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thesis entitled ,

VIBRATION CONTROL IN "SMART" CANTILEVERED

BEAMS FEATURING FIBER—OPTIC SENSORS

presented by

Blane Patrick Hansknecht

has been accepted towards fulfillment
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VIBRATION CONTROL IN ’SMART’ CANTILEVERED
BEAMS FEATURING FIBER-OPTIC SENSORS

By

Blane Patrick Hansknecht

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

ABSTRACT

VIBRATION CONTROL IN ’SMART’ CANTILEVERED
BEAMS FEATURING FIBER-OPTIC SENSORS

Blane PatricBleansknecht

This thesis work focuses on the development of ’smart’ materials,
which have the capability to sense their environment and to respond so as to
optimize performance, using sensors and actuators incorporated into the
structure of the material itself.

A review of the field of fiber-optic sensors is presented. Both polarimetric
and interferometric fiber-optic sensors were investigated, and then imbedded
within carbon-epoxy composite laminates, using improved preservation methods
to protect the fiber sensors during the cure process. Standard, acrylate-coated
optical fibers were shown to be sufficiently durable for such use. Frequency
dependent phase shifts in polarimetric fiber-optic signals are characterized.

Research efforts involving actuators suitable for use in smart structures are
also reviewed. Both polymeric piezoelectric distributed actuators and electro-
rheological (ER) fluids were used to control vibrations in cantilevered beams
based on fiber-optic sensor signals. The reduction in the ER fluid effect with
increasing shear strain is described. The amplitudes of forced vibrations were
reduced by 80% at resonance with piezoelectric films, and by as much as 95%

over a span of frequencies using ER fluids.

ACKNOWLEDGMENTS

The author gratefully acknowledges the support and contributions of
Dr. M.V. Gandhi and Dr. B.S. Thompson, as well as Corning Glassworks

Inc. and Hercules Inc. for their donations of research materials.

iii

TABLE OF CONTENTS

1. LIST OF FIGURES, p. vi
II. NOMENCLATURE, p. viii

III. INTRODUCTION
A. ’Smart’ Materials, p. 1
B. Motivation for Work and Applications, p. 6
1. Why Smart Structures
2. Why Fiber-optic Sensors

IV. BODY OF THESIS
A. Background, p. 7

1. Fiber-optic Sensors
a. Strain
b. Damage and Fatigue
c. Pressure
(1. Temperature
e. Applications

2. Actuators
a. Piezo-electric Ceramics and Polymers
b. Electro-rheological Fluids
c. Shape Memory Metals
d. Magnetostrictive Materials
e. Applications

B. Principles of Light Waveguides, p. 11

1. Snell’s Law

2. Bend Losses

3. Birefringence

4. Polarization State

C. Interferometric Sensors and Light Interference Principles, p. 15
1. Mach-Zehnder
2. Michelson
D. Polarimetric Sensors and Principles of Operation, p. 21
1. Two-lead
2. Single-ended

iv

E. Procedure for Imbedding Fiber-Optic Sensors
in a Polymeric Composite Laminate, p. 25
1. Composite Manufacture Process
a. Lay-up
b. Curing
2. Imbedding Fiber-optic Sensors
a. Orientation
b. Protection
3. Effect of Curing on Performance
F. Actuators, p. 30
1. Piezo-Electric Films and Ceramics
a. Principles of Operation and Applications
b. Advantages vrs Drawbacks
2. Electro-Rheological (ER) Fluids
a. Principles of Operation and Applications
b. Advantages vrs Drawbacks
3. Shape Memory Metals, Magneto-Strictive
Materials, and Other Potential Actuators
a. Principles of Operation and Applications
b. Advantages vrs Drawbacks
G. Control Algorithms, p. 36
1. Phase-based for Piezo-Electric Actuators
2. Frequency-based for ER Fluid Actuators
3. Robust, Amplitude-based for ER Fluid Actuators
H. Experimental Program, p.39
1. Goals
2. Experimental Procedures
3. Results and Accomplishments

