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F LIBRARY 3
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This is to certify that the

thesis entitled

DYNAMIC ANALYSIS OF A LESS
THAN TRUCKLOAD SHIPMENT

presented by

Jorge Aparecido Marcondes

has been accepted towards fulfillment
of the requirements for

M. 8. degree in Packaging_

 

 

/ Major professé/
S. Paul Singh, PhD.
Date May 12, 1988

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

 

 

 

 

 

 

 

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2/05 p:lClRC/DateDuo.indd-p.1

DYNAMIC ANALYSIS OF A
LESS THAN TRUCKLOAD SHIPMENT

By

Jorge Aparecido Marcondes

A THESIS

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

MASTER OF SCIENCE

School of Packaging

1988

0 for

v

ABSTRACT

DYNAMIC ANALYSIS OF A
LESS THAN TRUCKLOAD SHIPMENT

By

Jorge Aparecido Marcondes

The effect of shock and vibration forces in the distribution
environment has been studied extensively by engineers. This
study investigated the dynamics of three different package

systems in a Less Than Truckload (LTL) shipment.

A truck was positioned on vibration actuators and a time
domain input simulating road data was used as the drive
signal. Front and rear truckbed RMS accelerations were
measured. Three different resonant frequency (low, medium
and high) packages were positioned at the top of front and

rear stacks and their RMS acceleration were recorded.

The results show that the rear of the truck is not always
the worst position for acceleration magnification in LTL
shipments. Accelerations as high as 10 g's were encountered
during vibration. The front axle constributes about 20% and
the fifth wheel about 30% of the vibration input to the rear

truckbed.

This thesis is dedicated to
my parents Benedicto and Mercedes

my wife Patricia

iii

ACKNOWLEDGMENTS

I wish to express my sincere gratitude to my major professor
Dr. S. Paul Singh for his guidance and friendship throughout
this study. I am also very grateful to the members of my

committee, Dr. Gary J. Burgess and Dr. George E. Mase.

I also extend my appreciation to Fruehauf Corp. and Yellow
Freight Systems, Inc., for providing laboratory facilities
and collecting data during the experiments. I appreciate the
support of Dr. Harold A. Hughes for the use of facilities at
the School of Packaging. Thanks to Dr. James Goff, Dr. Diana
Twede and Mr. Jeff Waldeck for providing materials used in

the experiments.

Grateful acknowledgment is extended to Ms. Akemi Suzuki and
Mr. Mituru Mori, Embalagens Jaguare, Brazil, and to FAPESP,
Fundacao de Amparo a Pesquisa do Estado de Sao Paulo,
Brazil, for the initial support. To CAPES, Coordenacao de
Aperfeicoamento de Pessoal de Nivel Superior, Brazil. my

appreciation for completing the financial support.

Finally, I would like to thank all of those who helped in

one way or another during the course of this work.

iv

TABLE OF CONTENTS

LIST OF TABLES.
LIST OF FIGURES
LIST OF SYMBOLS AND ABBREVIATIONS

1.0 INTRODUCTION . .
Objectives

2.0 REVIEW OF LITERATURE

3.0 EXPERIMENTAL DESIGN. . .

Package Systems.

Truck System

Actuator System.
Accelerometers . . . . . .
Instrumented Package Positions
Experimental Set Up.

wwwwcow
(DUMiiCDNI—t

4.0 DATA AND RESULTS . . . . .
4.1 Vibration Input .
4.2 Truckbed Vibration.
4.3 Package Response.
4.4 Random Vibration.

5.0 CONCLUSIONS AND RECOMMENDATIONS.

APPENDICES. . . . . . . . . . . .
A. Statistical Concepts.
B. Transportation Concepts

LIST OF REFERENCES.

Page
vi
vii

xi

14
14
15
19
19
21
21

25
25
30
32
37

43
46
46
52

55

Table

10.

11.

LIST OF TABLES

Location of Recording Channels.

Amplitude of Input Drive Signal (Inches).
RMS Stroke Values Versus Frequency.
Truckbed G Levels for Front and Rear.

Peak G Acceleration of the Floor (Truckbed)
Versus Frequency. . . . . . . . . . .

Output Acceleration (g) on Packages A, B and C

Packages RMS and Peak G Accelerations Versus
Frequency

Relative Magnification Factor (from Truckbed to.

Packages) Versus Frequency.

Maximum FRF Between Actuators Stroke and the
Floor Acceleration at the Rear.

Magnification Factor of Acceleration in
Packages A, B and C Due to the Acceleration at
the Rear Truckbed, Based on Random Vibration

Values and Frequencies of Peak Magnification
Factor for the Three Different Packages

vi

Page
26
26
28

31

31

34

38

39

4O

41

42

LIST OF FIGURES

Figure
1. Package System A.
2. Package System B.
3. Package System C.
4. Tractor/Trailer Truck System.
5. Position of Axles and Wheels.
6. Curbside Rear Wheel on its Actuator.
7. Truck Positioned on the Actuator System
(Rear View).
8. Packages in the Front (Before Testing)
9. Packages in the Back (Before Testing).
10. LTL Shipment (Front of Trailer).
11. LTL Shipment (Rear of Trailer)
12. Positioning of Instrumented Packages in LTL
Shipment
13. Normal Distribution of Drive Signal.
14. Distribution of Input Drive Signal
15. Front Axle: Average Between Curb and
Roadsides Front Axle of RMS Stroke Inches
as a Function of Frequency
16. Fifth Wheel: Average Between Curb and
Roadsides Fifth Wheel of RMS Stroke Inches
as a Function of Frequency
17. Rear Axle: Average Between Curb and

Roadsides Rear Axle of RMS Stroke in Inches
as a Function of Frequency

vii

Page
16
16
17
17
18

20

20
22
22
23

23

23

27

27

29

29

29

Figure

18.

19.

20.

21.

22.

23.

24.

Truckbed RMS Acceleration as a Function of
Frequency (Front).

Truckbed RMS Acceleration as a Function of
Frequency (Rear)

G Levels Input and Response (Front).
G Levels Input and Response (Rear)
Random Signal.

Half Sine Wave

Magnification Factor

viii

Page

33

33

35

36

47

48

54

1.0 INTRODUCTION

The effects of shock and vibration forces on packages in the
distribution environment system have been studied
extensively by engineers. Although there are various
different ways of transporting goods from one place to
another, trucks and trains are the most common means of
bulk surface transportation of most packaged goods. To
evaluate the protective role of packaging systems,
measurements of the environment (roads, rails, etc.) have
been done to quantify the input shock and vibration levels.
Based on environmental conditions and a knowledge of the
fragility of the product to be protected, packages may be

designed to isolate the product from shock and vibration.

