Redraw Return
Options
List

Return

 

 

 

 

 

 

Figure A-2. ENPORT directory path for MCK model injection utility.
Once the MCK option indicated in Figure 12 has been selected, a small amount of user

input is required. User input is achieved using the ENPORT dialog screen shown in
Figure A-3.

32

33

 

lEnter file name : |V1833.MCK I

Processing file command:

 

 

 

 

READING
DIMENSION

FORCE INFORMATION
MASS MATRIX
STIFFNESS MATRIX
DAMPING MATRIX
END FILE

| Macro Type? D Modal BMultiportI

1.0000E+OO
1.0000E+OO 1.0000E+OO
2.0000E+OO 1.0000E+OO

oar-Hm

 

 

 

 

Nodes required
Connectors required

.0 O.
O)

 

 

 

 

 

Figure A-3. Sample ENPORT dialog screen for MCK model injection.

The shadowed boxes in Figure A-3 indicate the user input portions of the dialog screen.
All other fields shown in the figure are status and debug information. The two
numerical fields following the ”FORCE INFORMATION " heading are the values
found in the first row of the corresponding heading of associated MCK data file (see
Figure 11). Similarly, the numerical fields following the "MASS MATRIX",
”STIFFNESS MATRIX", and "DAMPING MATRIX” headers, are the number of
elements read, first element received, and last element received respectively. After all
appropriate information has been entered, ENPORT returns the user to the system
graph. A location for topological expansion of the MCK data is requested and the

appropriate system graph model is constructed.

APPENDIX B

THE EXAMPLE SYSTEM

This Appendix contains additional information regarding the example system
presented in Chapter 6.

34

APPENDIX Bl

MCK FILE FOR THE EXAMPLE SYSTEM

Table B-1 . MCK file for the example system.

READING

FILE
FEM10.MCK

NAME
FEM10 (eight chars max - for future macro use)

TITLE
FEM test file.

DESCRIPTION
This file contains the mass and stiffness matrices for
a 3-element 2-DOF FE model. The boundary nodes (1 and 2)
are not included. The following are the physical parameters:
Material : Steel

E - 30x10‘6 lb/in‘z
I - b*h‘3/12
p I 484 1b/ft‘3
b - 1' h - 1” l - 10” per element.
DIMENSION (10 is max for now)
0006

FORCE INFORMATION (0 8 Ignore, 1 = Include)
I
1.0000E+01
0.0000E+OO
0.0000E+OO
0.0000E+OO
1.0000E+02
0.0000E+OO

OHOOOH

l

MASS MATRIX (Format is Sx,1p,E13.4,1x....)
* bbsx.xxxxE+xx bbsx.xxxxE+xx bbsx.xxxxE+xx bbsx.xxxxE+xx bbsx.xxxxE+xx

I
3.5880E+03 0.0000E+OO 6.21008+02 -1.49SOE+03 0.0000E+OO

0.0000E+00;

0.00008+00 9.2000E+03 1.4950E+03 -3.4500E+03 0.0000E+00
0.00008+00;

6.2100E+02 1.4950E+03 3.5880E+03 0.0000E+00 6.2100E+02
-1.49508+03;

-1.4950£+03 -3.4SOOE+03 0.0000E+00 9.2000E+03 1.4950E+03
-3.45008+03;

0.00008+00 0.00008+00 6.2100E+02 1.4950E+03 1.7940E+03
-2.5300E+03;

0.0000E+00 0.00003+00 -1.4950£+03 -3.4500E+03 -2.5300E+03
4.6000E+03;

35

Table B-1 (cont'd).

STIFFNESS MATRIX

6.0000E+04
0.00003+00;
0.00008+00
0.0000E+00;
-3.0000E+04
1.5000E+05;
1.SOOOE+05
5.00003+05;
0.0000E+00
-1.SOOOE+05;
0.0000E+00
1.0000E+06;

l

0.0000E+OO
2.0000E+06
-1.SOOOE+OS
S.OOOOE+OS
0.0000E+00
0.0000E+OO

DAMPING MATRIX (OPTIONAL)

I
]

END-FILE

36

-3.0000E+O4
-1.SOOOE+05
6.0000E+O4
0.0000E+OO
-3.0000E+O4
1.SOOOE+OS

1.SOOOE+05
S.OOOOE+05
0.0000E+OO
2.0000E+06
-1.SOOOE+OS
S.OOOOE+OS

0.0000E+OO
0.0000E+OO
-3.0000E+O4
-1.5000E+05
3.0000E+O4
-1.5000E+OS

APPENDIX B2

ENPORT MODEL FILE FOR EXAMPLE PROBLEM (MULTIPORT)

Table 8-2. ENPORT model file for multiport example.

READING
FILE MODEL 15:41:19 11/11/91 ENPORT/PC 4.01
FEMMUL.ENP Model_name: mul port
TITLE

Multiport expansion of 6 DOF MCK with spring mass oscillator.

DESCRIPTION
This is a 6 degree of freedom FE model with a spring mass attached.
The multiport expansion technique has been used to represent the FE
model.

SYSTEM GRAPH DESCRIPTION

NODE TYPE XLOC YLOC ACT MACRO
SV101 MEGV -400. 200. T
1V101 M16V -400. 100. T
1V102 MIGV -300. 100. T
1V103 M16V -200. 100. T
1V104 MlGV -100. 100. T
1V105 MlGV 0. 100. T
1V106 MlGV 100. 100. T
11 MIGV -400. -100. T
C1 MCGV -200. -100. T
1J1 MIGV 0. 400. T
02 MOGV 0. 600. T
1J2 MIGV 0. 800. T
1J3 MlGV 200. 600. T
CSPG MCGV 400. 500. T
ISPG MIGV 200. 900. T
RSPG MRGV 400. 700. T

CONNECTOR TYPE FROM TO VERTICES
$8101 86 V SV101 1V101
18101 86 V 1V101 11
18102 86 V 1V102 11
18103 86 V 1V103 11
18104 86 V 1V104 11
18105 86 V 1V105 11
18106 86 V 1V106 11
C8101 86 V 1V101 C1
08102 86 V 1V102 C1
C8103 86 V 1V103 C1
C8104 BG V 1V104 C1
C8105 8G V 1V105 Cl
C8106 86 V 1V106 C1

37

38

Table 8-2 (cont'd).
V22 80 V 1J1 02
VDIF2 86 V 02 IJ3
VSPG2 80 V 1J3 CSPG
V3 80 V 02 1J2
VISPG 80 V 1J2 ISPG
VSPG 80 V 1J3 RSPG
V1 80 V 1J1 1V105
NODE EQUATIONS
Named_parameters: 0
Number of outputs: 16
Node: SV101 Connectors: 88101
Equation: Y - SIN ( X, P ) 1 1 2
X_list X_list Parameters Index
E88101 TIME 1.0000E+00 0
4.2190E+01 0
Node: Il Connectors: 18101 18102 I8103
Equation: Y - MATRIX ( X, P ) 6 6 0
P18101 PI8102 P18103
F18101 3.2510E-04 4.2076E-OS -4.7933E-05
FI8102 4.2076E-05 1.4687E-04 -4.5737E-05
F18103 -4.7933E-05 -4.5737E-05 3.8578E-04
FI8104 9.14338-05 8.1985E-05 4.5209E-05
F18105 6.7466E-05 5.9117E-05 2.3810E-04
FI8106 9.01028-05 7.91398-05 2.9024E-04
P18104 P18105 P18106
F18101 9.1433E-05 6.74668-05 9.0102E-05
FI8102 8.1985E-05 5.9117E-05 7.9139E-05
FI8103 4.52098-05 2.3810E-04 2.9024E-04
FI8104 2.3822E-04 2.6082E-04 3.36818-04
F18105 2.60828-04 2.8643E-03 1.8484E-03
F18106 3.3681E-04 1.8484E-03 1.5809E-03
Node: 01 Connectors: 08101 08102 08103
Equation: Y - MATRIX ( X, P ) 6 6 0
908101 908102 908103
E08101 6.00008+04 0.00008+00 -3.00003+04
E08102 0.0000E+00 2.0000E+06 -1.5000E+05
E08103 -3.00008+04 -1.50003+05 6.0000E+04
E08104 1.SOOOE+OS 5.00008+05 0.0000E+00
E08105 0.0000E+00 0.00008+00 -3.0000E+04
E08106 0.0000E+00 0.0000E+00 1.5000E+05
908104 908105 908106
E08101 1.5000E+05 0.0000E+00 0.0000E+00
E08102 5.00008+05 0.0000E+00 0.00008+00
E08103 0.0000E+00 -3.0000E+04 1.5000E+05
E08104 2.0000E+06 -1.5000£+05 S.0000E+05
E08105 -1.50008+05 3.0000E+04 -1.5000E+05
E08106 S.0000E+05 -1.SOOOE+05 1.0000E+06

Table 8-2 (cont'd).

Node: CSPG
Equation:
X_list
EVSPG2

Node: ISPG
Equation:
X_list
FVISPG

Node: RSPG

Equation:
X_list
EVSPG

END-FILE

Connectors:

Y I GAIN
X_list
QVSPG2

Connectors:

Y I ATT
X_list
PVISPG

Connectors:

Y I GAIN
X_list
FVSPG

(Xv?)

I X: P )

( X: P )

1 1 1
Parameters
5.0000E+02

1 1 1
Parameters
1.0000E+01

1 1 1
Parameters
1.0000E+01

Index
0

Index
0

Index

APPENDIX 83

ENPORT MODEL FILE FOR EXAMPLE PROBLEM (MODAL)

Table 8-3. ENPORT model file for modal example.

READING

3ILE MODEL
PEMMOD.ENP

15:45:18 11/11/91 ENPORT/PC 4.01
Model_name: fem mode

TITLE
This is a 6 DOF FE model with spring mass oscillator attached.

DESCRIPTION
This is a 6 DOF Finite Element Model injected into ENPORT using
the modal expansion technique. A damped spring mass oscillator
has been attached to the injected Finite Element model.

SYSTEM GRAPH DESCRIPTION

40

NODE TYPE XLOC YLOC ACT MACRO
SM101 MEGV -400. 200. T
0M101 MOGV -400. 100. T
0M105 MOGV 2400. 100. T
T3101 MTGV -400. 0. T
T3102 MTGV -300. 0. T
T3103 MTGV -200. 0. T
T3104 MTGV -100. 0. T
T3105 MTGV 0. 0. T
T3106 MTGV 100. 0. T
T3125 MTGV 2400. 0. T
T3126 MTGV 2500. 0. T
T3127 MTGV 2600. 0. T
T3128 MTGV 2700. 0. T
T3129 MTGV 2800. 0. T
T3130 MTGV 2900. 0. T
1M101 MIGV -400. -200. T
1M102 M1GV 300. -200. T
1M103 M1GV 1000. -200. T
1M104 MIGV 1700. -200. T
1M105 M1GV 2400. -200. T
1M106 M1GV 3100. -200. T
1M101 M1GV -400. -300. T
1M102 M1GV 300. -300. T
1M103 M1GV 1000. -300. T
1M104 MIGV 1700. -300. T
1M105 M1GV 2400. -300. T
1M106 M1GV 3100. -300. T
CM101 MCGV -300. -300. T
CM102 MCGV 400. -300. T
CM103 MCGV 1100. -300. T
CM104 MCGV 1800. -300. T

41

'Tabk:833(¢onflkb.
c3105 300v 2500. -300. 1
CM106 300v 3200. -300. 1
1 310v 2400. 300. 1
02 300v 2400. 400. 1
102 310v 2400. 500. 1
ISPG 310v 2600. 500. 1
103 310v 2300. 400. 1
aspc 330v 2200. 500. 1
0530 300v 2200. 300. 1
003330103 1333 3303 10 vznrrcss

53101 30 v SM101 03101

13101 30 v 03101 13101

13102 30 v 03101 13102

13103 30 v 03101 13103

13104 30 v 03101 13104

13105 30 v 03101 13105

T8106 30 v 03101 TF106

13125 30 v 03105 13125

T8126 30 v 03105 TF126

13127 30 v 03105 13127

T8128 30 v 03105 13123

13129 30 v 03105 13129

13130 30 v 03105 13130

13101 30 v 13101 13101

13102 30 v 13102 13102

13103 30 v 13103 13103

13104 30 v 13104 13104

13105 30 v 13105 13105

13106 30 v TF106 13106

13125 30 v 13125 13101

13126 30 v TF126 13102

13127 30 v 13127 13103

18128 30 v 13123 13104

13129 30 v 13129 13105

13130 30 v 13130 1M106

13101 30 v 13101 13101

13102 30 v 13102 13102

13103 30 v 13103 13103

13104 30 v 13104 13104

13105 30 v 13105 13105

18106 30 v 13106 IM106

03101 30 v 13101 c3101

c3102 30 v 13102 c3102

c3103 30 v 13103 c3103

c3104 30 v 13104 03104

03105 30 v 13105 c3105

08106 30 v 13106 CM106

v22 30 v 1 02

v0132 30 v 02 103

v3 30 v 02 102

vrspc 30 v 102 1630

vspc 30 v 103 aspc

vspcz 30 v 103 0530

v1 30 v 1 03105

42

Table B-3 (cont'd).