V. CONCLUSIONS, p. 49
VI. RECOMMENDATIONS, p. 51

VII. REFERENCES p. 53

LIST OF FIGURES

Figure 1: Light Propagation in Single- and Multi-Mode Optical Fibers.
Figure 2: Interference Fringe Patterns Falling On Slitted Photodiodes.
Figures 3-7: Frequency Dependent Phase Shift in F iber-Optic Signal:
A Comparison With the Signal of a Displacement Sensor
Located at the Beam Tip, For 16, 18.5, 25, 55, and 88.5 Hz.
Figure 8: Composite Lay-Up for Curing Process.
Figure 9: Imbedding Fiber-Optic Sensors in Polymeric Composite Laminates.
Figure 10: Fiber-Optic Sensor Imbedded in Carbon-Epoxy Composite Plate.
Figure 11: Imbedded Single-Ended Polarimetric Fiber-Optic Sensor Signal.
Figure 12: Photomicrograph of ER Fluid at 0.0 kV/mm and at 2.0 kV/mm.
Figure 13: ER Fluid Sandwich Beam Structure.

Figure 14: Frequency Response Curves of an ER Beam with 0.0 kV/mm vrs
2.0 kV/mm Applied Voltage.

Figure 15: ER Beam Frequency Shift and Damping Increase with Increasing
Applied Voltage.

Figures 16-18: Reduction in ER Fluid Effect with Increasing Magnitudes of
Vibration for 3.0 kV/mm, 2.0 kV/mm, and 1.0 kv/mm Applied
Voltages.

Figure 19: Robust Closed-Loop Control in an ER Fluid Beam by Amplitude
Scanning Over Several Voltage Levels.

Figure 20: Fiber-Optic Sensor Configurations.

vi

Figure 21:
Figure 22:

Figure 23:

Figure 24:

Figure 25:
Figure 26:

Figure 27:

Figure 28:

Figure 29:

Figure 30:
Figure 31:

Figure 32:

Mach-Zehnder Interferometric Fiber-Optic Sensor Optical Set-Up.
Polarimetric Fiber-Optic Sensor Optical Set-Up.

Idealized Interferometric Fiber-Optic Signal with Cantilever
Beam Tip Deflection.

Surface- Bonded and Imbedded Fiber-Optic Sensor Equipped
Carbon-Epoxy Composite Beams.

Smart Structure Experimental Set-up.

Photograph of Smart Structure Experimental Apparatus.
Comparison of Single-Ended Polarimetric Fiber-Optic Sensor
Signal with Non-Contacting Displacement Sensor at Beam Tip

for Small Excitation Amplitudes at Resonance (41.2 Hz).

Same as Figure 27, but Low-Pass on a Bandpass Filter Set to
110 Hz to Filter Noise from 120 Hz Overhead Lights.

Comparison of Frequency Response Curves Generated Using
Proximeter and Polarimetric Fiber-Optic Sensor Signals.

Phase-Based Control Algorithm Response to Tip Velocity Signal.
Forced Response as Phase-Based Closed-Loop Control Begins.

Normalized Vibration Amplitude vrs Excitation Frequency for
Comparison of Natural Response vrs Smart Structure Response.

vii

NOMENCLATURE

a ............. optical fiber core radius

Cs .......... strain-optic constant

d31 .......... piezo-electric strain constant

B ............ Young’s modulus

E0 ........... light wave amplitude

f .............. linear force

k. ............ spacial frequency, propagation constant
k0 .......... free space propagation constant

L. ........... length of fiber subject to stress

ni ............ index of refraction

Pij .......... strain-optical tensor componants

q ............ retardation of coupled light

r ............. optical fiber outer radius

R ............ bend radius in an optical fiber

(1 ............ profile parameter

[3 ............ birefringence

fix,By....propagation constants

Y ............ light loss from bends in a waveguide

6 ............ groove angle

A ............ index elevation

8 ............. initial phase angle of light

82 ........... extinction ratio of a polarizer

A. ........... wavelength of light

10 ........... free space wavelength

vp ........... Poisson’s ratio

8 ............. angle of polarization with respect to stress
61 ........... angle of incidence