All packaged products go through several handling and
transportation environments before reaching 13MB end users.
Both human and mechanized handling such as conveyor belts,
material handling equipment, trucks, ships, aircraft and
trains are some examples. Focusing on trucks which are the
main carriers, the origin of all shock and vibration comes

from two sources:

2

1) External sources such as road or surface irregularities,

braking, and forward acceleration:

2) Internal sources due to the vehicle itself such as engine

vibration, drive mechanisms, and wheel unbalance. (Harris,

1961).

Therefore, not only the route but also the type of vehicle
to be used plays a fundamental role when designing an
optimum package for shock and vibration protection. In
addition, the size and position of the load within the truck
changes the dynamics of the truck and therefore the response
of the package inside the truck. This is important since
many commodities are shipped by Less Than Truckload (LTL)
shipments from regional distribution centers to sale

outlets.

ij._e.c._t_,iy_e.s.._.:.._

The purpose of this study was to understand the dynamics of
a loaded truck and how they effect packages in a LTL

shipment. The specific objectives were as follows:

1) Quantify the response of the truck suspension to a given

vibration input.

3
2) Observe the effect of the truckbed vibration on

instrumented. packages 1x3 determine 'vibration. transmission

levels.

3) Establish relationships between package resonance and

packages position within the truck.

4) Compare the results for LTL shipments from this study to

Full Truckload (FTL) shipments based on prior research.

5) Compare contributions of each axle or wheel to the

overall acceleration of the package.

The above objectives were chosen to raise and answer some
questions which have not yet been considered in LTL
shipments. The results show that some previously held ideas
are incorrect and that there are dynamic phenomena
associated to LTL shipments as opposed to FTL shipments

which may be the cause of increased damage.

2.0 REVIEW OF LITERATURE

There have been many studies aimed at uncovering the primary
features of shock and vibration that relate to product
damage during transportation using common carriers. Several
of these studies use analytical concepts such as RMS
acceleration, magnification factors and Power Spectral
Density (PSD) plots. In order to hold the literature review
to a non-mathematical format, the reader is referred to
Appendices A and B for the mathematical details of these
concepts. Also, since there appears to be some overlap in
the areas studied, no attempt will be made to present the
literature in an order which suits the development of
analytical ideas. Rather, the literature will simply be

presented in chronological order.

The studies, Preliminary Analyses of Data Obtained in the
Joint Army/AEC/Sandia Test of the Truck Transport
Environment (Foley, 1960) and The Environment Experienced by
Cargo on a Flatbed Tractor-Trailer Combination (Foley, 1966)
were undertaken to gather and analyze data on heavy load
shipments. These tests were aimed at determining the

dynamic environment for truck shipments using a 15—ton

5

radioactive cask as the cargo and at developing techniques
for the reduction, presentation, and analysis cf data. The
results were given in PSD plots for blacktop and concrete

highways at 35 and 50 mph, at a location 24 in. to the rear

of the cask.

Harris and Credes (1961) presented concepts and definitions
related to shock and vibration levels encountered by road
and rail vehicles. A table of typical shock and vibration
data for tractor-trailer combinations under normal operating
conditions was presented. Similar data for trucks and trains

were also published.

The Dynamic Environment of Spacecraft Surface Transportation
(Schlue, 1966) studied shock and vibration characteristics
for the purpose of designing transportation vehicles for
spacecraft. The objective of this work was to measure shock
and vibration forces over both rough, irregular roads and
smooth highways. Comparisons were made for vans on three
trips over smooth and rough roads, and the conclusions
reached were:

a) Air-suspension systems are adequate for spacecraft
shipment.

b) Equipment should be hard mounted to the floor, especially
if dynamic characteristics of support structures or shock

mounts are not known.

6

c) The position on the truckbed corresponding to the lowest
vibration input was a function of frequency, individual van
characteristics, and to some extent, input excitation
amplitude. The aft and center positions are the most
consistent with respect to vibration levels (aft highest,
center lowest).

d) Vibration levels at frequencies greater than 100 Hz were

insignificant.

Preliminary Measurement and Analysis of the Vibration
Environment of Common Motor Carriers (Sharpe et a1, 1974)
was a study aimed at assessing the nature of the dynamic
vibration environment of commercial motor carriers carrying
package loads. Some conclusions reached were:

a) Vertical accelerations were the most severe and
therefore the only ones that need be measured.

b) Simply enveloping PSD data was equivalent to selecting
the worst possible conditions and therefore may be an
excessively severe test requirement. Some type of product
validation testing at various PSD levels for specified

periods of time would be better.

The objectives of the Joint Services Highway Shock Index
Project (Grier et A1, 1975) were to conduct static loading
and dynamic impact tests on a representative series of
commercial highway cargo trucks to obtain data for the shock

levels transmitted to the cargo bed and to analyze the

7

static and dynamic data collected from these tests to
develop a method for determining the shock index of
commercial cargo trucks.

The results of the study were:

a) A practical graph method which uses planned payload(s)
and vehicle payload axle spring rates, was developed for
determining the shock index of commercial cargo trucks.

b) For a two-axle cargo-truck, the roughest ride on the
truckbed was over the rear axle. For a truck-tractor-
semitrailer combination, the roughest ride occurred either
over the rear axles of the trailer or over the tractor rear
axles (fifth wheel), depending on which axle had the higher
payload.

c) The tests showed that of the three major variables
(percentage of maximum payload, tire pressure, and speed),
percentage of maximum payload had the greatest influence on
the shock index. Tire pressure and speed were relatively
unimportant.

d)For highway travel, vertical accelerations were generally
greater than either lateral or longitudinal accelerations
and were a major factor in potential cargo damage.

e) High, erratic shock values occurred with. either very
light or very heavy payloads. The most erratic results
occurred in the area of the fifth wheel.

f) Under maximum load conditions, independent of load
location, tire pressure, and truck speed, vertical

accelerations exceeding: 10 g’s were recorded on several

8

occasions by each of the forward, middle and rear impact
registers when the test vehicles ran over test bumps.

g) The shock index graph may be employed to define practical
shock parameters for selecting cargo trucks based on ride
performance and for preparing cargo truck specifications or

standards.