NODE EQUATIONS

Named_parameters: 0
Number of outputs: 28
Node: SM101 Connectors: 88101
Equation: Y SIN ( X, P ) 1 1 2
X_list X_list Parameters
E88101 TIME 1.0000E+00
4.2190E+01
Node: TF101 Connectors: T8101 18101
FT8101 - MTF101 * F18101
E18101 8 MTF101 * ET8101
Equation: Y CON ( X, P ) 1 0 1
X_list X_list Parameters
MTF101 1.0000E+00
Node: TF102 Connectors: T8102 18102
FT8102 - MTF102 * F18102
E18102 - MTF102 * ET8102
Equation: Y CON ( X, P ) 1 0 1
X_list X_list Parameters
MTF102 1.0000E+00
Node: TF103 Connectors: T8103 18103
FT8103 - MTF103 * F18103
818103 - MTF103 * ET8103
Equation: Y CON ( X, P ) 1 0 1
X_list X_list Parameters
MTF103 1.0000E+00
Node: TF104 Connectors: T8104 18104
FT8104 - MTF104 * F18104
E18104 - MTF104 * ET8104
Equation: Y CON ( X, P ) 1 0 1
X_list X_list Parameters
MTF104 1.0000E+00
Node: TF105 Connectors: T8105 18105
FT8105 - MTF105 * F18105
E18105 s MTF105 * ET8105
Equation: Y CON ( X, P ) 1 0 1
X_list X_list Parameters
MTF105 1.0000E+00
Node: TF106 Connectors: T8106 18106
FT8106 - MTF106 * F18106
E18106 8 MTF106 * ET8106
Equation: Y CON ( X, P ) 1 0 1
Y list X list Parameters
313106 ‘ 1 . 00003+00

Index

Index

Index

Index

Index

Index

Index

Table 8-3 (cont'd).

Node:

Equation:
X_list
MTF125

Node:

Equation:
X_list
MTF126

Node:

Equation:
X_list
MTF127

Node:

Equation:
X_list
MTF128

Node:

Equation:
X_list
MTF129

Node:

Equation:
Y_'_1 ist
MT3130

Node:

Equation:
X_list
F18101

Node:

Equation:
X_list
F18102

Node:

Equation:
X_list
F18103

T3125
3T8125
818125

T3126
3T8126
E18126

T3127
3T8127
E18127

T3128
3T8128
E18128

T3129
3T8129
E18129

T3130
3T8130
E18130

1M101

1M102

IM103

Connectors:
I MTF125
I MTF125
con ( x,
X_list

Connectors:
I MTF126
I MTF126
CON ( X,
X_list

Connectors:
I MTF127
I MTF127
CON ( X,
X_list

Connectors:
I MTF128
I MTF128
003 ( x,
X_list

Connectors:
I MTF129
I MTF129
003 ( x,
X_list

Connectors:
I MTF130
I MTF130
003 ( x,
X_list

Connectors:

ATT ( X,
X_list
P18101

Connectors:

ATT ( X,
X_list
PI8102

Connectors:

ATT ( X,
X_list
PI8103

43

T8125 18125
* F18125
* ET8125
P ) 1 0 1
Parameters
8.3144E+00
T8126 18126
* F18126
* ET8126
P ) 1 0 1
Parameters
-3.7879E+00
T8127 18127
* F1812?
* ET8127
P ) 1 0 1
Parameters
-3.9697E+00
T8128 18128
* F18128
* ET8128
P ) 1 0 1
Parameters
1.3440E+00
T8129 18129
* F18129
* ET8129
P ) 1 0 1
Parameters
-1.6953E+00
T8130 18130
* F18130
* ET8130
P ) 1 0 1
Parameters
6.04128+00
18101
P ) 1 1 1
Parameters
5.196lE+04
I8102
P ) 1 1 1
Parameters
3.8072E+04
18103
P ) 1 1 1
Parameters
4.883lE+04

Index

Index

Index

Index

Index

Index

Index

Index

Index

Thbk:8#3(confld).

Node: 18104
Equation:
X_list
FI8104

Node: IMIOS
Equation:
X_list
FI8105

Node: 1M106
Equation:
X_list
FI8106

Node: CM101
Equation:
X_list
808101

Node: CM102
Equation:
X_list
E08102

Node: CM103
Equation:
X_list
E08103

Node: CM104
Equation:
X_list
E08104

Node: CM105
Equation:
X_list
808105

Node: 0M106
Equation:
X_list
E08106

Node: ISPG
Equation:
X_list
FVISPG

Node: RSPG

Equation:
X_list
EVSPG

Connectors:

ATT ( X,
X_list
P18104

Connectors:

ATT ( X,
X_list
P18105

Connectors:

ATT ( X,
X_list
P18106

Connectors:

GAIN ( X,
X_list
908101

Connectors:

0313 ( x,
X_list
908102

Connectors:

0313 ( x,
X_list
908103

Connectors:

GAIN ( X,
X_list
908104

Connectors:

0313 ( x,
X_list
908105

Connectors:

0313 ( x,
X_list
908106

Connectors:

ATT ( X,
X_list
PVISPG

Connectors:

GAIN ( X,
X_list
FVSPG

13104
P )

13105
P )

18106

03101
P )

03102
P )

08103

C8104

P )

08105

08106

1 1 1
Parameters
6.4808E+03

1 1 1
Parameters
1.0284E+04

1 1 1
Parameters
1.32158+05

1 1 1
Parameters
9.2496E+07

1 1 1
Parameters
1.7051E+07

1 1 1
Parameters
6.1746E+06

1 1 1
Parameters
1.6159E+05

1 1 1
Parameters
3.2115E+04

1 1 1
Parameters
1.0442E+04

1 1 1
Parameters
1.00008+01

1 1 1
Parameters
1.00008+01

Index

Index

Index

Index

Index

Index

Index

Index

Index

Index

Index

Table 8-3 (cont'd).

Node: CSPG
Equation:
X_list
EVSPGZ

END-3ILE

45

Connectors: VSPG2

! - 0313 ( x, 3 ) 1 1 1
X_list Parameters Index
9VSP02 5.00008+02 0

APPENDIX C

ORGANIZATION OF THE FORTRAN SOURCE CODE

The FORTRAN source code has been placed into three files. The first file,
"MBMCKFOR", contains file processing, flow control, and user dialog support
subroutines. The second file, "MBMCKG.FOR" , contains the subroutines which
control the creation of the modal and multiport topologies. The third file,
”MCKMTH.FOR" , contains the subroutines which perform the mathematical
manipulations necessary to construct the modal and multiport topologies. The
subroutines contained within the three files are supported by a common-block structure
contained in the files "MCKHDR.CBK" and "MCKSIZ.C8K". The source code
developed for this study may be considered as a "stand alone" module. The module
has a single entry point (subroutine MCKLOD) which is called from a single location
within the ENPORT source code (subroutine GFGNOC). Further information
regarding the organization of the source code is provided in Appendix Cl and
Appendix CZ. A complete listing of the FORTRAN source code is provided in

Appendix C3.

46

APPENDD( Cl

SUBPROGRAM CALLING TREE

Table 01 . The subprogram calling tree.

030300 (ENPORT)
MCKLOD
MCKGFN
MCKFRD
MCKHDR
MCKDMN
MCKFRC
MCKMAT
MCKMCR
MCKSHO
MCKRST
MCKBLD
MCKMOD
MCKEIG
INVMAT
LUDCMP
LUBKSB
MTXMUL
8ALAN2
31.31352
3033
EVECTS
MTXCML
MTXADD
DETCPY
DETMTX
MODDAT
SETVAL
MTXTRN
MTXMUL
MCKVIB
INVMAT
LUDCMP
LUBKSB
VIBDAT

SETVAL
47

APPENDIX C2

SUBPROGRAM LIST

Table 02. The subprogram list and associated source files.

BALAN2
DETCPY
DETMTX
ELMHS2
EQNINI
EVECTS
GETNOD
HQR3
INVMAT
LUBKSB
LUDCMP
MCKBLD
MCKDMN
MCKEIG
MCKFRC
MCKFRD
MCKGFN
MCKHDR
MCKLOD
MCKMAT
MCKMCR
MCKMOD
MCKRST
MCKSHO
MCKVIB

I MODDAT
MTXADD
MTXCML
MTXMU L
MTXTRN
SETVAL
VIBDAT

(MCKMTI-I.FOR)
(MCKMTHFOR)
(MCKMTHFOR)
(1100113303)
(311313030303)
(110311111303)
(31313030303)
(310103111303)
(MCKMTHFOR)
(MCKMTH.FOR)
(110313111303)
(MBMCKGFOR)
(M8MCK.FOR)
(MBMCKG.FOR)
(MBMCKFOR)
(M8MCK.FOR)
(MBMCK.FOR)
(MBMCK.FOR)
(3133103303)
(MBMCKFOR)
(M8MCK.FOR)
(MBMCKGFOR)
(31313031303)
(M8MCK.FOR)
(31313030303)
(MBMCKGFOR)
(130313111303)
(MCKMTHFOR)
(MCKMTHFOR)
(MCKMTHFOR)
(MBMCKGFOR)
(MBMCKG.FOR)

48

APPENDIX C3

FORTRAN SOURCE CODE LISTINGS

This appendix includes the FORTRAN source code for the software utility
created for ENPORT.

49

50

 

CCOMMONFILE:MCKSIZ Last Change: 09/19/91 RM
g---- MCK Reader File

5---- Components

0 MCXMAX, Maximum dimension of the MCK model.

3---- Declarations.

C INTEGER MCXMAX

: PARAMETER (303333 - 10)

 

CCOMMONEO38MCKHDR *

51

 

CCOMMONFILE:MCKMDR Last Change: 09/09/91 RM
C
C—--- MCK Reader File
0
C---- Components
0 MCXNAM, mode1_name
C MCXFNM, model_file_name
C MCKTTL, model_title
C MCXDSC, model_description.
C MCKDIM, Dimension of the MCX model.
C MCKNLD, Number of description lines.
0 MCKMCT, Number of elements counted in the mass matrix.
0 MCXCCT, Number of elements counted in the damping matrix.
C MCKKCT, Number of elements counted in the stiffness matrix.
C NUMNOD, Number of nodes required for the macro.
C NUMCON, Number of connectors required for the macro.
C NUMMAC, Number of macros added to the graph (for names only).
C FRCTOX, Token value for force (0 I ignore, 1 I include).
0 FRCVAL, Force value at the node (constant) used if FRCTOXIl.
C MASMAT, Mass matrix
C STFMAT, Stiffness matrix
C EIGMAT, Matrix of eigenvalues for the system.
C DMPMAT, Damping matrix
C MCKMAC, Macro option - TRUE I modal, FALSE I vibrations.
C
C---- Include the size specifications.
0
INCLUDE 'MCXSIz.08X'
0
C---- Declarations
CHARACTER MCXNAM*8, MCKFNM*32, MOXTTL*72, MCXDSC(10)*72
INTEGER MCXDIM, MCXNLD, MCXMCT, MCXCCT, MCKRCT
INTEGER NUMNOD, NUMCON, NUMMAC, 3ROTOX(MOXMAX)
REAL MASMAT(MCXMAX,MCXMAX), STFMAT(MCXMAX,MCKMAX)
REAL DMPMAT(MCXMAX,MCXMAX), EIGMAT(MCKMAX,MOXMAX)
REAL FRCVAL(MCXMAX)
LOGICAL MCXMAC
0
COMMON /MCKHD1/MCXNAM,MCXFNM,MCXTTL,MCXDSC
COMMON /MCXHD2/MCXDIM,MCXNLD,MCXMCT,MCXCCT,MCKXCT,NUMNOD,NUMCON
COMMON /MCXHD3/NUMMAC,FRCTOX
COMMON [MCXHD4/MASMAT,STFMAT,DMPMAT,EIGMAT,FRCVAL
COMMON [MCXHDSIMCXMAC
C

 

CCOMMONEO3zMORHDR —*

52

 

031LE:M8MOR.30R
0

C---- M8MCR.FOR: Mode1_build M,C,X file load/manipulation support.
0

 

C---- PURPOSE: This file contains all the code required to load
0 MCK matrix models from file.

0

C---- Contents:

0 MCKLOD, Load M,C,E matrices from file.

0 MCXRST, Restores the graph screen

0 MCXGFN, Get file name from user by dialog.

0 MCKFRD, Controls the MCX data file read.

0 MCXHDR, Reads MCK header from file.

0 MCKDMN, Reads MCK model dimension from file.

0 MCRFRC, Reads MCK force info from file.

0 MCXMAT, Reads MCK matrices from a file.

0 MCKMCR, Allows the user to change macro types.
0 MCKSHO, Determines number of nodes/connectors.
0

C---- Last Change: September 9, 1991. RM

0

CEOFE

0

SMESSAGEz'MCRLOD'

CMCXLOD>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/9/91 RM

#1}. filtfi filifi *1}! filti NIPfi filtfi *

0
SUEROUTINE MCKLOD
C
0---— PURPOSE: Loads a M,C,X set of matrices from file.
0
C---- Inputs:
0
0---- Outputs:
0
CHARACTER EVTP*4, FILNAM*12
INTEGER IR, 10, IPAG
LOGICAL TXTMOD
0
EXTERNAL MODSET, SPXEYL, MOVCUR, GETXEY, EVTTYP, MCXRST
EXTERNAL MCXBLD
C
C***MCKLOD**************************************************************
0
C---- Set text mode
IPAGI 0
TXTMODI .TRUE.
CALL MODSET(TXTMOD)
CALL SPREYL
0
C---- Get the MCK data from file.
0
100 CONTINUE
IRI 2
ICI 6
FILNAM I '*.MCX'
CALL MCXGFN(IR,IC,FILNAM,EVTP)
C
C---- Get the macro option (MODAL or VIBRATIONS).
0
CALL MCKMCR
C
C---- Calculate and display required nodes and connectors for macro.
0

CALL MCKSHO

53

0
CALL GETREY(0,0)
C
C---- Return section
800 CONTINUE
C
C---- Restore the graph screen.
0
CALL MCXRST
C
C---- Build the macro.
0
CALL MCX8LD
RETURN
0
END
0

CEND:MCKLOD<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'MCXRST'
CMCXRST>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/9/91 RM
0

SUEROUTINE MCKRST

C
C---- PURPOSE: Restores the graph window.
0
C---- Inputs:
0
0---- Outputs:
0
INCLUDE 'BGFXBX.08X'
INCLUDE 'VIEWEX.08X'
C
CHARACTER STRING*80
REAL VX, VY, X: Y
INTEGER IPAG, IX, 1!, I
LOGICAL TXTMOD
C
EXTERNAL MODSET, SPKEYL, PCWIND, NEWPLT, MOVCUR, WRTSTG
EXTERNAL CXY2IJ, PLTPXL, SYSDRW, GFXCUR, DRBOX, WRTCAT
C

C***Mcnsri******************************************t******************

C
C---- Reset to graphics mode and set up screen coordinates
IPAG I O
TXTMODI .FALSE.
CALL 300$31(1x1300)
CALL PCWIND(IPAG,XMNPXL,XMXPXL,YMNPXL,YMXPXL)
CALL NEWPLT(0,1,VPXMN,VPXMX,VPYMN,VPYMX)

C

C---- The following redraw sequence should not be herell It is here
0 because the redraw sequence is attached to the menu handler

C in MBVGED of M8MENU.FOR.