62 ........... angle of reflection

w ............ polarizer transmission axis angle
(Indy ..... orthogonal radial components of applied stress
(1) ........... angular frequency of light, % of light coupled

between orthogonal polarization modes.

viii

INTRODUCTION

One traditional measure of the progress of humanity has been by the materials
they have used, thus the progression: stone age, iron age, bronze age. ’Smart’
materials represent a new generation following the synthetic materials age. They
are characterized by their ability to sense their environment and to react so as to
perform optimally for a given set of conditions. Class I smart materials are
passive, featuring a microsensor system, Class II smart materials are active,
with imbedded actuators in addition to imbedded sensors, and Class III smart
materials are intelligent, adding adaptive learning capabilities. Unless stated
to the contrary, any further references to ’smart’ materials or structures should
be understood to refer to Class II smart materials. This thesis brings together
research in fiber-optic sensors, their incorporation into polymeric composite
laminates, various actuators, and closed-loop control programs to produce
Class II smart materials.

The following section of this thesis reviews the fields of fiber-optic sensors
and of suitable actuators for use in smart materials. The next sections explain
the propagation of guided light and light interference principles, thus, how
interferometric fiber-optic sensors function. A model for polarimetric fiber-optic
is also presented. A procedure for imbedding fiber-optic sensors in polymeric
composite laminates is described. The characteristics,advantages, and drawbacks
of piezo-electric films, electrorheological fluids, and other potential actuators are
addressed. Finally, an experimental program uses these sensors and actuators,

with control algorithms, to reduce the amplitude of vibration in cantilevered

beams. The remainder of this introduction is devoted to a discussion of the
attributes and types of fiber-optic sensors.

The development of fiber-optic sensors has taken place almost entirely
in the last fifteen years, and their use in the area of smart materials is more
recent yet. Even so, fiber-optic sensors are already successfully competing
with conventional sensors. Fiber-optic sensors exhibit a number of advantages
over other sensors. They are extremely lightweight, therefore, less intrusive
than accelerometers, for example. Since the waveguide is dielectric, they are
immune to electromagnetic interference, and yet could still be used to detect
magnetic fields by coating the fiber with a magnetostrictive material. They can
also be used to detect temperature, pressure, strain and vibration. Vibration
control in large space structures is one case where fiber-optic sensors are
achieving success.

Perhaps the greatest advantage that fiber-optic sensors have for smart
structures applications is their ability to be imbedded directly in fibrous
polymeric composite materials. This enables the monitoring of conditions
within the structure. The cure process can be optimized, and the fibers
can remain as life-long sensors protected by the structure around them.

Structural sensors are already used in high stress applications such as
military aircraft to warn pilots when the integrity of the plane is endangered
or compromised. The sensors used are typically strain gauges, which are

subject to debonding and can only detect strain or damage over a small

region. Fiber sensors, on the other hand, could be incorporated into the
structure of the plane and sense strain or damage over considerable lengths.

On commercial flights, this early damage detection would be an invaluable
safety feature for preventing crashes caused by fatigue failure, which inspection
crews can overlook, as occurred on the tragic Aloha flight in 1989.

The term ’fiber sensor’ used so far actually covers a number of optical
fiber-based sensor configurations including attenuation-based sensors,
polarimetric-based sensors, interferometric-based sensors, and sensors
relying on specialty fiber coatings; furthermore, each of the above sensor
categories consists of a number of subcategories. Other fiber sensors rely
on optical time-domain reflectometry, which detects backscattered light
from defects and environmental effects such as bending. The Pockels
effect may be used to introduce birefringence for measuring voltages.

Attenuation-based sensors typically rely on a physical mechanism of
some sort which induces microbending in the optical fiber when the structure
that the fiber is to monitor is disturbed. The microbends cut off an amount of
the light passing through the fiber in a manner analogous to pinching a
garden hose to stop the water from flowing. This method has the advantage
that since the only feature of interest in the light guided by the fiber is its
intensity, no laser is required. Less costly photodiodes, and inexpensive,
easy to handle multimode fibers may be used. The disadvantages of this method

are lower sensitivity than other methods, and the need for some means of

inducing the microbending, which is at odds with the smart materials
philosophy of incorporating the sensor within the structure it is to monitor.