Advances in Shipping Damage Prevention (Caruso and Silver
1976) was another study aimed at observing cargo losses in
tractor-trailers for different suspension systems, degrees
of loading, rear wheel positions, road types, and drivers.
Their conclusions were:

a) The results did not necessarily apply only to heavy cargo
rigidly attached to the trailer bed.

b) Similar suspension systems on different trailers produced
similar responses.

0) PSD levels at frequencies greater than 50 Hz were
negligible.

d) Each suspension type had a different power density at the
first frequency peak (about 5 Hz) but similar power density
spectra beyond the second peak (about 13 Hz).

e) Single-leaf steel suspension springs produced the worst
ride conditions.

f) The worst ride occurred in a lightly loaded trailer over
the rear wheels.

g) The worst ride for typical roads occurred during high-

speed driving on interstate highways.

9
h) Different drivers had little effect on the overall

results.

Shock and vibration environment studies for large shipping
containers with heavy cargo during truck transportation were
undertaken by Magnuson (1977 and 1978). The results of his
work are:

a) The vibration history observed. was random and had a
normal Gaussian distribution with respect to acceleration
levels.

b) The highest vibration level was generally always in the
vertical direction.

c) Although the vertical acceleration was almost always the
most severe, there were exceptions unique to the vehicle
and its operating conditions.

d) Shipments weighing more than 15 tons showed little
difference in vibration amplitude regardless of the type of

suspension system.

The objective of the study, Shock and Vibration Environment
in a Livestock Trailer (Turczin et al, 1980) was to
ascertain the shock and vibration environment on the floor
of a livestock trailer typical of those used in the shipment
of cattle. Some conclusions reached were:

a) Vibration levels above 40 Hz were insignificant.

b) The highest energy levels were produced in the vertical

direction (peaks were measured to 0.08 g rms).

10

Tevelow (1983) characterized. the military logistical
transportation vibration environment with respect to the
shipment of fuzes using various types of vehicles (truck,

sea, rail and air). His study summarizes twelve previous

reports on trucks.

Pichler (1984) presented condensed information (n1 dynamic
environment data used in Brazil. The measurements were done
on the most important highway connecting the Northwest to
Southern part of the country where the highest volume of

goods are transported.

Goff et al (1984) reported vertical disturbances caused by
large amplitude transients. Accelerometers mounted (n1 both
packaged. products and the truckbed itself monitored the
degree of vibration magnification. Data was taken from a
half-hour test over city and county roads, interstate
expressways, bridges, and railroad grade crossings. However,
only accelerations in the rearmost portion of the trailer
were recorded. Three different suspension systems were
studied:

a) moveable leaf spring tandem axle trailer with axle at
rear portion;

b) same as a), but axle at forward position;

c) fixed position air-ride tandem axle trailer.

11

The study was divided into two parts using different cargo:
cartoned freezers in the first part and uncartoned furniture

in the second part.

American President Companies (1986) concluded a study in
December 1986 describing the double—stack/truck/vessel ride
characteristics. Accelerations were recorded while the
products were transportedi by ship, APL stack train, and
truck trailer. Instruments were positioned so that the
acceleration of each container and product could be
recorded. An overview of the results of the test revealed
that vessel transportation generated the lowest acceleration
levels during the entire trip. The double-stack intermodal
cargo transportation system proved to be the smoothest of
the available inland transportation modes. Trucking remained
the highest vibration environment among the tested modes of
transportation. The study states: "A key factor emerging
from the tests results is that, in the movement of this type
of cargo, the loading of the container itself is of prime
importance. All packages should be tightly loaded from front
to rear of the container in such a manner that no movement
of the cargo is allowed. This will reduce the levels of
acceleration experienced by the product to the same levels
by the container, thereby further improving the ride
quality". Results were presented in graphs of G level as
function of the percentage of occurrence for the following

situations:

12

a) Cargo performance in.2a double stack railcar (combined,
lateral, longitudinal and vertical acceleration).

b) Cargo performance in a truck (combined acceleration).

0) Container performance trucking (lateral, longitudinal and
vertical acceleration).

d) Cargo performance under handling & stowage (combined,

lateral, longitudinal and vertical acceleration).

Goodwin and Holland (1987) studied the rail distribution
environment from Rochestery NY, to ‘Los .Angeles, CA, via
Chicago, IL. They took into consideration two modes of
shipment, Trailer on a Flat Car (TOFC) and Container in a
Well Car (CIWC). A change in the mode from TOFC to CIWC was
made in Chicago. This intermodal shipping channel generated
dynamic data on shock and vibration which was analyzed and
used as a basis for packaging lab test simulation. The end
result was a laboratory preshipment test using the random
vibration characteristics of this route to simulate the
dynamics of other distribution channels. Power Spectral
Density (PSD) plots were developed for each of the three
axes, longitudinal, lateral and vertical for the same
loading in both transportation modes. Percentages of shocks
measured. were then reported for: similar loading: in ‘both
modes and four directions, longitudinal, lateral and two

vertical axis (rear and front).

 

13

This study is aimed at expanding the information base on LTL
shipments, specifically on the effects of truck vibration on
low, medium and high natural frequency packages. A knowledge
of the effect of the truck vibration on the different
dynamic characteristics of packages is crucial for planning
LTL shipments with emphasis on arranging packages in the

truck to minimize transportation damage.

 

3.0 EXPERIMENTAL DESIGN

The experiment designed to meet the objectives of this study
was set. up at the laboratories of Fruehauf Corporation
located in Detroit, Michigan. All of the data for this study
was collected at the Fruehauf laboratories using a vibration
system consisting“ of six independent ‘vibration actuators
positioned under the truck wheels to vibrate the truck and
simulate road conditions. (Figures 6, 7 10, 11 and 12 ).
Each wheel and axle is referred according to its position in
the truck as described later in the text. As the vehicle
travels over the road, irregularities in the surface create
independent excitation inputs at the individual wheels,
which may be vertical, side to side (transverse) or front to
back (longitudinal). In this experiment, only vertical
excitations were used since earlier studies show these to

be the most critical.

3.1 Package Systems:

The description of each package tested on the truck is as

follows:

14

15

Package A: (Figure 1)
Corrugated fiberboard box, 8.75” x 8” x 10.50”, containing a
concrete brick weighting 11.5 lbs, with cushioning material,

having a natural frequency of 9 Hz.

Package B: (Figure 2)

Corrugated fiberboard box, 12.75" x 10” x 9.50”, containing
23 cans of tomatoes. The 24th. can was replaced by a wooden
block containing an accelerometer. This block was placed in
one of the corners of the box. Package B has a total weight

of 28 lbs and natural frequency of 21 Hz.