C

810 13 (GRDVIS) 1333
vx= VPXMN +0.5*030151
815 v1: VPYMN +0.5*GRDIST
820 CALL 0x2210(vx,vx,rx,11)
CALL PLTPXL(IPAG,IX,IY,15)
vx- vy +GRDIST
13 (VY.LT.VPYMX) 0010 820
vx- vx +0301s1
13 (VX.LT.VPXMX) 0010 815
33013

54

I3 (3RMVIS) CALL DRBOX(VPXMN,VPYMN,VPXMX,VPYMX)
CALL SYSDRW

C---- Clear the dialog region (23-24)
DO 840 1- 23,24
CALL MOVCUR(IPAG,I,1)
840 CALL WRTCAT(IPAG,32,ICLR8,80)
0---- Put up a graphics cursor
XI VPXMN +GRDIST*0.5
YI VPYMN +GRDIST*0.5
CALL GFXCUR(X,Y,'P')
C---- Put up label and set field 1 (col 13) with default of 'N'
813130: ' Nod/Con/M: '
CALL WRTSTG(0,23,1,ICLRL,STRING,12)
C---- Put up the special key list.
CALL SPXEYL
C
RETURN
0
END
0

CEND:MCXRST<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C

$MESSAGE:'MCXGFN'

CGETFNM>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 04/13/91 RR

SUEROUTINE MCXG3N(1RS,ICS,3ILNAM,EVTP)

C
C---- PURPOSE: Get file name from user by dialog.
0
0---- Inputs: IRS, start row for dialog area
0 ICS, start col for dialog area
0 FILNAM, default file name (may be changed)
0
C---- Outputs: EVTP, I CANC or CRET
C FILNAM, name of file selected (iff EVTPICRET)
0 .
INCLUDE 'COMMEX.CBX'
INCLUDE 'VIEWBX.08X'
C
CHARACTER FILNAM*12, EVTP*4, STRING*80
CHARACTER DFTNAM*12
INTEGER IRS, ICS, IR, L
LOGICAL YES
0
EXTERNAL LNMSGD, MOVCUR, WRTCAT, WRTSTG, GETSTR, LJSTR, UPCASE
EXTERNAL YES
0

c***ucxcm**************************************************************

C

C---- Convert to actual dialog start location
IRSI IRS +1
ICSI 108 +1

C-—-- Put up dialog box

DO 10 IRI IRS,IRS+2
CALL MOVCUR(0,1R,ICS)

10 CALL 331031(0,32,0,31)
DO 15 13: IRS-1,IRS+1
CALL MOVCUR(0,IR,ICS-l)
15 CALL WRTCAT(0,32,ICLRL,31)

STRING= 'Enter file name:'
CALL WRTSTG(0,1RS,ICS,ICLRL,STRING,16)
D3TNAMI FILNAM

55

C---- Get file name from user

100 FILNAMI DFTNAM
CALL GETSTR(IRS,ICS+17,12,3ILNAM,EVTP)
13 (31LNAM.EQ.' ') EVTPI 'CANC'

C
C---- Crunch the input
0
IF (EVTP.EQ.'CANC') THEN
GOTO 800
ELSEIF (EVTP.EQ.'CRET'.OR.EVTP.EQ.'DONE') THEN
CALL LJSTR(FILNAM,STRING,L)
31LNAMI STRING
CALL UPCASE(FILNAM)
CALL MCXFRD(31LNAM)
ELSE
GOTO 100
ENDIF
C
C---- Time to return
0
800 CONTINUE
RETURN
0
END

CEND:MCRGFN<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
0
$MESSAGE:'MOXFRD'
CMCRFRD>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/09/91 RM
0

SUEROUTINE MCXFRD(FILNAM)

C
0---- PURPOSE: Controls the MCK data file read.
0
C---- Inputs: FILNAM, default file name (may be changed)
0
C---- Outputs:
0
INCLUDE 'COMMBX.08R'
INCLUDE 'VIEWEX.08X'
INCLUDE 'MCXHDR.08K'
C
CHARACTER FILNAM*12, STRING*80, NXTCOM*S, NXTCML*40
INTEGER LCS, LN
C
EXTERNAL LNMSGD, NEWLF, MCKHDR, MCXDMN, MCXMAT
C

c***um**************************************************************

C

C---- Open the specified file.

0
STRING I '*** Error opening file : '
MESSAGE I STRINGl/FILNAM
OPEN(PRUNIT,FILEIFILNAM,STATUSI'OLD',ERRI900,

*' FORMI'FORMATTED',ACCESSI‘SEQUENTIAL')
C
C---- Locate the first command string.
0

CALL NEWLF(STRING,LCS)

NXTCOM I STRING

IF (LCS.LE.0) THEN

MESSAGI ' *** Fatal error while reading file.‘
GOTO 900

ELSE

LNI 7

c-—-—

20

c----

C

c-——-

0

c .....

c .....

c .....

c .....

c —————

56

MESSAGI ' Processing file command: '
CALL WRTSTG(0,LN,7,ICLRM,MESSAG,SS)
ENDIF

Interpret the string as a command
CONTINUE

IF (NXTCOM.EQ.' HEAD') THEN
NXTCMLI' HEADING'

ELSEIF (NXTCOM.EQ.' DIME') THEN
NXTCMLI' DIMENSION'

ELSEIF (3x1003.30.' 3030') 1333
NXTCMLI' FORCE INFORMATION'
ELSEIF (NXTCOM.EQ.' MASS') THEN
NXTCMLI' MASS MATRIX'

ELSEIF (NXTCOM.E9.' STIF') THEN
NXTCMLI' STIFFNESS MATRIX'

ELSEIF (NXTCOM.E9.' DAMP') THEN
NXTCMLI' DAMPING MATRIX'

ELSEIF (NXTCOM.EQ.' END-') THEN
NXTCMLI' END-FILE'

ELSE

MESSAGI ' *** Bad command in file: '//NXTCOM
GOTO 900

ENDIF

Inform user of file read status
13 (LN.LE.21) 1333

LNI LN+1

MESSAGI NXTCML -

CALL NRTSTG(0,LN,7,ICLRM,MESSAG,55)
ENDIF

All routines below return MESSAG filled in if OXAYI.FALSE.

IF (NXTCOM.EQ.' HEAD') THEN

- Read the MCK file header.

CALL 303333( 3x1co3 )

ELSEIF (NXTCOM.EQ.' DIME') THEN

- Read the MCR matrix dimensions from file and post results.
CALL MCKDMN( NXTCOM )

WRITE(STRING,100) 303313

CALL WRTSTG(0,LN,25,ICLRM,STRING,4)

ELSEIF (NXTCOM.EQ.' FORC') THEN

- Read the force info from file and post the results.
CALL MCRFRC( NXTCOM )

33113(s13130,100) 330103(1)

CALL WRTSTG(0,LN,25,ICLRM,STRING,4)

33113(s13130,110) FRCVAL(1)

CALL WRTSTG(0,LN,30,ICLRM,STRING,13)

ELSEIF (3x1003.30.' 33ss') 1333

- Read the MCK mass matrix from file and post results.
CALL MCRMAT( 'MASS',NXTCOM )

WRITE(STRING,100) MCXMCT

CALL WRTSTG(0,LN,25,ICLRM,STRING,4)

33113(s13130,110) 330331(1,1)

CALL WRTSTG(0,LN,30,ICLRM,STRING,13)
33113(513130,110) 33s331(303013,303313)

CALL WRTSTG(0,LN,45,ICLRM,STRING,13)

ELSEIF (NXTCOM.EQ.' STIF') THEN

- Read the MCK stiffness matrix from file and post results.
CALL MCKMAT( 'STIF',NXTCOM )

WRITE(STRING,100) MCKKCT

CALL WRTSTG(0,LN,25,ICLRM,STRING,4)

33113(s13130,110) STFMAT(1,1)

CALL WRTSTG(0,LN,30,ICLRM,STRING,13)

57

WRITE(STRING,110) STFMAT(HCRDIH,HCKDIH)
CALL WRTSTG(O,LN,45,ICLRH,STRING,13)
ELSEIF (NXTCOH.EQ.' DAMP') THEN
C ------ Read the MCK damping matrix from file and post results.
CALL HCKHAT( 'DAMP',NXTCOH )
WRITE(STRING,100) 3cxcc1
CALL WRTSTG(O,LN,25,ICLRH,STRING,4)
13(3c3cc1.33.0) 1333
WRITE(STRING,110) DHPMAT(1,1)
CALL WRTSTG(O,LN,30,ICLRH,STRING,13)
WRITE(STRING,110) DHPHAT(HCXDIM,HCKDIH)
CALL WRTSTG(O,LN,45,ICLRH,STRING,13)

ENDIF
ELSEIF (NXTCOH.EQ.' END-') THEN
C ------ Successful completion of file read
MESSAG- ' Model has been loaded from file.‘
GOTO 900
ENDIF
100 RORHAT(I4)
110 FORMAT(1P,E13.4)
C
C---- Crunch on the next command if possible.
C
11 (OKAY) 6010 20
C
C---- Write message and quit.
C

900 00311333
CALL WRTSTG(O,24,l,ICLRH,HESSAGE,80)

cc CALL GETREY(0,0)

910 CONTINUE
REWIND(PRUNIT)
CLOSE(PRUNIT)
RETURN

C
END

CEND:HCKPRD<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
SHESSAGE:'HCKHDR'
CHCKPRD>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/09/91 RM
C

SUBROUTINE HCKHDR( NXTCOM )

C
C---- PURPOSE: Reads the MCK header from file.
C
C---- Inputs:
C
C---- Outputs: OKAY, logical flag for operation status.
C MESSAGE, status message.
C NXTCOM, next command in file.
C
INCLUDE 'COHHBK.CBK'
INCLUDE 'HCXHDR.CBK'
C
CHARACTER STRING*80, NXTCOH*S
INTEGER LCS, LEN, NCHARS
C
EXTERNAL NCHARS , NEWLF
C

C***ucxHDR********************************ttt***************************

C
OKAY-.FALSE.
C
C---- Get the file name.

58

CALL NEWLF(STRING,LCS)
IP(LCS.GE.5) oo1o 900
3x1c03 - STRING(1:S)

13 (3x1c03.3q.' 11') 1333

C ------ Get the file name from the file.

c----

CALL NEWLE(STRING,LCS)
13 (LCS.GE.8) co1o 900
3cxr33 - STRING(7:18)
ELSE

6010 900

ENDIF

Get the MCK macro name.

CALL NEWLF(STRING,LCS)
IE(LCS.GE.5) 0010 900
3x1cou . STRING(1:S)

Ir (3x1con.3g.' NA') 1333

C ------ Get the macro name from the file.

C--—-

c .....

c----

c .....

50

C

c--_-

C

CALL NEWLF(STRING,LCS)
11 (LCS.GE.8) 6010 900
HCNNAH . STRING(7:14)
ELSE

3010 900

33013

Get the title.

CALL NEWLP(STRING,LCS)
IE(LCS.GE.5) GOTO 900

NXTCOM 8 STRING(1:S)

13 (NXTCOH.EQ.' TI') THEN

- Get the mck title from the file.
CALL NEWLP(STRING,LCS)

IF (LCS.LT.7) GOTO 900

HCKTTL - ' '

LEN z NCHARS(STRING)

IF (LEN.GE.7) HCKTTL 8 STRING(7:LEN)
ELSE

GOTO 900

ENDIF

Get the description.

MCRNLD - 0
CALL NEWLP(STRING,LCS)
IF(LCS.GE.5) GOTO 900
NXTCOM = STRING(1:5)
IF (NXTCOH.EQ.' DE') THEN
- Get the ka description from the file.
'CALL NEWLF(STRING,LCS)
IE (LCS.GE.7) THEN
HCKNLD = MCKNLD+1
HCKDSC(MCKNLD)=' '
LEN . NCHARS(STRING)
IF (LEN.GE.7) HCKDSC(HCKNLD) - STRING(7:LEN)
GOTO 50
ENDIF
NXTCOM 8 STRING(1:S)
ENDIF

All done.

59

OKAY-.TRUE.
RETURN

C

C---- Trouble.

C

900 CONTINUE

MESSAG - ' *** Error while reading HEADING data.’
910 OKAY-.PALSE.

RETURN
C

END
CEND:MCKHDR<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'MCRDMN'
CMCKDIM>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/09/91 RM
C

SUEROUTINE MCKDMN( NXTCOM )

C
C---- PURPOSE: Reads MCK model dimension from file.
C
C---- Inputs:
C
C---- Outputs: OKAY, logical flag for operation status.
C MESSAGE, status message.
C NXTCOM, next command in file.
C
INCLUDE 'COHHBK.CBK'
INCLUDE 'HCKHDR.CEX'
C
CHARACTER STRING*80, NXTCOM*5
INTEGER LCS
C
EXTERNAL NEWLE
C

CtitnchMN***tttittttttttt*ttt********t********************************t

C

OKAY=.PALSE.
C
c---— Get the dimension of the MCK model.
C

READ(PRUNIT,200,ERR=9OO,END89OO) 3c3013
200 FORMAT(6X,I4)

C
C---- Advance to the next command.
C
CALL NEWLF(STRING,LCS)
IF(LCS.GE.3) GOTO 900
NXTCOM s STRING(l:5)
C
C---- All done.
C
OKAYs.TRUE.
RETURN
C
C—--- Trouble.
C

900 CONTINUE

MESSAG 8 ' *** Error while reading DIMENSION data.’
910 OKAY=.FALSE.

RETURN
C

END
CEND:MCKDMN<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C

60

SNESSAGEz'MCRFRC'
CMCKPRC)>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 10/21/91 RM
C

SUBROUTINE HCKERC( NXTCOM )

C
C---- PURPOSE: Reads force information from a file.
C
C---- Inputs: None.
C
C---- Outputs: OKAY, logical flag for operation status.
C MESSAGE, status message.
C NXTCOM, next command in file.
C
INCLUDE 'COMMBK.CBK'
INCLUDE 'MCKHDR.CBK'
C
CHARACTER STRING*80, NXTCOM*5, SEORCE*13, SFRCTK*1
INTEGER LCS, IP, ICOUNT
C
EXTERNAL NEWLP
C

cxsencxfncsseeeeeeeeeeee*eeeeee*e**************sees*********************

C

OKAY-.PALSE.
g---- Read the [ start specifier.
C CALL NEWLP(STRING,LCS)

IE (STRING(3:3).NE.'[') GOTO 900
§---- Read the matrix data.

ICOUNT 8 O
100 CONTINUE
CALL NEWLP(STRING,LCS)
11 (STRING(3:3).EQ.']') 1333
GOTO 210
ELSEIF (LCS.LE.3) THEN
MESSAG 8 STRING
GOTO 910
ENDIF
C---- Parse the string into numbers and tokens.
IP 8 7
333013 . $13130(19:19)
IP 8 18
830303 . STRING(IP:IP+12)
ICOUNT 8 ICOUNT + 1
C---- Store the number in the proper place.
33An(srnc1x,'(14)') rac1ox<100031)
READ(SFORCE,'(1P,E13.4)') FRCVAL(ICOUNT)

GOTO 100
C
C---- Advance to the next command.
C

210 00311303

CALL NEWLF(STRING,LCS)
IF(LCS.GE.3) 0010 900
3x1003 . STRING(1:5)

C

C---- All done.

C
OKAY8.TRUE.
RETURN

61

C---— Trouble.
C
900 CONTINUE
MESSAG 8 ' *** Error while reading FORCE data.’
910 OKAY8.EALSE.
RETURN
C
END
CEND:MCKPRC<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'MCKMAT'
CMCKMAT>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/09/91 RM
C
SUBROUTINE HCKMAT( STG, NXTCOM )

C
C---- PURPOSE: Reads MCK matrices from a file.
C
C---- Inputs: STG, String to define action (MASS, STIE, DAMP).
C
C-—-- Outputs: OKAY, logical flag for operation status.
C MESSAGE, status message.
C NXTCOM, next command in file.
C
INCLUDE 'COMMBK.CBK'
INCLUDE 'MCKHDR.CBK'
C
CHARACTER STG*4, STRING*80, NXTCOM*5, STRNUM*13, TOK*1
INTEGER LCS, I, IP, ICOUNT, IRON, ICOL
C
EXTERNAL NEWLY
C

C***Mcmr***************i*****fl******t*********************************

C

OKAY-.PALSE.
C
C---- Read the [ matrix start specifier.
C

CALL NEWLF(STRING,LCS)

IF (STRING(3:3).NE.'[') GOTO 900
C
C---- Read the matrix data.
C

ICOUNT 8 0

ICOL 8 0

IRON 8 l

100 CONTINUE
CALL NEWLF(STRING,LCS)
IF (STRING(3:3).EQ.')') THEN
GOTO 210
ELSEIF (LCS.LE.3) THEN
MESSAG 8 STRING
GOTO 910
ENDIF
C---- Parse the string into numbers and tokens.
IP 8 4
DO 110 I81, 5
STRNUM 8 STRING(IP:IP+12)
C ------ Check for a blank spot.
I? (STRNUM.EQ.' ') GOTO 100
ICOUNT 8 ICOUNT + l
ICOL 8 ICOL + l
C ------ Increment the row and column counter.
IF (ICOL.EQ.MCKDIM+1) THEN
ICOL 8 l

62

IROW 8 IRON + 1
ENDIF
C ------ Store the number in the proper matrix.
IE (STG.EQ.'MASS') THEN
READ(STRNUM,'(lP,El3.4)') 3A33A1(1303,100L)
ELSEIF(STG.EQ.'STIP') THEN
READ(STRNUM,'(lP,El3.4)') STFMAT(IROW,ICOL)
ELSEIF(STG.EQ.'DAMP') 1333
READ(STRNUM,'(1P,El3.4)') DMPMAT(IROW,ICOL)
ENDIF
C ------ Check for an end of row token.
103 . STRING(IP+13:IP+13)
IP (TOK.EQ.';') GOTO 100
IP 8 IP + 14
110 CONTINUE

GOTO 100
C
C---- Advance to the next command.
C

210 00311303
CALL NEWLP(STRING,LCS)
IE(LCS.GE.3) 0010 900
3x1003 - s1313c¢1:5)

C

C---- Store the number of elements counted.

C
IF (STG.EQ.'MASS') THEN
MCKMCT 8 ICOUNT
ELSEIF(STG.EQ.'STIF') THEN
MCKKCT 8 ICOUNT
ELSEIP(STG.EQ.'DAMP') THEN
MCKCCT 8 ICOUNT
ENDIF

C

C---— All done.

C
OKAY8.TRUE.
RETURN

C

C---- Trouble.

C

900 CONTINUE

MESSAG 8 ' *** Error while reading MASS MATRIX data.‘
910 OKAY8.FALSE.

RETURN
C

END
CEND:MCKMAT<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'MCKMCR'
CMCKMCR >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/10/91 RM
C

SUBROUTINE MCKMCR

C
C---- PURPOSE: Allows the user to change macro types.
C
INCLUDE 'SIZEMB.CBK'
INCLUDE 'BGFXBK.CBK'
INCLUDE 'GREDBK.CBK'
INCLUDE 'VIEWBK.CBK'
INCLUDE 'MCKHDR.CBK'
C

CHARACTER STRING*80, EVTTYP*4, EVTP*4
INTEGER IR, IC, 11, 12, ICE, 1, IATT, IPAG, ICS, IFl, IF2

C

63

LOGICAL ANSI

EXTERNAL MODSET, WRTSTG, MOVCUR, GETCUR, EVTTYP, SPREYL
EXTERNAL PCWIND, NEWPLT
INTRINSIC MAX, MIN

C***Mcmcn*************fit***********************************************

C

c----

C

c----

c----
100

c--——

c -----

c----
800

Set up the screen label fields.

IR 8 16

ICS 8 6

STRING8 ' Macro type? _ Modal _ Vibrations'
CALL WRTSTG(IPAG,IR,ICS,ICLRL,STRING,42)

Set up the data fields with the default values.
Fields 1 and 2: Line 20, cols ICS+18 and ICS+27

CONTINUE

IP18 ICS+18

IP28 ICS+27

STRING8 'X'

CALL WRTSTG(IPAG,IR,IF1,ICLRD,STRING,1)
STRING8 ' '

CALL WRTSTG(IPAG,IR,IF2,ICLRD,STRING,1)

Position the cursor initially.
IC8 131

Read the selection here
CALL MOVCUR(IPAG,IR,IC)
CALL 031x32(11,12)
3v1P- 3v111p(11,12)

Process the selection
IF (EVTP.EQ.'CANC') THEN
GOTO 800
ELSEIF (EVTP.EQ.'DONE') THEN
CALL MOVCUR(IPAG,IR,IF1)
CALL GETCAT(IPAG,I,IATT)
ANSl8 CHAR(I).EQ.'X'
MCKMAC8 ANSI
GOTO 800
ELSEIF (EVTP.EQ.'DATA'.OR. EVTP.EQ.'CRET') THEN
- Blank the unmarked field and mark the selected field
ICB8 IF1+IF2 -IC
STRING8 ' '
CALL WRTSTG(IPAG,IR,ICB,ICLRD,STRING,1)
STRING8 'X'
CALL WRTSTG(IPAG,IR,IC,ICLRD,STRING,1)
ELSEIF (EVTP.EQ.'MOVE') THEN
IF (12.EQ.75) THEN ! Left
IC8 IFl
ELSEIF (12.EQ.77) THEN ! Right
IC8 IF2
ENDIF
ENDIF
GOTO 100

Return section
CONTINUE

RETURN
C

END
CEND:MCKMCR<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
SMESSAGEz'MCXSHO'
CMCKSHO >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/10/91 RM
C

SUBROUTINE MCKSHO

C
C---- PURPOSE: Shows the user the required number of nodes and
C connectors for the desired macro type.
C
INCLUDE 'MCKHDR.CBK'
INCLUDE 'VIEWBK.CBK'
C
CHARACTER STRING*80, STR1*5, STR2*S
INTEGER I, NUMPRC
C
EXTERNAL NRTSTG
C

ceeeucxsaoessseeesesstas*eaaaeeeeeeeeeaetteeeat«at*******e**************

C
C---- Determine the number of forces.
C
NUMFRC 8 0
DO 10 I81, MCKDIM
IP (FRCTOK(I).EQ.1) NUMFRC 8 NUMFRC + 1
10 CONTINUE

C
C---- Determine the number of nodes and connectors.
C
I! (MCKMAC) THEN
303300 - (4*303013) + (303330)*(2+303013)
303003 . (3 . 303013) + (((2t303013)+1) * 303330)
I!" (MCKCCT.EQ.O) THEN
NUMNOD 8 NUMNOD - MCKDIM
NUMCON 8 NUMCON - MCKDIM
ENDIF
ELSE
NUMNOD 8 3 + MCKDIM + NUMFRC
NUMCON 8 3 * MCKDIM + NUMFRC
IF (MCKCCT.EQ.O) THEN
NUMNOD 8 NUMNOD - l
NUMCON 8 NUMCON - MCKDIM
ENDIF
ENDIF
C
C---- Show the results.
C

33113(s131,100) 303300
33113(s132,100) 303003

100 FORMAT(I4)
STRING 8 ' Nodes required : '//STRl
CALL WRTSTG(O,18,7,ICLRM,STRING,28)
STRING 8 ' Connectors required : '//STR2
CALL WRTSTG(O,19,7,ICLRM,STRING,28)

C
C--—- Return section
800 CONTINUE
C
RETURN
C

END

65

CEND:MCKSHO<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C

 

 

CPILE:MEMCKG.POR

C

C---- MBMCK.FOR: M,C,K model builder support.

C

C---- PURPOSE: This file contains all the code required to build
C MCK modal and vibrations models automatically.

C

C---- Contents:

C MCKELD, Controls automatic building process.

C MCKMOD, Controls building of MODAL macro.

C MCKVIB, Controls building of VIBRATIONS macro.
C GETNOD, Finds node index from a grid location.
C EQNINI, Init. equations for automatic assignment.
C VIBDAT, Guides change in equations for nodes.
C MCKEIG, Controls eigen. eval. of M,K matrices.
C MODDAT, Guides change in equations for modal mac.
C SETVAL, Guides change in equations for nodes.
C

C---- Last Change: September 11, 1991. RM

C

CEOPH

C

SMESSAGEz'MCKBLD'

CMCKBLD>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/11/91 RM

*IIU ill} Ilffi fill} filtfi filtfi filtfi

C
SUEROUTINE MCKBLD
C
C---- PURPOSE: Controls the automatic building process.
C
C---- Inputs:
C
C---- Outputs:
C
INCLUDE 'SIZEMB.CEK'
INCLUDE 'SIZESL.CEK'
INCLUDE 'GREDBK.CEK'
INCLUDE 'VIEWEK.CEK'
INCLUDE 'COMMBK.CEK'
INCLUDE 'GPSTBK.CBK'
INCLUDE 'MCKHDR.CBK'
C
CHARACTER STRING*80, EVTP*4
INTEGER INOD, I, J, INDX(MCKMAX)
REAL X, Y, ANS(MCKMAX,MCKMAX)
C
EXTERNAL WRTSTG, LNMSGD, NODPIK
C
C***MCKBLD*************t******************ttt***************************
C
C---- Clear the text field in the graph window.
C
STRING8' ' k
CALL WRTSTG(O,23,l,ICLRL,STRING,80)
C
C---- Check that there is enough room in the data base to hold the
macro.
C

11 ( (INELS+NUMNOD).GE.MNEL) 1333
3355A0-' 33035s1vz 303333 or NODES...CANNOT BUILD MACRO!‘
CALL L33300(24)

GOTO 800

ELSEIF ( (13305+303003).03.3330) 1333
MESSAG8' EXCESSIVE 303333 or CONNECTORS...CANNOT BUILD MACRO!‘
CALL LNMSGD(24)

c--_-

40

C

c---—

C

C

c .....