Package C: (Figure 3)

Wooden block measuring 9.75“ x 8.75” x 8.75”, weighing 15.5
lbs and having a natural frequency in the range 64 to 74 Hz.
The accelerometer was located in the center of the wooden

block.

3.2 Truckaxstem:

The truck used in this experiment was a tractor/trailer type
provided by Yellow Freight Systems, Inc. Figure 4 shows the
particular truck used in the experiment and Figure 5 shows
the location and designation of the axles and wheels. The
truck’s main characteristics are as follows:
DrwareightmDoubles“VaanraiIer:

Manufacturer: Fruehauf Corp.

 

Figure 1. Package System A

 

Figure 2. Package System B

 

Figure 4. Tractor/Trailer Truck System

18

 

 

 

 

20’ 7 1/2” I

 

 

 

 

11’75/8”
(d) (e) i: (i)
ll
(1) (2):: IN”
(a) (b) H (0)
= E 1L a

 

 

 

 

 

1) Front axle
2) Fifth wheel
3) Rear axle

a) Roadside front axle
b) Roadside fifth wheel
c) Roadside rear axle

side view

top view

d) Curbside front axle
e) Curbside fifth wheel

0 Curbside rear axle

Figure 5. Position of axles and wheels

19

Model No.: FBBX — F1 — 27
Serial No.: 1H2V02714BE003223
Date of Manufacture: January, 1981
Tires: 11" x 24.5” ¢

SingleiAxleaTractor:

Manufacturer: General Motors Corp.
VIN: IGTM901W6HV511593
Max load at front (rated): 9,000 lb

Max load at rear (rated) : 20,000 lb

3 .3 Actuator---..S_xs.t.em:

The vibration system consists of six independently
controlled vibration actuators, each of which restricts the
wheels from moving back and forth and side to side, thereby
permitting only vertical motion. Figure 6 shows a picture of
one wheel placed on an actuator and Figure 7 shows the back
of the truck and the positioning of the rear wheels over
their respective actuators with interlocking restraining
devices. The drive signal used to control the actuators
replicates six minutes of driving at approximately 40 mph on

Interstate Highway I—94 in the Detroit area.

3 . 4 Accelerometers:

Strain gage accelerometers were used to monitor

accelerations. For each experimental run, four

 

Figure 7. Truck positioned on the actuator system (rear view)

21

accelerometers were used. One was mounted under the truckbed
just below the load and the other three accelerometers were

installed inside packages A, B and C.

3.5 Instrumentedwfiackageansiticns:

Measurements were made with stacks located in two different
positions inside the trailer:

1) only in the front, over the fifth wheel with no stowage.
2) only in the back over the axles; the stacks were stowed
by horizontal bars and plywood sheets at the front and by
the doors at the very back. These package arrangements are

shown in Figures 8 and 9.

3.6 ExperimentalmSetmup:

a) In the front of the trailer, boxes A, B and C were
positioned at the top of the LTL shipment as shown in Figure
12. The LTL shipment consisted of various kinds of packages
ranging in weight and size. Figure 10 shows the location of

the LTL shipment in the front of the truck.

b) In the back of the trailer, the packages were positioned
in the same way as described in Figure 12. Figure 11 shows

the instrumented packages located in the back LTL shipment.

 

t

Figure 9. Packages in the back (before testing)

Boxes A, B and C with accelerometers

Accelerometer 4

‘— ACtUBtOfS —--D

 

Figure 1 O. LTL shipment (front of trailer)

maandc

" with accelerometers

 

 

 

 

 

 

 

l —

+r-- .

_
—_

 

 

 

 

 

 

g2 Q Mamet“ 4

Figure 11 . LTL shipment (rear of trailer)

 

 

 

 

Box A Box 3 Box C

 

Actuators accelerometer 4

Figure 12. Positioning of instrumented packages in LTL shipment

24

Figures 10,11 and 12 also show the location of the control
accelerometer located underneath the truckbed during

different simulations.

4.0 DATA AND RESULTS

4.1 Vibrationwlnput:

Table 1 describes the location of the six recording channels
relative to their respective actuators and Table 2 shows
the statistics of the input drive signal amplitude. Refer to
Appendix A for a description of the terms used. The data
presents the mean, and maximum and minimum amplitude of each
actuator during the 350 seconds of run time. The average
distribution function of occurrences as a function of
actuator amplitudes (Figures 13 and 14) shows an

approximately normal Gaussian distribution.

Table 3 shows RMS stroke values determined for different
locations at frequencies that generated high RMS values.
Figures 15, 16 and 17 show the RMS stroke as a function of

the frequencies of actuators.

It is evident that the roadside of the trailer generally
produces larger maximum and minimum values for input
amplitudes than the curbside at high frequencies. We can say
in general that for this particular road, there were more

severe vibration levels for the roadside axle. A11 input

25

26

Table 1. Location of Recording Channels.

Channel Wheel
1 Roadside front axle
2 Roadside fifth wheel
3 Roadside rear axle
4 Curbside front wheel
5 Curbside fifth wheel
6 Curbside rear axle

.——--——-———-—-——————----———--—-—-———-——--——--_——————————-—_—
———-————————-—-——---n-c—u----—-————————--——_——--———-———--——-——.

———‘-————-—“———————--————-—————————--———-———_—-———-——-————-——
--—-———-————————-—-—————-----——-—-————_-—————-——-—-—-————--—

Channel Mean (u) Maximum Minimum Std Dev (0)
1 2.51E-04 1.62 -1.07 0.158
2 -6.37E-05 1.86 -1.34 0.181
3 3.39E-04 2.96 -1.66 0.159
4 -9.71E—04 1.33 -1.44 0.178
5 2.36E-04 1.22 —1.22 0.139

 

 

(I)

III

0

c

2 I

5 I

o

0 I

O I
I
I
I
I
I
I
l
p.