C

C

c .....

C

C

C—-——

C---—

c----

C

c .....

C

C

C-_—_

c_-_-

CCCCC

c----

C_—-—

500
510

67

GOTO 800
ENDIF

Get the position for adding the macro.

x-xc
1-10
CALL NODPIK(24,'ADD',EVTP,X,Y,INOD)
13 (EVTP.EQ.'DATA') 1333
13 (1300.33.0) 1333
CALL LNMSGD(24)
0010 40
33013
ELSEIF (EVTP.EQ.'CANC') 1333
0010 800
33013

Build the proper macro using X,Y as upper left corner.
13 (MCKMAC) 1333

- Build the graph.

CALL 303300(x,1)

- Perform the eigen analysis.

CALL MCKEIG

Set the flag to say, ”There is now a system graph"
E7SFLG(1)8.TRUE.
E7CFLG(1)8.TRUE.

Assign causality silently (sets E7SFLG(2), E7CFLG(2)).
CALL ASSCAU(.TRUE.,.FALSE.)

Initialize the equations for automatic assignment.
CALL EQNINI
E7CFLG(4)8.FALSE.
E7CFLG(5)8.PALSE.

- Set the proper values.
CALL MODDAT

ELSE
CALL MCKVIB(X,Y)
Set the flag to say, ”There is now a system graph”
E7SFLG(1)=.TRUE.
E7CFLG(1)8.TRUE.
Assign causality silently (sets E7SFLG(2), E7CFLG(2)).
CALL SSAVE
CALL ASSCAU(.TRUE.,.FALSE.)
Initialize the equations for automatic assignment.
CALL EQNINI
E7CFLG(4)8.FALSE.
E7CFLG(S)8.FALSE.

Get the inverse of the mass matrix.

CALL INVMAT(MASMAT,MCKDIM,MCKMAX,INDX,ANS)
00 510 181,303013
00 500 J=l,MCKDIM
MASMAT(I,J)8ANS(I,J)
00311303
00311303

68

C

C-—-- Fill in the source values and the matrix table for R,C,I nodes.

C
CALL VIBDAT('SRCE')
CALL VIBDAT('MASS')
CALL VIBDAT('STIF')
13(303001.33.0) 1333

CALL VIBDAT('DAMP')

ENDIF
ENDIF

C

C---- Return section

C

800 CONTINUE

C
RETURN

C
END

CEND:MCKBLD<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'MCKMOD'
CMCKMOD>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/17/91 RM
C

SUBROUTINE MCKMOD(X, Y)

C
C---- PURPOSE: Controls the automatic building OF MODAL macro.
C
C---- Inputs: X, Y - Upper left corner of macro box.
C
C---- Outputs:
C
INCLUDE 'SIZEMB.CBK'
INCLUDE 'SIZESL.CBK'
INCLUDE 'GREDBK.CBK'
INCLUDE 'VIEWBK.CBK'
INCLUDE 'COMMBK.CBK'
INCLUDE 'GFSTBK.CBK'
INCLUDE 'BGEXBK.CBK'
INCLUDE 'MCKHDR.CBK'
C
REAL X, Y, XPOS, YPOS, POINTS(2,10)
CHARACTER ST1*1, ST2*2, TYPE*4, NAME*8
INTEGER*2 I, J, ISTART, IEND, INPTCT
C
EXTERNAL GFXCUR, DRNOD, ADDNOD, GETNOD, ADDBND, DRBND
C

c***MCKMOD**************************************************************

C

C---- Get rid of the graphics cursor.

C CALL GFXCUR(X,Y,'R')

3---- Increment the number of macros count to insure unique names.
C NUMMAC 8 NUMMAC + 1

5---- Build the name constant string

C WRITE(ST1,690) NUMMAC

§---- Build the source nodes.

TYPE 8 'MEG '
DO 150 I81,MCKDIM

150

c----

160

c----

170
180

c----

190

c----

69

13(330103(1).3Q.1) 1333
33113(s12,700) 1
13 (ST2(1:1).EQ.' ') 312(1:1)8'o'
NAME 8 's3'//s11(1:1)//s12(1:2)
3305 8 X+(MCKDIM+l)*(I-l)*GRDIST
3303 8 3
CALL DRNOD(NAME,XPOS,YPOS,TYPE)
CALL ADDNOD(NAME,TYPE,XPOS,YPOS)

33013

00311303

Build the O junctions (input ports).

1333 8 '300 '

00 160 181,303013

13(330103(1).3Q.1) 1333
33113(s12,700) 1
13 (s12(1:1).3o.' ') ST2(1:1)8'O'
NAME 8 '03'//s11(1:1)//s12(1:2)
3303 8 X+(MCKDIM+1)*(I-l)*GRDIST
1303 8 3-0301s1
CALL DRNOD(NAME,XPOS,YPOS,TYPE)
CALL ADDNOD(NAME,TYPE,XPOS,YPOS)

33013

00311303

Build the transformers.

1333 8 '310 '
00 180 181,303013
13(330103(1).3Q.1) 1333
00 170 381,303013
33113(s12,700) J + ( (1-1) . 303013 )
13 (ST2(1:1).EQ.' ') 512(1:1)8'o'
NAME 8 '13'//s11(1:1)//s12(1:2)
3305 8 X+((J-l)+( (1-1)*(303013+1) ))*030151
YPOS 8 Y-2*GRDIST
CALL DRNOD(NAME,XPOS,YPOS,TYPE)
CALL ADDNOD(NAME,TYPE,XPOS,YPOS)
00311303
33013
00311303

Build the l junctions.

1133 8 '310 '

00 190 181,303013

33113(s12,700) 1

13 (ST2(l:l).EQ.' ') s12(1:1)8'o'
NAME 8 '13'//s11(1:1)//s12(1:2)
330s 8 x+(303013+1)*(1-1)*0301$1
130s 8 184*030151

CALL DRNOD(NAME,XPOS,YPOS,TYPE)
CALL ADDNOD(NAME,TYPE,XPOS,YPOS)
00311303

Build the I junctions.

1333 8 '310 '

00 200 181,303013

33113(s12,700) 1

13 (ST2(1:1).EQ.' ') 512(1:1)8'o'
3A33 8 '13'//s11(1:1)//s12(1:2)
3305 8 x+(303013+1)*(1-1)*0301s1

 

200

c----

210

c----

220

C-—--

230

c--——

70

YPOS 8 Y-5*GRDIST

CALL DRNOD(NAME,XPOS,YPOS,TYPE)
CALL ADDNOD(NAME,TYPE,XPOS,YPOS)
CONTINUE

Build the C junctions.

1133 8 '300 '

00 210 181,303013

33113(s12,700) 1

13 (s12(1:1).39.' ') 312(1:1)8'o'

NAME 8 '03'//s11(1:1)//s12(1:2)

3305 8 X+((MCKDIM+l)*(I-l)*GRDIST) + 0301s1
3305 8 3-5*030151

CALL DRNOD(NAME,XPOS,YPOS,TYPE)

CALL ADDNOD(NAME,TYPE,XPOS,!POS)

00311303

Build the R junctions.

13(303001.33.0) 1333

1133 8 '330 '

00 220 181,303013
33113(s12,700) 1
13 (ST2(l:l).EQ.' ') 512(1:1)8'o'
NAME 8 '33'//s11(1:1)//s12(1:2)
XPOS 8 x+((303013+1)*(1-1)8030151) + 0301s1
3305 8 Y-4*GRDIST
CALL 03300(3333,33os,130s,1133)
CALL ADDNOD(NAME,TYPE,XPOS,YPOS)
00311303

33013

Add the connectors from effort sources to O-junctions.

133101 8 o
1333 8 '30 '
00 230 181,303013
13(330103(1).3Q.1) 1333
33113(s12,700) 1
13 (ST2(1:1).EQ.' ') ST2(l:l)8'O'
NAME 8 'ss'//s11(1:1)//s12(1:2)
x3os 8 x+(303013+1)*(1-1)*030151
3308 8 1
CALL GETNOD(XPOS,YPOS,ISTART)
330s 8 X+(MCKDIM+1)*(I-l)*GRDIST
3305 8 1-030151
CALL GETNOD(XPOS,YPOS,IEND)
CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(1:1),1)
33013
00311303

Add the connectors from O-junctions to transformers.

00 250 181,303013
13(330103(1).3Q.1) 1333
3303 8 x+(303013+1)*(1-1)*030151
330s 8 3-030131
CALL GETNOD(XPOS,YPOS,ISTART)
00 240 J81,MCKDIM
33113(s12,700) J + ( (1-1) * 303013 )
13 (ST2(l:l).EQ.' ') 512(1:1)8'o'
3A33 8 '1s'//s11(1:1)//s12(1:2)

240
250

c-_—-

260
270

C----

280

c-_-_

290

c---_

71

3308 8 X+((J-l)+( (181)8(303013+1) ))*030151
130s 8 1-2*030131
CALL GETNOD(XPOS,YPOS,IEND)
CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(1:l),l)
00311303

33013

00311303

Add the connectors from transformers to 1-junctions.

00 270 181,303013
13(33C1o3(1).3o.1) 1333
00 260 J81,MCKDIM

33113(s12,700) J + ( (1-1) . 303013 )
13 (ST2(1:1).EQ.' ') 512(1:1)8'o'
NAME 8 '1s'//s11(1:1)//s12(1:2)
3303 8 X+(MCKDIM+l)*(J-l)*GRDIST
1305 8 Y-4*GRDIST
CALL 031300(xpos,330s,1330)
3305 8 X+((J-l)+( (181)8(303013+1) ))*030151
3305 8 Y-2*GRDIST
CALL GETNOD(XPOS,YPOS,ISTART)
CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(l:l),l)
00311303

33013

00311303

Add the connectors from l-junctions to I nodes.

00 280 181,303013

33113(s12,700) 1

13 (ST2(l:l).EQ.' ') 512(1:1)8'o'

NAME 8 '13'//s11(1:1)//s12(1:2)

XPOS 8 x+(303013+1)*(1-1)*030151

YPOS 8 384*0301s1

CALL GETNOD(XPOS,YPOS,ISTART)

3308 8 x+(303013+1)*(1-1)*030151

230s 8 Y-S*GRDIST

CALL GETNOD(XPOS,YPOS,IEND)

CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(1:1),1)
00311303

Add the connectors from l-junctions to C nodes.

00 290 181,303013

33113(s12,700) 1

13 (ST2(1:1).EQ.' ') 512(1:1)8'0'

3A33 8 '03'//s11(1:1)//s12(1:2)

3303 8 X+(MCKDIM+1)*(I-l)*GRDIST

330s 8 3-4*030151

CALL GETNOD(XPOS,YPOS,ISTART)

3305 8 X+((MCKDIM+l)*(I-l)*GRDIST) + GRDIST
1305 8 y-s*030151

CALL GETNOD(XPOS,YPOS,IEND)

CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(1:1),1)
00311303

Add the connectors from l-junctions to R nodes.

13(303001.33.0) 1333

 

72

DO 300 I8I,MCKDIM
WRITE(ST2,700) I
I! (ST2(l:l).EQ.' ') ST2(1:1)8'0'
NAME 8 'RB'l/STl(1:1)//ST2(1:2)
XPOS 8 X+(MCKDIM+1)*(I-l)*GRDIST
YPOS 8 Y-4*GRDIST
CALL GETNOD(XPOS,YPOS,ISTART)
XPOS 8 X+((MCKDIM+1)*(I-l)*GRDIST) + GRDIST
YPOS 8 Y-4*GRDIST
CALL GETNOD(XPOS,YPOS,IEND)
CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(1:l),1)
300 CONTINUE
ENDIF
C
690 EORMAT(II)
700 EORMAT(12)
C
C---- Return section

C
800 CONTINUE
C

RETURN
0

END
CEND:MCKMOD<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
SMESSAGEz'MCKVIB'
CMCKVIB>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/11/91 RM
C

SUBROUTINE MCKVIB(X, Y)

C
C---- PURPOSE: Controls the automatic building or VIBRATIONS macro.
C
C---- Inputs: X, Y - Upper left corner of macro box.
C
C---- Outputs:
C
INCLUDE 'SIZEMB.CBK'
INCLUDE 'SIZESL.CBK'
INCLUDE 'GREDBK.CBK'
INCLUDE 'VIEWBK.CBK'
INCLUDE 'COMMBK.CBK'
INCLUDE 'GFSTBK.CBK'
INCLUDE 'BGFXBK.CBK'
INCLUDE 'MCKHDR.CBK'
C
REAL X, Y, POINTS(2,10)
CHARACTER NAME*8, STl*l, ST2*2, TYPE*4
INTEGER*2 I
INTEGER ISTART, IEND, INPTCT
C .
EXTERNAL GFXCUR, DRNOD, ADDNOD, GETNOD, ADDBND, DRBND
C

C***”CKVIB********************itt***************************************
C

C---- Get rid of the graphics cursor.
C
CALL GFXCUR(X,Y,'R')
C
C---- Increment the number of macros count to insure unique names.
C

NUMMAC 8 NUMMAC + 1
C

 

c----

c--—-

150

c---_

160

c---—

c----

c----

c--_-

73

Build the name constant string
33113(s11,690) NUMMAC
Build the source nodes.

1133 8 '330 '
00 150 181,303013
13(330103(1).3Q.1) 1333
33113(s12,700) 1
13 (ST2(1:1).EQ.' ') ST2(l:l)8'0'
NAME 8 'sv'//s11(1:1)//s12(1:2)
CALL DRNOD(NAME,X+(I-l)*GRDIST,Y,TYPE)
CALL ADDNOD(NAME,TYPE,X+(I-l)*GRDIST,Y)
33013
00311303

Build the l junctions (input ports).

1133 8 '310 '

00 160 181,303013

33113(s12,700) 1

13 (ST2(l:l).EQ.' ') ST2(l:l)8'0'

NAME 8 '1v'//s11(1:1)//s12(1:2)

CALL DRNOD(NAME,X+(I-l)*GRDIST,Y-GRDIST,TYPE)
CALL ADDNOD(NAME,TYPE,X+(I-l)*GRDIST,Y-GRDIST)
00311303

Build the "I” multi-port.

NAME 8 '1'//s11(1:1)

1333 8 '310 '

CALL DRNOD(NAME,X,Y-3*GRDIST,TYPE)
CALL ADDNOD(NAME,TYPE,X,Y-3*GRDIST)

Build the 'C' multi-port.

NAME 8 'C'//STl(l:l)

1333 8 '300 '

CALL DRNOD(NAME,X+2*GRDIST,Y-3*GRDIST,TYPE)
CALL ADDNOD(NAME,TYPE,X+2*GRDIST,Y-3*GRDIST)

Build the "R” multi-port.

13 (303001.33.0) 1333

NAME 8 '3'//s11(1:2)

1233 8 '330 '

CALL DRNOD(NAME,X+4*GRDIST,Y-3*GRDIST,TYPE)
CALL ADDNOD(NAME,TYPE,X+4*GRDIST,Y-3*GRDIST)
33013

Add the connectors from effort sources to 1-junctions.

133101 8 o
1333 8 '30 '
00 170 181,303013
13(330103(1).3Q.1) 1333
33113(s12,700) 1
13 (ST2(1:1).EQ.' ') 512(1:1)8'0'
3A33 8 'ss'//s11(1:1)//s12(1:2)
CALL GETNOD(X+(I-l)*GRDIST,Y,ISTART)
CALL GETNOD(X+(I-l)*GRDIST,Y-GRDIST,IEND)
CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(1:1),l)

74

ENDIF
170 CONTINUE
C
C---- Add the connectors from l-junctions to I,C, and R nodes.
C

CALL GETNOD(X,Y-3*GRDIST,IEND)
00 180 181,303013
33113(s12,700) 1
13 (ST2(1:1).EQ.' ') 312(1:1)8'o'
3A33 8 '10'//s11(1:1)//s12(1:2)
CALL GETNOD(X+(I-1)*GRDIST,Y-GRDIST,ISTART)
CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(l:l),l)
180 00311303

CALL GETNOD(X+2*GRDIST,Y-3*GRDIST,IEND)
00 190 181,303013
33113(s12,700) 1
13 (ST2(l:l).EQ.' ') ST2(1:1)8'0'
NAME 8 'CB'//STl(l:1)//ST2(1:2)
CALL GETNOD(X+(I-l)*GRDIST,Y-GRDIST,ISTART)
CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(1:1),1)
190 00311303

13(303001.33.0) 1333

CALL GETNOD(X+4*GRDIST,Y-3*GRDIST,IEND)

00 200 181,303013
33113(s12,700) 1
13 (ST2(1:1).EQ.' ') ST2(l:l)8'O'
3A33 8 '33'//s11(1:1)//s12(1:2)
CALL GETNOD(X+(I-l)*GRDIST,Y-GRDIST,ISTART)
CALL ADDBND(NAME,ISTART,IEND,TYPE,POINTS,INPTCT)
CALL DRBND(NAME,ISTART,IEND,TYPE(1:l),l)

200 00311303
33013

690 3033A1(11)
700 3033A1(12)

C

C---- Return section

C

800 CONTINUE

C
CALL GFXCUR(X,Y,'P')
RETURN

C
END

CEND:MCKVIB<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
SMESSAGE:'GETNOD'
CGETNOD>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/11/91 RM
C
SUBROUTINE GETNOD(X, Y, INOD)
C
C---- PURPOSE: Finds the node array index based on a grid location.
C
C---- Inputs: X, Y - Grid location of node to find.
C
C---- Outputs: INOD - Array index of the located node.
C
INCLUDE 'SIZEMB.CBK'
INCLUDE 'SIZESL.CBK'
INCLUDE 'GREDBK.CBK'

75

INCLUDE 'COMMEK.CEK'
INCLUDE 'BGEXEK.CBR'

C
REAL X, Y, GRDISZ
INTEGER I, INOD
INTRINSIC ABS

C
EXTERNAL ACTNOD

C

c***GETNOD************************i*************************fi***********

C

 

C
C---- Identify node by grid location
INOD8 0
GRDISZ8 GRDIST/2.0
DO 20 I8 l,INELS
IP (ABS(X-NXLOC(I)).LT.GRDISZ) THEN
13 (ABS(Y-NYLOC(I)).LT.GRDISZ) 1333
C ---------- A node has been found
INOD8 I
I? (ACTND(INOD)) THEN
MESSAG8' Active node found.‘
RETURN
ENDIF
C Node is not active, save it and seek active one
INOD8 -INOD
ENDIF
ENDIF
20 CONTINUE
C
C---- Return section
C
C
RETURN
C
END

CEND:GETNOD<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
gMESSAGEz'EQNINI'

CEQNINI>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/13/91 RM
C SUBROUTINE EQNINI

§---- PURPOSE: Initialize equations for automatic assignment.

C---- INPUTS: none

C

C---- OUTPUTS: E7SFLG(3),E7CFLG(3) set to show eqn status
C

INCLUDE 'COMMBK.CBK'
INCLUDE 'VIEWBK.CBK'

C
INTEGER IR, IPAG

C
EXTERNAL DEFEQS, REDOEQ, CHGFCN, LSTEQS, LSTLBI, MBVNPR
EXTERNAL LNMSGD, MOVCUR, WRTCAT, MNUSEL, SHOHLP

C

c***EQNINI****************************t*********************************

C
IPAG8 O
C---- Check status of data base
IF (.NOT.E7CFLG(1)) THEN
MESSAG8 ' *** There is no system graph.’
CALL LNMSGD(24)

76

RETURN
ENDIF
IF (.NOT.E7CPLG(2)) THEN
MESSAG8 ' *** Causality does not match the graph.‘
CALL LNMSGD(24)
RETURN
ENDIF
C---- Check on equation status next
13 (.NOT.E7SELG(3)) THEN
C ----- Set all node equations to their default status
E7CELG(4)8.FALSE.
E7CFLG(5)8.FALSE.
IR8 1
CALL DEFEQS(IR)
37s3LC(3)8 OKAY
3703LC(3)8 OKAY
IE (.NOT.OKAY) THEN
MESSAG8 ' *** Unable to set default equations.‘
CALL LNMSGD(24)
RETURN
ENDIF
ELSE
13 (.301.3703LC(3)) 1333
C ------- Recover the equations to the maximum extent possible
E7CFLG(4)8.FALSE.
37C3LC(5)8.3ALs3.
CALL REDOEQ
37C3LC(3)8 OKAY
13 (.NOT.OKAY) 1333
MESSAG8 ' *** Unable to recover equations.’
CALL LNMSGD(24) '

RETURN
ENDIF

ENDIF

ENDIF
C
C---- Get next option selection.
C

E7CELG(4)8 .PALSE.

E7CELG(5)8 .FALSE.
C

RETURN
C

END

CEND:EQNINI<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
SMESSAGE:'VIBDAT'
CVIBDAT >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/13/91 RM
0

SUBROUTINE VIBDAT(MATRX)

C .

C---- PURPOSE: Guides Change in existing equations for nodes.

C

C---- INPUTS: MATRX - Matrix to fill in ('SRCE', 'MASS', 'STIF' or
'DAMP')

C

C---- OUTPUTS: none

C

C-—-- NOTES: Equation structure can be Changed for a multiple-output
C node, either NYL sgl-out eqns or 1 NYL-out eqn.

C All change data is held on a working basis until it is
C complete. Then it is stored if it fits into the eqn d-b.
C

INCLUDE 'COMMBR.CBK'

INCLUDE
INCLUDE
INCLUDE
INCLUDE
INCLUDE
INCLUDE

'VIEWBK.CBK'
'EQVUBK.CEK'
'SIZEMB.CBK'
'SIZESL.CBK'
'GREDBK.CBK'
'MCXHDR.CBK'

77

C

c***VIBDAT*****************************fi********************************

C

CHARACTER MATRX*4, ELSEL*8, ST1*10, ST2*10

CHARACTER NVOTL(MXVOTQ)*12, NVINL(MXVINQ)*12, EVTTYP*4
CHARACTER ST11*1, ST22*2, NAME*8
INTEGER NODE, IQ, IQl, IQZ, I, NUMOUT,
INTEGER NPR, FNCZI, NCHARS, IDX

REAL VAL

NUMIN, J

EXTERNAL
EXTERNAL
EXTERNAL FNDISP,
EXTERNAL NCHARS,
INTRINSIC MAX,

LNMSGD,
LSTLST,

MOVCUR,
EQNLST,
EDTILQ,
GETRL,
MIN,

WRTCAT,
TRPQDT,
PTPLST,
GETKEY,
INT,

WRTSTG,
GETSTR,
FNCZI,
EVTTYP,
REAL

CLEARS,
GETINT,
MTXDSP,
SETVAL

C---- Get the node name.

C

10

15

C—-——

20
30

c--_-

33113(s11,10) NUMMAC
3033A1(11)
13 (MATRX.EQ.'MASS') 1333
ELSEL 8 '1'//s11(1:1)
3Ls313 (MATRX.EQ.'STIF') 1333
ELSEL 8 'C'//STl(l:1)
3Ls313 (MATRX.EQ.'DAMP') 1333
ELSEL 8 '3'//s11(1:1)
3Ls313 (MATRX.EQ.‘SRCE') 1333
WRITE(ST11,690) NUMMAC
00 15 181,303013
13(330103(1).3Q.1) 1333
33113(s122,700) 1
13 (ST22(l:1).EQ.' ') 5122(1:1)8'0'
NAME 8 'sv'//s111(1:1)//s122(1:2)
VAL 8 33CVAL(1)
CALL SETVAL('CON
33013
00311303
0010 800
33013

',NAME,VAL)

Get the node index.
00 20 30038 l,INELS

13 (ELNAM(NODE).EQ.ELSEL) 0010 30
NODE8INELS
CONTINUE

Check on validity of node request

CALL EQNLST(NODE,'U',IQl,IQZ,NUMOUT,NVOTL,NUMIN,NVINL)
13 (.NOT.OKAY) 1333

CALL LNMSGD(24)

0010 800

33013

00 4o 18 1,303001

YL(I)=NVOTL(I)

00311303

DISPAG,
TBLDSP,
PLYDSP

78

 

C---- Do each eqn of this node

C 198 I01

200 CONTINUE

3---- Fill in the equation_view data base from the model db.
C CALL TREQDT('GET',IQ)

§---- Get the (new) function type.

300 CONTINUE
ENAM8 'MATRIX'
I! (FNAM.EQ.'MATRIX'.AND.NUMOUT.EQ.1) THEN
MESSAG8 ' *** Use SUM, not MATRIX, for single outputs.’
CALL LNMSGD(24)

GOTO 800
ENDIF
C
C---- (Re-)set the number of outputs
C
NYL8 NUMOUT
C

00 310 18 1,303001
33113(s12,315) 1
315 3033A1(12)
13 (ST2(1:1).EQ.' ') 512(1:1)8'o'
13 (MATRX.EQ. 'MASS') 1333
XL(I) 8 '313'//s11(1:1)//s12(1:2)
ELSEIF (MATRX.EQ.'STIF') 1333
XL(I) 8 'ch'//s11(1:1)//s12(1:2)
3Ls313 (MATRX.EQ.'DAMP') 1333
xL(1) 8 '333'//s11(1:1)//s12(1:2)

ENDIF
310 CONTINUE
C
C---- Set the number of inputs.
C
NXL8 MCKDIM
C
C---- Set the number of parameters.
C
NPR8 NYL*NXL
NPL8NPR
C
C---- Set parameter values.
C
DO 332 I 8 1,NYL
DO 331 J81,NXL
IDX 8 J + (MCKDIM*(I-l))
IF (MATRX.EQ.'MASS') THEN
WRITE(PL(IDX),333) MASMAT(I,J)
ELSEIF (MATRX.EQ.'STIF') THEN
WRITE(PL(IDX),333) STFMAT(I,J)
ELSEIF (MATRX.EQ.'DAMP') THEN
13 (MCKCCT.EQ.O) 1333
PL(IDX) 8 ' 0.00003+oo'
ELSE
WRITE(PL(IDX),333) DMPMAT(I,J)
ENDIF
ENDIF
331 CONTINUE

332 00311303
333 3033A1(13,312.4)

79

C
C---- Equation completed
C
500 CONTINUE
CALL TRPQDT('PUT',IQ)
I? (.NOT.OKAY) THEN
CALL LNMSGD(24)
GOTO BOO
ENDIF
C
C---- Modify the equation data base (delete excess equations).
C
FNAM 8 'NULL'
NYL 8 O
NXL 8 O
NPL 8 0
DO 540 IQ 8 IQI+1,IQ2
540 CALL TRPQDT('PUT',IQ)
C
690 PORMAT(Il)
700 PORMAT(I2)
C
800 CONTINUE
RETURN
END
CEND:VIBDAT<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
C

SMESSAGE:'MCKEIG'
CMCKEIG>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/20/91 RM

C_---

SUBROUTINE MCKEIG
PURPOSE: Controls the eigen evaluation of M,K matrices. The
results are used to automatically assign parameters
to a modal vibration macro.