Amplitude (inches)
Figure 13. Normal distribution of input drive signal

9.00 -

8.10 —

7.20 —

9
to
O

I

5"
a
O

I

OCCURRENCESH 000
5.: a
a: or
o
I

 

 

0.00 -
-1.00 —0.80 -0.60 —0.40 —0.20 0.00 0.20 0.400.60 0.801.00

AMPLITUDE (inches)

Figure 1 4. Histogram of Input Drive Signal

28
Table 3. RMS Stroke Values Versus Frequency.

RMS stroke (inches)

Frequency __________________________________________________
(Hz)
Location Roadside Curbside Average

Front axle 0.075 0.091 0.083

1 Fifth wheel 0.084 0.062 0.068

Rear axle 0.060 0.063 0.062

Front axle 0.021 0.010 0.016

6 Fifth wheel 0.028 0.028 0.028

Rear axle 0.023 0.027 0.025

Front axle 0.006 0.005 0.006

12 Fifth wheel 0.009 0.005 0.007
Rear axle 0.009 0 007 0.008

Front axle 0.005 0.003 0.004

18 Fifth wheel 0.008 0.004 0 007
Rear axle 0.006 0.003 0.005

Front axle 0.004 0 002 0 003

24 Fifth wheel 0.003 0.003 0 003
Rear axle 0.004 0.002 0.003

Front axle 0. 0. 0.
30 Fifth wheel 0.002 0.002 0.002
Rear axle 0 0 0

—------_——-—-—--—--—--—---—--———————————_————---_-—-——————_—
~—-—-——~-———.-————_——————————~————--——a———~—————-———————-——-——-—~"—

o o
8 8

.0
O
u

RMS STROKE (inches)

.9
O
to

9
o
‘

Figure 15.

9
8

° 9
0
w

RMS STROKE (inches)
.0 .o o
8 8

.°
2

Figure 1 6.

RMS Strohenncheei

Figure 1 7.

p
8

O
O
0

p
2

9
O
u

i

 

 

p
M_ l

A l
O 5 10 ‘IS 20 25 so 35 00 45 50

Frequency (Hz)

Front axle: Average between curb and roadsides
front axle of RMS stroke (inches) as a function of
frequency

V

.
1

8-02

 

l 1 A A
0 s 10 Is 20 as 30 as no as so
Frequency (Hz)

Fifth wheel: Average between curb and roadsides
fifth wheel of RMS stroke (inches) as a function of
frequency

W 5-0:

 

 

 

Frequency(Hz)
Rear axle: Average between curb and roadsides
rear axle of RMS stroke in inches as a function of
frequency

30

functions for displacement amplitudes are very close when

compared to each other.

For the rear axle, the numbers of occurrences for both
wheels are also very close to one another (Table 2). Maximum
amplitudes however do vary for each location. Comparing
values of RMS stroke for the input at the fifth wheel and at
the rear axle we observe that they are very similar. In
general all inputs at different locations are similar
because similar wheels were used for both axles and the

distances between them were equal.

In general, the average input stroke to the different
actuator varies between 0.14 and 0.18 inches, but isolated

strokes as high as 3 inches were measured.

4.2 Truckbediibration:

Table 4 shows the vibration response of the truckbed due to

the effect of the actuator input described in section 4.1.

According to Table 4, the maximum and minimum accelerations
exceeded 1 g for both the fifth wheel and the rear axle
which means that anything not hard mounted to the floor is
very likely to bounce. Values of RMS acceleration at
different frequencies and peak accelerations are presented

in Table 5.

31
Table 4. Truckbed G Levels for Front and Rear.

Position Mean (u) Maximum Minimum Std. Dev. (0)
Front —6.33E-06 1.24 -1.34 0.201
Rear 8.26E-05 2.40 —3.11 0.292

Table 5. Peak G Acceleration of the Floor (Truckbed) Versus
Frequency.

Frequency Location RMS Peak G
(Hz) acceleration (g) acceleration (g)

1 Front 0.008 0.0113

Rear 0.010 0.0141

6 Front 0.055 0.0778

Rear 0.100 0.1414

12 Front 0.020 0.0283

Rear 0.030 0.0424

18 Front 0.035 0.0495

Rear 0.025 0.0354

24 Front 0.018 0.0255

Rear 0 008 0.0113

30 Front 015 0.0212

32

Figures 18 and 19 show the behavior of RMS acceleration in

g’s as a function of the frequency of vibration at the

truckbed.

The acceleration level of maximum occurrence (average
acceleration level) at the truckbed is approximately zero
for both front and back of the trailer. It can also be
observed from Table 4 that“ 68% of the time, acceleration
levels are between -0.2 and + 0.2 g's for the front and
between -0.3 and +0.3 g's for the back of the truck.
However, acceleration levels between —0.6 and +0.6 g's for
the front and between —0.9 and +0.9 g’s for the back were
also measured. Maximum and minimum accelerations do exceed 1
g for both the fifth wheel and the rear axle, but occur
infrequently. These rare events however can generate damage

in packaged goods and should not be overlooked.

4 . 3 Package--.Resports. as:

The acceleration responses of the three instrumented
packages that were put on the top of the stacks are

presented in Table 6.

Figure 20 shows the truckbed vibration acceleration and the
responses for packages A, B and C at the front of the
trailer. Figure 21 shows the response for the packages at
the back of the trailer. The response curves of the

packages, especially at the back, show a skew distribution

RMS Acceleration (g’s)

RMS Acceleration (9’ s)

33

5-02

10

 

 

I I I l I l I I I

 

l
O 5 10 1 5 20 25 3O 35 40 45 50

Frequency(i-iz)

Figure 1 8. Truckbed RMS acceleration as a function of
frequency (front)

E-02

10

I

 

 

 

l I I I I I I I I J u H2)
0 5 1 O 1 5 20 25 30 35 4O 45 5O

Frequencyu-lz)

Figure 1 9. Truckbed RMS acceleration as a function of
frequency (rear)

 

34
Table 6. Output Acceleration (g) on Packages A, B and C.

Package Location Mean (u) Maximum Minimum Std. Dev. (0)

A Front —9 32E—05 1.47 —2 83 O 555
Rear 6 77E-05 1.48 -8 38 0.850
B Front -1 06E-O4 1.68 —5 57 O 508
Rear -6 33E-O5 1.98 —9 56 O 651
C Front 1.34E-O4 0 98 -2 06 0.326
Rear 5.96E-05 1 20 -4 31 0.435

35

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37

to the left, indicating the presence of decelerations

generated by repetitive impacts.

Table 7 .shows the values of RMS acceleration and peak
acceleration for the three different packages at the front

and at the rear.

Table 8 compares values of peak acceleration of the truckbed
and. of the jpackages at the top showing relative

Magnification Factors.

The data shows vibration isolation at high frequencies as
expected. See Appendix B for a description of vibration
magnification and isolation. At frequencies higher than 30

Hz, all three packages show Magnification Factors below 1.0.