MASMAT
STFMAT
MCKMAX
MCKDIM

The (NxN) mass matrix.

The (NxN) stiffness matrix.

Allocated size of the above matrices.

The working dimension of the above matrices.

Inputs:

Outputs:
ANS - The inverted matrix.

Note: The A matrix is destroyed in this routine!

Include the MCK stuff.
INCLUDE
INCLUDE
INCLUDE
INCLUDE
INCLUDE
INCLUDE
INCLUDE
INCLUDE

'COMMBK.CBX'
'VIEWBK.CBK'
'SIZEMB.CBK'
'SIZESL.CBX'
'EIGNBK.CBK'
'LINZEK.CBK'
'SOLNBK.CBK'
'MCKHDR.CBX'

REAL
REAL
INTEGER

0031(3033Ax,3033Ax), ANS(MCKMAX,MCKMAX)
MINVK(MCKMAX,MCKMAX)

1, J, INDX(MCKMAX)

EXTERNAL INVMAT,

MTXMUL, BALANZ, ELMHSZ, HQR3

80

C
C***MCKBIG**************************************************************
C
C---— Duplicate the MASMAT matrix so as not to destroy it.
C
DO 6 I81,MCKDIM
DO 5 J81,MCRDIM
DUM1(I,J)8MASMAT(I,J)
CONTINUE
CONTINUE

---- Get the inverse of the mass matrix.
CALL INVMAT(DUM1,MCXDIM,MCKMAX,INDX,ANS)
---- Form the inv(M)*K matrix
CALL MTXMUL(ANS,MCKDIM,MCKMAX,STFMAT,MCKDIM,MCKMAX,MINVK)

888- Set up the AMX matrix.

GOO 000 060mm

00 31 181,303013
00 30 J81,303013
AMX(I,J) 8 0.0
AMX(I+MCKDIM,J+MCKDIM)8O
A3x(1,J+3C3013)8 -1 * 313V3(1,J)
AMX(I+MCKDIM,J) 8 0
30 00311303
AMX(I+MCKDIM,I) 8 1.0
31 00311303

C
C---- Balance the AMX matrix.
C
CALL BALAN2(AMX,MCKDIM*2,MAXXI)
C
C---- Put matrix in Hessenberg form.
C
CALL ELMHSZ(AMX,MCKDIM*2,MAXXI)
C
C---- Get the eigen values.
C
CALL HQR3(AMX,MCKDIM*2,MAXXI,WR,WI)
C DO 45 J81,MCKDIM*2
C PRINT *,NI(J)
C PRINT *,WR(J)
45 CONTINUE
C
C---- Find the eigenvectors.
C
CALL EVECTS(WI,MAXXI)
C
RETURN
END
C

CEND:MCKEIG<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:‘MODDAT'
CMODDAT >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/24/91 RM
C

SUBROUTINE MODDAT

C
C---- PURPOSE: Guides change in existing equations for nodes of a modal
C macro.

C

81

C---- INPUTS:

C

C---- OUTPUTS: none
C

INCLUDE 'COMMBX.CEX'
INCLUDE 'VIEWBK.CBX'
INCLUDE 'EQVUBX.CBX'
INCLUDE 'SIZEMB.CBX'
INCLUDE 'SIZESL.CBX'
INCLUDE 'GREDBK.CBK'
INCLUDE 'MCKHDR.CEX'

C

CHARACTER ST1*1, ST2*2, NAME*8

INTEGER I, J

REAL EIGTRN(MCKMAX,MCXMAX), TEMP(MCKMAX,MCRMAX), VAL
C

EXTERNAL MTXTRN, SETVAL
C

c***HODDAT**************************************************************
C

C---- Build the name constant string
C
WRITE(ST1,690) NUMMAC
C
C---- Set the source node values.
C
DO 150 I81,MCKDIM
IP(FRCTOK(I).EQ.1) THEN
HRITE(ST2,700) I
13 (ST2(1:1).EQ.' ') ST2(l:l)8'O'
3A33 8 's3'//s11(1:1)//s12(1:2)
VAL 8 PRCVAL(I)
CALL SETVAL('CON ',NAME,VAL)
ENDIF
150 CONTINUE
C
C---- Set the transformer node values.
C
DO 180 I81,MCKDIM
IF(PRCTOK(I).EQ.1) THEN
DO 170 J81,MCKDIM
WRITE(ST2,700) J + ( (I-l) * MCKDIM )
IF (ST2(1:1).EQ.' ') ST2(1:1)8'O'
NAME 8 'TF'l/ST1(1:1)//ST2(1:2)
VAL 8 EIGMAT(I,J)
CALL SETVAL('CON ',NAME,VAL)
170 CONTINUE
ENDIF
180 CONTINUE
C
C---- Set the inertia elements (get R'*M*R).
C
CALL MTXTRN(EIGMAT,MCKDIM,MCKMAX,EIGTRN)
CALL MTXMUL(EIGTRN,MCKDIM,MCKMAX,MASMAT,MCKDIM,MCKMAX,TEMP)
CALL MTXMUL(TEMP,MCXDIM,MCKMAX,EIGMAT,MCKDIM,MCKMAX,EIGTRN)
C

00 200 181,303013

33113(s12,700) 1

13 (ST2(l:l).EQ.' ') 512(1:1)8'0'

3A33 8 '13'//s11(1:1)//s12(1:2)

VAL 8 310133(1,1)

CALL SETVAL('ATT ',NAME,VAL)
200 00311303

82

 

C
C---- Set the compliance elements (get R'*C*R).
C
CALL MTXTRN(EIGMAT,MCKDIM,MCKMAX,EIGTRN)
CALL MTXMUL(EIGTRN,MCKDIM,MCKMAX,STFMAT,MCKDIM,MCKMAX,TEMP)
CALL MTXMUL(TEMP,MCKDIM,MCKMAX,EIGMAT,MCKDIM,MCKMAX,EIGTRN)
C
DO 210 I81,MCKDIM
WRITE(ST2,700) I
13 (ST2(1:1).EQ.' ') ST2(1:1)8'0'
NAME 8 '03'//s11(1:1)//s12(1:2)
VAL 8 EIGTRN(I,I)
CALL SETVAL('GAIN ',NAME,VAL)
210 CONTINUE
C
C---- Set the dissipation elements (get R'*r*R).
C
I1"(MCKCCT.NE.O) THEN
CALL MTXTRN(EIGMAT,MCKDIM,MCKMAX,EIGTRN)
CALL MTXMUL(EIGTRN,MCKDIM,MCKMAX,DMPMAT,MCKDIM,MCKMAX,TEMP)
CALL MTXMUL(TEMP,MCKDIM,MCKMAX,EIGMAT,MCXDIM,MCKMAX,EIGTRN)
C
DO 220 I81,MCKDIM
WRITE(ST2,700) I
I? (ST2(1:1).EQ.' ') ST2(1:1)8'O'
3A33 8 '33'//s11(1:1)//s12(1:2)
VAL 8 EIGTRN(I,I)
CALL SETVAL('GAIN ',NAME,VAL)
220 CONTINUE
ENDIF
C

690 3033A1(11)
700 3033A1(12)

RETURN

END
C
CEND:MODDAT<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'SETVAL'
CSETVAL >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 09/23/91 RM
C

SUBROUTINE SETVAL(FTYPE,ELSEL,VAL)

C
C---- PURPOSE: Guides change in existing equations for nodes.
C
C---- INPUTS: PTYPE - Function type for the node.
C ELSEL - Name of the node to modify.
C VAL - Value for the node.
C
C---- OUTPUTS: none
C
INCLUDE 'COMMBK.CBK'
INCLUDE 'VIENBK.CBK'
INCLUDE 'EQVUBK.CBR'
INCLUDE 'SIZEMB.CBK'
INCLUDE 'SIZESL.CBK'
INCLUDE 'GREDBK.CBK'
INCLUDE 'MCKHDR.CBK'
C
CHARACTER ELSEL*8, PTYPE*8
REAL VAL
C

CHARACTER PNMOLD*8, STRING*80

C

83

CHARACTER NVOTL(MXVOTQ)*12, NVINL(MXVINQ)*12, EVTTYP*4

INTEGER
INTEGER
LOGICAL

EXTERNAL
EXTERNAL
EXTERNAL

NODE,
NPR,
SGLOLD,

LNMSGD,
LSTLST,
FNDISP,

IQ:

IQI,
NEWPCN
MOVCUR,

EQNLST,
EDTILQ,

IQZ,

1:

WRTCAT,

TRPQDT,
PTPLST,

NUMOUT,
PNCZI, NCHARS, NXLOLD, NXLOLD, NPLOLD

NUMIN, NIV

SPKEYL
TBZDSP

NRTSTG,
GETSTR,
FNCZI,

CLEARS,
GETINT,
MTXDSP,

DISPAG,
TBLDSP,
PLYDSP

EXTERNAL NCHARS,
INTRINSIC MAX,

GETRL,
MIN,

GETXEY,
INT,

EVTTYP
REAL

c***SETVAL****************************fi*********************************

C
c----
C

20

30
C

c----

C

C----

200

C“---

c----

c---_

300

Get the node index.

DO 20 NODE8 l,INELS

IP (ELNAM(NODE).EQ.ELSEL) GOTO 30
NODE8INELS
CONTINUE

Check on validity of node request.

CALL EQNLST(NODE,'U',IQl,IQZ,NUMOUT,NVOTL,NUMIN,NVINL)
13 (.NOT.OKAY) 1333

CALL L33500(24)

0010 800

33013

303138 313(30313,303001)

 

Do each eqn of this node

IQ8 IQI
CONTINUE

Fill in the equation_view data base from the model db.
CALL TRFQDT('GET',IQ)

Mark state of model eqn_data_base for later use

SGLOLD8
PNMOLD8
NYLOLD8
NXLOLD8
NPLOLD=
Get the

CONTINUE

NYL.EQ.1

FNAM

NYL

NXL

NPL

(new) function type

PNAM 8 PTYPE

PNAM 8

13 (33A3.3Q.'

ImNI
') 0010 800

IF (FNAM.NE.PNMOLD) THEN
C ------ Check the changed function type
CALL LJSTR(FNAM,STRING,I)

FNAM=

STRING

CALL 030A53(33A3)
13 (33021(33A3).3Q.0) 1333

MESSAG8 ' *** Invalid function type: '//FNAM
CALL LNMSGD(24)
GOTO 800

ELSE

IE (FNAM.EQ.'MATRIX'.AND.NUMOUT.EQ.1) THEN
MESSAG8 ' *** Use SUM, not MATRIX, for single outputs.‘
CALL LNMSGD(24)
GOTO 300

ENDIF

ENDIF
ENDIF
NEWPON- ENAM.NE.ENMOLD
C
C---- (Re-)set the number of outputs.
C
NYL8 1
C
C---- Get the number of inputs and parameters for this function
C
CALL PTPLST(PNAM,NIV,NPR)
C
NXL8 NIV
NPL8 NPR
C
C---- Set parameter values.
C

33113(3L(1),333) VAL
333 3033A1 (13,312.4)

C---- Equation completed.

500 00311303
CALL 133001('301',10)
13 (.NOT.OKAY) 1333
CALL LNMSGD(24)

GOTO 800
ENDIF

C

800 CONTINUE
RETURN
END

C

CEND 3 SETVAL<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C

CPILE:MCXMTH.FOR

C

85

 

C---- MCKMTH.FOR: Math support for building M,C,K macros.

C

C---- PURPOSE:

C

C.) 0
l
I
I
0
0
3
fl’
0
5
('1’
I

0000000000000

This file contains math functions required to build

MCK macros.

INVMAT,
LUDCMP,
LUBXSB,
MTXMUL,
MTXCML,
MTXTRN,
MTXADD,
DETCPY,
DETMTX,
BALANZ,
ELMHSZ,
HQR3,

Finds inverse of a matrix.

Performs a LU decomposition of a matrix.
Performs back substitution on LU matrix.
Multiplies two square matrices.
Multiplies a matrix by a constant.

Finds transpose of matrix (square only).
Adds two matrices.

Copies reduced matrix for finding det.
Finds the determinant of a matrix.
Balances a square matrix.

Puts square matrix in Hessenberg form.
Finds eigenvalues of matrix in Hess. form

C---- Last Change: September 19, 1991. RM

C

 

CEOPH
C

SMESSAGEz'INVMAT'

CINVMAT>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/19/91 RM

SUBROUTINE INVMAT(A,N,NP,INDX,ANS)

Inverts a matrix.

- The (NxN) matrix to be inverted.
- The dimension of the matrix to be inverted.

Physical size of the incoming matrix.
Index matrix (Nle).

The inverted matrix.

The A matrix is destroyed in this routine!

A(NP,NP), ANS(NP, NP),

1303(3)

LUBKSB

Ififitfit‘fifiifiiifitififitfifiififi

c***1m1‘*************************************tit**********************

C
C
C---- PURPOSE:
C
C---- Inputs: A
C N
C NP -
C INDX -
C
C---- Outputs:
C ANS -
C
C---- Note:
C
DIMENSION
INTEGER N, NP
REAL D
INTEGER I, J
C
EXTERNAL LUDCMP,
C
C
C---- Set up the identity matrix.
C
DO 12 I81,N
DO 11 J81,N
ANS(I,J)8O.O
ll CONTINUE
ANS(I,I) 8 1.0
12 CONTINUE
C

C---- Perform a LU - decomposition of the marix.

C

CALL LUDCMP(A,N,NP,INDX,D)

86

C
C---- Invert by back substitution.
C
DO 13 J81,N
CALL LUBKSB(A,N,NP,INDX,ANS(1,J))
13 CONTINUE
C
RETURN
END
C
CEND:INVMAT<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'LUDCMP'
CLUDCMP>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/19/91 RM

SUBROUTINE LUDCMP(A,N,NP,INDX,D)
C---- PURPOSE: Performs a LU decomposition of a matrix.

C---— Inputs: A - The (NxN) matrix to be decomposed.

C N - The dimension of the matrix to be inverted.
C NP - Physical size of the incoming matrix.

C

C---- Outputs:

C ANS - The inverted matrix.

C

C---- Note: The A matrix is destroyed in this routine!

C

C---- Note: The source code has been omitted from this listing.
C See reference [8] for details.

C

1313033 NMAX
REAL VV

PARAMETER (NMAX8100,TINY81.OE-2O)
013335103 A(NP,NP),INDX(N),VV(NMAX)

REAL D, AAMAX, SUM, DUM

INTEGER I, J, K, IMAX
C
C***LUDCHP***************itt*****************tttt***************t******t

C
See reference [8]

RETURN
END
C
CEND:LUDCMP<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'LUBKSB'
CLUBKSB>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/19/91 RM
C
SUBROUTINE LUBKSB(A,N,NP,INDX,B)
C
C---- PURPOSE: Performs back substitution on LU matrix.
C
C---- Inputs: A - The (NxN) matrix to be decomposed.
N - The dimension of the matrix to be inverted.
NP Physical size of the incoming matrix.
INDX Permutation list from LUDCMP.
B - + or - for odd or even number of exchanges.

---- Outputs:

0000000

87

C---- Note: The A matrix is destroyed in this routine!

C

C---- Note: The source code has been omitted from this listing.
C See reference [8] for details.

C

1313033 NMAX
PARAMETER (NMAX8100,TINY81.OE-20)
013333103 A(NP,NP),INDX(N),B(N)

INTEGER I, J, II, LL
REAL SUM
C

C***LUBKSB*******i*****************t'k*t********i************************

C
See reference [8]

RETURN

END
C
CEND:LUBKSB<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'MTXMUL'
CMTXMUL>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 R3
C

SUBROUTINE MTXMUL(MX1,NI,NP1,MX2,NZ,NP2,ANS)

C
C---- PURPOSE: Multiplies two matrices (square only).
C
C---- Inputs: MXl, MX2 - The matrices to be multiplied.
C N1, N2 - The working dimension of the matrix (square).
C NPl, NP2 - Physical size of the incoming matrices.
C
C---- Outputs:
C ANS - The resulting matrix.
C
INTEGER N1, N2, NPl, NP2
REAL MXl, MX2, ANS
DIMENSION MX1(NP1,NP1), MX2(NP2,NP2), ANS(NP1,NP1)
C
INTEGER I, J, K
C

c***MTXHUL*************e*******************8**8*8***********************

C
C---- Multiply the matrices.

C
00 18 181,31
00 17 J81,N2
ANS(I,J) 8 0.0
00 16 381,32
ANS(I,J)8 ANS(I,J) + MX1(I,K)*MX2(K,J)
16 00311303
17 00311303
18 00311303
0
331033
330
C

CEND:MTXMUL<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C

$MESSAGE:'MTXCML'

CMTXCML>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 RM
C

88

SUBROUTINE MTXCML(MX,N,NP,CONST,ANS)
C
C---- PURPOSE: Multiplies a matrix by a constant (square only).
C
C---- Inputs: MX,
C N

The matrices to be multiplied.
The working dimension of the matrix (square).

C NP Physical size of the incoming matrices.
C CONST Constant multiplier.
C
0---- Outputs:
C ANS - The resulting matrix.
C
INTEGER N, NP
REAL MX, ANS
013333103 33(33,33), ANS(NP,NP)
REAL CONST

INTEGER I, J
C
Cti*MTXCML************************************t*************************
C
C---- Multiply the matrices.

C
00 1s 181,3
00 17 381,3
ANS(I,J)8 00351 . MX(I,J)
17 00311303
18 00311303
0
331033
330
C

CEND:MTXCML<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
gMESSAGE:'MTXTRN'

CMTXTRN>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 RM
C SUBROUTINE MTXTRN(MX,N,NP,ANS)

g---- PURPOSE: Finds the transpose of a matrix (square only).

g---- Inputs: MX - The matrices to take transpose of.

C N - The working dimension of the matrix (square).
C NP - Physical size of the incoming matrix.

C

0---- Outputs:

C ANS - The resulting matrix.

C

INTEGER N, NP

REAL MX, ANS

DIMENSION MX(NP,NP), ANS(NP,NP)
C

INTEGER I, J
C
Cti*HTXTRN************************************************************t*
C
C---- Multiply the matrices.
C

DO 18 I81,N

DO 17 J81,N

ANS(I,J) 8 MX(J,I)

17 CONTINUE
18 CONTINUE

 

89

RETURN

END
C
CEND:MTXTRN<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
SMESSAGEx'MTXADD'
CMTXADD>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 RM
C

SUBROUTINE MTXADD(MX1,N,NP,MX2,ANS)

C
C---- PURPOSE: Adds two matrices (square only).
C
C---- Inputs: MX1, MX2 - The matrices to be added.
C N - The working dimension of the matrix (square).
C NP - Physical size of the incoming matrices.
C
C---- Outputs:
C ANS - The resulting matrix.
C
INTEGER N, NP
REAL MX1, MX2, ANS
013335103 331(33,33), 332(33,33), A35(33,33)
C
INTEGER I, J
C

C***MTKADD****************tt‘tt***********************t******************

C
C---- Add the matrices.

C
00 18 181,3
00 17 381,3
ANS(I,J)8 MX1(I,J) + MX2(I,J)
17 00311303
18 00311303
0
331033
330
C

CEND:MTXADD<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
SMESSAGE:'DETCPY'
CDETCPY>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 RM
C

SUBROUTINE DETCPY(IDX,N,NP,MTX1,MTX2)

C
C---- PURPOSE: Copies the appropriate submatrix from MTXl to MTX2 based
C on the index. For example, if the index is 1, MTX2 will
C contain all of MTXl except row 1 and col 1. If index is
C 2, all but row 1 col 2 will be in MTX2 etc.
C
C---- Inputs: MTXl, MTX2 - The matrices to be copied.
C N - The working dimension of the matrix (square).
C NP - Physical size of the incoming matrices.
C IDX - Column index to be struck out.
C
C---- Outputs:
C MTX2 - The reduced (N-lxN-l) matrix.
C
INTEGER N, NP, IDX
REAL MTXl, MTX2
DIMENSION MTX1(NP,NP), MTX2(NP,NP)
C

INTEGER I, J, K, L

 

9O

c***DETCPY*************************************t**************i*********
C

C
00 10 181,3-1
3 8 1
L 8 1
00 9 381,3
13 (3.30.103) 1333
383+1
3L53
MTX2(I,L) 8 3131(1+1,3)
383+1
L 8 L+1
33013
9 00311303
10 00311303
0
331033
330
C

CEND:DETCPY<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
CDETMTX>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 RM
C

SUBROUTINE DETMTX(MTX,N,NP,DET)

C
C---- PURPOSE: Determines the determinate of MTX.
C
C---- Inputs: MTX - Mantrix to find determinant of.
C N - The working dimension of the matrix (square).
C NP - Physical size of the incoming matrices.
C
C---- Outputs:
C DET - The determinant.
C
INCLUDE 'MCKHDR.CBK'
C
INTEGER N, NP
REAL MTX, DET
DIMENSION MTX(NP,NP)
C
INTEGER J, INDX(MCKMAX)
C

C***DETMTX***************************ttt*t*********t********************

C
C
CALL LUDCMP(MTX,N,NP,INDX,DET)
00 11 381,3
031 8 DET*MTX(J,J)
11 00311303

RETURN
END
C
CEND:DETMTX<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
SMESSAGE:'BALAN2'
CBALAN2>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 RM
C
SUBROUTINE BALAN2(A,N,NP)
C
C---- PURPOSE: Balances a matrix (square only).
C
C-—-- Inputs: A, - The matrix to be balanced.

91

C N - The working dimension of the matrix (square).
C NP - Physical size of the incoming matrices.
C
C---- Outputs:
C A - The balanced matrix.
C
C---- Note: The source code has been omitted from this listing.
C See reference [8] for details.
C
REAL RADIX, SQRDX
PARAMETER (RADIX816.,SQRDX8256.)
INTEGER N, NP
DIMENSION A(NP,NP)
C
INTEGER I, J, LAST
REAL C, R! cl ’08
C

cstngALanzessstseseeesassestaeesssssssssssswswssssatsauss*estssttssssass

C
See reference [8]

RETURN

END
C
CEND:BALANz<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'ELMH82'
CELMHSZ>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 RM

SUBROUTINE 3L3352(A,3,33)

C---- PURPOSE: Puts A matrix in Hessenberg form (square only).

C---- Inputs: A, The matrix to be balanced.

C N - The working dimension of the matrix (square).
C NP - Physical size of the incoming matrices.

C

C---- Outputs:

C A - The balanced matrix.

C

C---- Note: The source code has been omitted from this listing.

C See reference [8] for details.

C

C

INTEGER N, NP
REAL A
DIMENSION A(NP,NP)

INTEGER I, J, M
REAL X, Y
C

Ctt*ELMH32****************twtttttttttttittt*ttttttttttti****************

C
See reference [8]

RETURN
END
C
CEND : ELHHSZ<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'HQR3'

92

03933>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 33
5033001133 HQR3(A,N,NP,WR,WI)
C---- PURPOSE: Finds the eigenvalues of A matrix (square only).

C---- Inputs: A, - The matrix to be balanced.

C N - The working dimension of the matrix (square).
C NP - Physical size of the incoming matrices.

C

C---- Outputs:

C - Real parts of the eigenvalues.

C WI - Imaginary parts of eigenvalues.

C

C---- Note:

C WR AND WI CONTAIN THE REAL AND IMAGINARY PARTS,

C RESPECTIVELY, OF THE EIGENVALUES. COMPLEX CONJUGATE

C PAIRS OF EIGENVALUES APPEAR CONSECUTIVELY WITH THE

C EIGENVALUE HAVING THE POSITIVE IMAGINARY PART LAST.

C

C---- Note: The source code has been omitted from this listing.
C See reference [8] for details.

C

1313033 3, 33
REAL A, 33, 31
013335103 A(NP,NP),WR(NP),WI(NP)

INTEGER I, J, M, NN, ITS, L, R

REAL ANORM, X, Y, T, S, W, P, Q, 2, R, U, V
C
c***HQR3*ewas*ettteeesewss*easseetsttasseeesssesesssaeetw*sststswttsssss

C
See reference [8]

RETURN

END
C
CEND:HQR3<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C
$MESSAGE:'EVECTS'
CEVECTS>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Last Change: 9/23/91 RM

SUBROUTINE EVECTS(WI,NP)

C

C---- PURPOSE: Finds the eigenvectors of M,K matrices.

C

C---- Inputs:
WI - Eigenvalue corresponding to the eigenvector.
NP - Physical size of the incoming matrices.
MASMAT - Mass matrix.
STFMAT - Stiffness matrix.

---- Outputs:
EIGMAT - Matrix of eigenvectors.

---- Note:
WI CONTAINS THE REAL AND IMAGINARY PARTS,
RESPECTIVELY, OF THE EIGENVALUES. COMPLEX CONJUGATE
PAIRS OF EIGENVALUES APPEAR CONSECUTIVELY WITH THE
EIGENVALUE HAVING THE POSITIVE IMAGINARY PART LAST.

INCLUDE 'MCXHDR.CEX'

0 00000000000000

9:

 

93

REAL 31
1313033 33
013335103 31(33)

C
INTEGER I, J, R
REAL DUM1(MCRMAX,MCRMAX), ZDUM(MCXMAX,MCRMAX), DETVAL
REAL RNORM
C
EXTERNAL MTXCML, MTXADD, DETCPY, DETMTX
C

C***MCTS**************************************************************

C

C---- Build the eigenvector matrix.
C
J80
DO 200 I 8 l,MCKDIM*2-1,2
J 8 J + 1
C
C ------ Form the z 8 (K - WI‘2*M] matrix.
C

CALL MTXCML(MASMAT,MCXDIM,MCXMAX,-1.0*WI(I)*WI(I),DUMl)
CALL MTXADD(STFMAT,MCXDIM,MCRMAX,DUMl,ZDUM)

C
C ------ Get the normalized eigenvector for WI(J).
C
RNORM 8 0.0
DO 30, K 8 1,MCKDIM
CALL DETCPY(K,MCXDIM,MCKMAX,2DUM,DUM1)
CALL DETMTX(DUM1,MCXDIM-1,MCKMAX,DETVAL)
3103A1(3,J)8 ((-1)**3) * DETVAL
IF (RNORM.EQ.0.0.AND.EIGMAT(K,J).NE.0.0) THEN
RNORM 8 EIGMAT(K,J)
EIGMAT(K,J) 8 3103A1(3,J) / 33033
ELSEIF(RNORM.NE.0.0) THEN
3103A1(3,J) 8 EIGMAT(K,J) / 33033
ENDIF
30 CONTINUE
C
200 CONTINUE
C
RETURN
END
C

CEND:EVECTS<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
C

“3300?S