4. 4 R,a,n.d0m...¥ibration.=

A broad band Random Vibration input signal was also used to
simulate over-the-road vibration for 600 seconds. Frequency
response functions were developed between the various
locations in the truck and the packages to the input signal.
Table 9 shows the FRF between the three axles (front, fifth
wheel and rear) to the floor at the rear. Table 10 shows the
values of Magnification Factors for the packages A, B and C
due to the input acceleration at the rear of the truckbed.
Table 11 shows Magnification Factors at different forcing

frequencies.

38

Table 7. Packages RMS and Peak G Accelerations Versus
Frequency.

_——-u—_—~———————..—_——_————-._-——-—_——————-—-——-——————————--~———-

(Hz) RMS Peak G
Pkg A Pkg B Pkg C Pkg A Pkg B Pkg C
1 Front 0.010 0.010 0.010 0.014 0.014 0.014
Rear 0.015 0.015 0.010 0.021 0.021 0.014
6 Front 0.320 0.265 0.145 0.453 0.375 0.205
Rear 0.350 0.295 0.192 0.495 0.417 0.272
12 Front 0.048 0.060 0.032 0.068 0.085 0.045
Rear 0.075 0.055 0.032 0.106 0.078 0.045
18 Front 0.025 0.032 0.020 0.035 0.045 0.028
Rear 0.025 0.032 0.020 0.035 0.045 0.028
24 Front 0 008 0 020 0 007 0 011 0 028 0.010
Rear 0.010 0.020 0.015 0 014 0.028 0.021
30 Front 0 005 0.010 0.005 0 007 0.014 0.007
Rear 0 008 0.015 0 008 0 011 0 021 0.011

39

Table 8. Relative Magnification Factor (from Truckbed to
Packages) Versus Frequency.

Relative Magnification Factor

 

Frequency Location
(Hz)
Package A Package B Package C

1 Front 1.25 1.25 1.25
Rear 1.50 1.50 1.00
6 Front 5.81 4.82 2.64
Rear 3.50 2.95 1.92
12 Front 2.40 3.00 1.60
Rear 2.50 1.83 1.07
18 Front 0.72 0.92 0.57
Rear 0.99 1.28 0.80
24 Front 0.44 1 11 0.39
Rear 1.24 2 21 1.86
30 Front 0.33 0 66 0.33
Rear '0.78 1 49 0.78

----—----——_————-——————---—-——"——--———_—-—_-——_--_---_—-—--—
——-————*—I—su—-—-ea—-—~————_————-———‘n—-———————-—-—-----—u——~h——-—-h

 

40

Maximum FRF Between Actuators Stroke and the Floor

Acceleration at the Rear.

0.7 0.7 0.70 2.0 2.5 2.25 2.6 2.2 .40
1.2 1.2 1.20 1.8 1.8 1.80 2.3 2.2 2.25
2.7 1.2 1.95 2.1 2.8 2.45 3.3 5.1 4.20
2 8 2 2 2 50 3.7 3 8 3 75 5.8 6 8 6.30
3 2 2 9 3.05 5 2 4.1 4 65 6.0 7 4 6.70
5 2 3 5 4 35 3 3 4.2 3 75 8.2 7 8 8.00
5 1 3 4 4.25 4 2 4.5 4 35 6.7 7 5 7.10

Table 9.
Freq
(Hz)

0 5
5 10

10 15

15 20

20 25

25 30

30 35

35 40

4O 45

45 50

C01 (1):

Col (2):

Col (3):

Col (4):

Col (5):

Col (6):

Col (a):

C01 (b):

C01 (0):

FRF between the roadside front axle actuator stroke
(input) and floor acceleration at the rear of the
trailer (output).

FRF between the curbside front axle actuator stroke
(input) and floor acceleration at the rear of the
trailer (output).

FRF between the roadside fifth wheel actuator
stroke (input) and floor acceleration at the rear
of the trailer (output).

FRF between the curbside fifth wheel actuator
stroke (input) and floor acceleration at the rear
of the trailer (output).

FRF between the roadside rear axle actuator stroke
(input) and floor acceleration at the rear of the
trailer (output).

FRF between the curbside rear axle actuator stroke
(input) and floor acceleration at the rear of the
trailer (output).

Average of columns 1 and 2.
Average of columns 3 and 4.
Average of columns 5 and 6.

41

Table 10. Magnification Factor of Acceleration in Packages
A, B and C Due to the Acceleration at the Rear Truckbed,
Based on Random Vibration.

-—___—_———-..--———--—.————--———-——_——————__—————_———-———-———-——

Frequency Magnification Factor
(Hz) ______________________________________________
Pkg A Pkg B Pkg C
0 0 1 0 1.0 1 0
2 5 1.2 1 2 1 2
5 0 3 7 2.1 2 0
7 5 1 7 2.5 2 7
10.0 0.6 1.5 1.0
12.5 0.5 1.0 0.4
15.0 0.4 0.8 0.3
17.5 0.4 0.7 0.3
20.0 0.3 0.6 0.3
22.5 0.2 0.5 0.3
25.0 0.1 0.4 0.2
27 5 0.1 0 3 0 1

42

Table 11. Values and Frequencies of Peak Magnification
Factor for the Three Different Packages.

m—~~——‘*—————————-——————n~e—————_a—_-——.-.—v-—e—fl—~*~~nmg———u*~~—~“*——*~m—fl

Package Peak M Frequency (Hz)
A 3.9 6
B 2.7 7

——————————-—-—--————————————_————-———-———.——-—-—————--—-—————
~‘--~—_—-—c—u—--Ie--‘—u—-—-I———r--—-———e————-—pu—-——u-——¢—-——-———————-—-———

5.0 CONCLUSIONS AND RECOMMENDATIONS

This study concludes the following:

1) For the same input at the axles, the response at the back
truckbed of the trailer is 50% larger than that at the front
(Figures 18 and 19). The average Magnification Factor from
the input at the wheels to the truckbed is 2 for the front

and 3 for the back for this truck.

2) Acceleration levels around 1.5 g's for the products are
very common in LTL shipments. However, levels as high as 10
g’s were recorded indicating severe bouncing. This shows
that when testing for LTL shipments it may be important to
conduct repetitive shock testing to check survivability of

the product.

3) It cannot be generalized from LTL shipment data that one
position. is 'better than another inside the truck.
Magnification Factors (between the truckbed and the
packages) between 0.4 and 6.0 are present both at the front

and at the back.

43

44

4) Low natural frequency packages have in general larger
Magnification Factors, showing more bouncing in LTL
shipments because the stacks exhibit resonance around 6 - 7
Hz, but the Magnification Factor does not vary in much when
comparing packages at the top of the same stack. This is
because the multiple degree of freedom system formed by the
stack itself and the instrumented package at the top have
almost the same fundamental mode, with very little
difference. (Table 11 shows that the peak Magnification
Factors occur around 6 - 7 Hz indicating this to be the

resonant frequency of the whole stack).

5) Roadside cnr curbside locations input little difference

along the same axle.

6) Low natural frequency packages (below 10 Hz) show more
bouncing and larger accelerations than high natural
frequency packages (Figures 20 and 21). The number of
impacts with small package acceleration generally increases
with the natural frequency of the package. This shows that
packages with high natural frequencies move less than
packages with low natural frequencies because resonance of
the truckbed occurs at low frequencies. This causes higher
magnification to low natural frequency packages in LTL

shipments.

45

7) Low natural frequency packages have a broader
distribution for the response acceleration levels than high
natural frequency packages. Package responses do not show
normal Gaussian distribution. Instead they are skew to the
negative accelerations. Large negative values for
acceleration (deceleration) are caused when the package

impacts the stack.

8) The front axle and the fifth wheel also contribute with
the input. to the rear truckbed. Based. on ‘the 'Frequency
Response Functions (FRF) determined (Table 9) it can be seen
that the front axle contributes about 20% of the vibration
input to the rear truckbed. Similarly the fifth wheel
contributes about 30%. The remainder (50%) is due to the
input from the rear axle. The FRF's were determined by
measuring the response at the rear of truckbed due to the
individual axles. This was obtained by holding the two other
axles fixed, giving a known input to the axle being studied

and measuring the response.

APPENDICES

APPENDIX A

STATISTICAL CONCEPTS

All phenomena described In; mathematical functions relating
several variables are said to be deterministic which simply
means that a given set of conditions produces a different
result. As an example is the mathematical relationship
between speed, distance and time, v = d/t. Non deterministic
phenomena cannot be characterized by a mathematical function
because of inherent uncertainties in one or more casual
factors which affect the outcome. An example is the tossing
of a coin. The case of vibration in the transportation
environment is another example of a non deterministic
phenomena because of the many factors such as road
conditions, truck suspension characteristics, driver
quality, and traffic situations which cannot be accounted
for exactly. Since any of the above conditions are likely to
change at any time, any data gathered from non deterministic
phenomena of this type are described by random time

functions.

46

47

A random time function, such as the time history' of a
vibration signal, despite: its apparent irregularity' when
graphed, shows a certain degree of statistical constancy.
Because of its random nature, no single parameter is enough
to characterize the whole phenomena. Therefore, averaging
procedures are applied to identify important governing
characteristics of the phenomena. Consider for example the
time function x(t) which represents the acceleration of an
object due to vibration over the time interval t = 0 to

t : T where T is called the period of the signal.

Some important averaging statistics related.1x> this signal
are given below. For each case, the general definition for a
random signal will be given and the definition will then be
applied to the special case of a half sine wave of amplitude
A and period T described by the expression:

x(t) = A sin (mt/T)

Refer to Figures 22 and 23 for a graphical representation.

X(t) ll

................................. PEAK

............................................ RMS
... ................. .... . ......... AVERAGE

 

 

Figure 22. Random Signal

48

 

x(t) A
................................... PEAK
. .......................................... RMS
........................................ AVERAGE
OL‘ T WMMM,1 t

 

 

Figure 23. Half Sine wave

Peakwnyalue: Generally indicates the maximum acceleration
that the vibrating part experiences over the period of the

signal. For the sine wave, the peak value is A.

Ayersgeworwexpectedmyalue: Over the duration of the signal,

the average acceleration is defined to be:

-m_m_ T
x(t) = E[x(t)] : (1/T) J x(t)dt
0
For the sine wave:
WWW”. T
x(t) = (l/T) J A sin(nt/T)dt : (2/n)A
0

MeanmSQuarchaluei This statistic provides a measurement of

the energy of vibration.

.-m-1---m-lm- T'
[X(t)]2 = E[X2(t)] = (1/T) J X2(t)dt
0

 

49

For the sine wave:

[x(t)]2 = (l/T) j Azsin2(nt/T)dt : A=/2

0
Yariance;.This statistic is a measure of the spread in data
about the mean value.
02 : (1/T) (x - x)2dt : x2 - (x)2
0

For the sine wave:

02 = (1/2 - 4/1t2)A2 : 0.0947 A2

Root MeaanquarethMSl; This is the square root of the mean

square value.

 

RMS = [Mean Square Value

For the sine wave:
RMS acceleration : A2/2 = 0.707 A

StandardeeyiatiQn: This is the average deviation from the

mean value.

 

o : “£3 - (;)2

For the sine wave: 0 = 0.308 A
Gaussfmeistnibutioni The distribution of accelerations
measured during transportation over time has an

approximately normal distribution. The probability of
measuring an acceleration between the limits x and x+dx,
where dx is small is:

1

P(x) : ----- exp(-x2/202)dx
0 2n

50

Frequency.....-.Domain.._._-Rep.r_esexitat. 10.11;- This is the most common
method of representing the characteristics of random
vibration. Every random signal may over a suitably chosen
time period T be represented as a superposition of pure sine
waves each with its own amplitude and frequency. The process
of obtaining these component sine waves is known as Fourier
decomposition. The random signal x(t) over the duration T
may then be represented in graphical form as component sine
wave amplitude versus corresponding frequency. In general,
this frequency domain representation exhibits strong
contributions from certain frequencies and only minor

contributions from others.

BDSm;WPpwermDensitymSpectrumg,The Fourier representation of
a complex waveform decomposed into simple sine waves is an
exact description of the real waveform only over the time
interval T. One of the characteristics of random vibration
however is that the complex waveform does not repeat itself
exactly for each successive period T. Therefore, an
alternate but related procedure is used. A complex waveform
is first fed into an electronic bandpass filter which
electronically extracts from the signal the component sine
waves present within a narrow band (BW) of frequencies. Over
a long period of time, accelerations are sampled and from n
samples, the RMS acceleration is determined. The power

density is then calculated according to:

51

2(RMSi)2
i
PD : ———————————

n * BW
PD 2 Power Density (gz/Hz)
RMSi : RMS acceleration value (g)
n 2 Number of instants sampled
BW : Bandwidth (usually normalized to 1 Hz)

A Power Density Spectrum shows the values of Power Density

as a function of frequency.

APPENDIX B

TRANSPORTATION CONCEPTS

In statistical terms, the power density at any given
frequency is the variance about a mean value of zero
acceleration. Therefore, based on the probabilities
associated with the normal Gaussian distribution, we may
predict the acceleration levels associated with any of the

component frequencies of the complex waveform.

Accelerations of i 1 PD values occur 68.3 % of time
(interval from -o to +0); accelerations of i 2 PD values
occur 95.4 % of time (interval from —20 to +20);
accelerations of i 3 PD values occur 99.7 % of time

(interval from ~30 to +30). (Brandenburg, 1985)

It is commonly accepted that the worst vertical acceleration

of a truck ride is about 0.5 g for low frequencies.

(Brandenburg, 1985)

52

53

When considering trucks and trailers. there are three major
vibration modes. Following the terminology accepted by

Tevelow (1983), these modes are:

1)Bounce: oscillation resulting in a up and down motion.
2)Bit§hingi creates rocking motion, longitudinal or side to
side.

3)Exame,Mb.e,nd_ingmgo,r,__b,eaming_;_ describes the flexure of the
vehicle body such that the ends of the frame are moving up
and down, at the same time and same direction while the

center goes to opposite direction.

Bounce and pitching are rigid body motions and bending is

not.

Magnificatiganactcr; (Also called Transmissibility) is the
ratio of dynamic output to dynamic input of a vibration

system.

Output acceleration Output stroke

Input acceleration Input stroke

When the damping in the system is negligible, the

theoretical magnification factor is:

where r : Frequency ratio = f/fn with f the input vibration

frequency and fa the natural frequency of the object being

54

vibrated. It is clear from above that when r = 1, M goes to
infinity. This is the point where the system experiences
resonance. When r is several times greater than 1, M is
insignificant, and the system reaches vibration isolation.
For values of r between 0 and 1 the system is said to
vibrate "in-phase" (same direction of oscillation for both
input and output) and for values of r greater than 1 it is
said to vibrate ”out-of—phase" (opposite, directions of
oscillation) . Figure 24 shows a graph of the Magnification

Factor M versus r, which is the ratio of forcing to natural

 

 

frequency.
RESONANCE

|M| A i

I
IN-PHASE I OUT-OF-PHASE

1
1
E

1 l E VIBRATION
l ISOLATION
i a»

0 r<1 I r>1 r
r=1

 

Figure 24. Magnification Factor

LIST OF REFERENCES

K

American President Companies,

LIST OF REFERENCES

Characteristicsifitudy. Equipment Engineering.

3; Brandenburg, R. K. anui Lee, J.J.L, Fundaments of

Dynamics, MTS Systems Corporation, 1985.

“i Carus

a; ,
I I .
.. . ,.

a.
v
I ,r

f

l

\

.-

1|.

Foley

Foley

f Frueh

ngoff,

Goodw

\Grier

g;Harri

Ma nu

~ i
J
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o, H., and W. Silver, Advances in Shipping Damage

Prevention, Shock and Vibration Bulletin 46,
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J. T. PreliminarxJnalysi s....if..Data...Q.b:t.ained..in--ihe
J 0i nt-.:___Army.2AE .C/ Sandie. ...T-est ....... 0. f“...- ..T nuck........_T ran an art

Enyironment, Shock and Vibration Bulletin 35,
1966. .

a 1.

DoublesStackAIruckAYesseleide.

Dec.1986.

Packaging

Part 4,

Partv5,

. J T TheJnxircnmenthaeri enceLbr.mG argoona

Flatbed ...-......Trac 12.01:. ...Trailer_____.9_0mbina Lion .
Laboratories, SC-RR—66-677,1966. , r \wX

~.. U" ,
kx‘i zfifihi‘b _.W_’_/

Sandie

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1988.

J.W.; Grebe, J.; Twede, D. and Townsend, T.

. You-1-1.

Nelmfieew-I.L_Emm-_lhe..-Rcad. Technical Report 1* 26.
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in, D. L. and Holland, R. R. ShockmmandMWYibration
Dynamic 6...- .013... intermodal...- Distributim. Environment.-- _
Tra-iler.-_Qn.-.a-E.l.at._Qar....-.Q0ntainer.-.In-..a.-..lrl.e-ll_-.C.ar. . 1 9 8 7.

J. H. Macleod, N. J. Fisher, F. R. and L.
Joint-... Schummghwaxw Shock.--I nd exflProj set.

S. Marr,
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Traffic Management Command, 75— 17, 1975, AD 850571.

8. C . M. . and C. E. Crede. Sheski-andlihrat.ion...__Handb-on.

Vol. 3, Mc Graw Hill Book Company, NY, 1961.

son. C. F. . Shock-maMihraticniEnyircnmentammr__Lar.ge

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SandiawLabgratoriesI.SANDYZzlllQpel977.

55

(Part 1),

56

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Pichler, E.F , Embalagem e Aoondicionamento para

Transporte-_--..-_-.e.-....Exportaeag. Instituto de Pesquisas
Tecnologicas, SP, Brazil, 1984.

S C: h 1 u e . J . W . . The.--D.xnam.i.c---Eny.ir Qnment.--o.£..5.p.as:.ecr.a£ t--.S.ux:f.ace.
Transpo r.t.a.t.i.on., Shggkwandi—V ibrat ion ~~Bul letin 3 5 . Part
5, 1966. "

Sharpe, W.N. , Jr. ; Kusza, T.J.; Sherman, F.W. , and J.C.
G0 f f . Preliminarymneasu rement----.a.nd----.An.a.has.15.11%

Yib.r.a.t-i.o.n.---E.nxirgnmentwp.f..--_.C.Qmem-MQ.t..QL_-gamers.. Shock
and Vibration Bulletin 44, Part 4, 1974. .11-

Teve low, F . L. , The-___mil.i.t.a.ry._.._.L.Qg.is.t.i.c.a.l....__I ransportatipn
Vib.ratioLWEnxirQnms-znt._;.........-......-I.t.s.1-....Qharac.t.e_riza_ti_o_n__.and
rel.ey.an.<3.e___to...-M.I.L:.SID..Euz.e--.Kihratiomleating . U . 8. Army
Electronics Research and Development Command, Mggggy
Qiam endlhabpratp r .i. as . 1 9 8 3 .

Thomsom, W.T., Theory of Vibration With Application, 3rd
Ed., Prentice Hall, 1988.

Turczyn, M.T.; Stevens, D.G., and Camp, T.H. , Shock__a_nsi

Y.ihration_Enxirgnmeni_in-.a._LixestQQk_Irailen. Smwd
Vibrationgfiglletin 50, Part 2, 91-101, 1980.