A better smart materials approach using an attenuation-based sensor

has been proposedl, which imbeds a fiber in a composite material in order to
signal when the material has suffered serious fatigue or impact damage. The
fiber has its protective coating etched off at regular intervals so that its
failure strength approximates the failure strength of the material of which it is
a part. If the material is damaged, the fiber breaks, resulting in a noticeable
drop in the intensity of the light passing through the fiber. This application has
the advantages of the previous method without the disadvantages. It is
limited, though, by the fact that it is a one-time sensor designed only to
warn of impending failure. It cannot be used to monitor the structure or its
environment during normal use.

Polarimetric and interferometric fiber-optic sensors can be used to
measure the vibration, strain, and/or heat of the structure they are bonded to
or imbedded in, to allow self-actuated control of an intelligent structure in
response to the environment it senses. Because these sensors operate by
detecting changes in the phase or polarization state of light, not just the
intensity, they require a laser source and single-mode optical fiber. These
sensors are readily adaptable for imbedding in a composite structure and are
also more sensitive than attenuation-based sensors. Both of these sensors

will be discussed in greater detail in the body of this thesis.

There are, in addition, interferometric sensor configurations which were
not considered in the research of this thesis: Fabry-Perot, Sagnac, Bragg, and
modal interferometers. Fiber-optic Fabry-Perot sensors require sensitive splicing
techniques and are more fragile than other sensors. Modal interferometers

are less sensitive than other interferometers and require specialized fiber. An

excellent review of various fiber-optic sensors is given by Turner, et a12.
Experimental and postulated specialty coating fiber sensors operate
on the same general principal as one of the above sensors, except that the
modification of the light passing through the fiber is caused by coatings on the
fiber. For example, by coating a fiber with a magneto-strictive material, the
strength of magnetic fields can be detected: the field induces a contraction or
expansion of the magneto-strictive material, which strains the fiber, resulting
in a detectable modification of the light passing through the fiber. Similarly,
electric voltages could be detected by a fiber coated with a piezo-electric
polymer. Even various chemicals could be detected by coating the fibers
in a phosphorescing substance, and observing the intensity of light produced
by the coating (in the presence of certain chemicals) and transmitted through
the fiber. Since the fiber itself is glass, the sensor is chemically inert.
Other coatings, especially polyimides, are under study for protecting fibers
that are to be imbedded in composites. During the cure cycle, polyimide coated

fibers are subject to less loss of mass, and the lifetime of the polyimide-coated

fiber is greater than that of untreated fibers, according to R.O. Claus, et al3.

Motivation for Work and Applications

Why use smart structures?
- reacts to environmental stimuli without the need for human
intervention to achieve optimal state: minimize vibrations,
alter dimensions, change work path, etc.

Why use fiber-optic sensors in smart structures?
- lightweight
- very small
- inert, corrosion resistant
- can integrate measurements over a large area
- sensitive
- immune to electromagnetic interference
- multifunctional: databus compatible
- signal processing by integrated optics
- can be multiplexed
- no electrical or fire hazard
- suitable for imbedding in composites
- Applications:
- sense strain, vibration, temperature, and pressure
- measure magnetic and electric fields
- cure monitoring
- impact sensing
- thermal mapping
- monitor structural integrity
- damage detection
- fatigue life evaluation

A. BACKGROUND

The primary goal of this investigation is to imbed fiber-optic sensors into a
composite structure which incorporates actuators such as electro-rheological
fluids or piezo-electric polymeric films in order to form a "smart structure,"
a structure that reacts to the environment it senses in an autonomous
manner. Previous studies have developed the use of optical fiber in sensors,
and have imbedded the fibers in composites, but no work to date has used
the above in conjunction with suitable actuators and control algorithms to
produce an integrated self-actuating "smart structure". The actuators that
were used in this thesis work were piezo-electric polymeric thin films and
electro-rheological fluids. Other actuators suitable for "smart structures"
include piezo-electric ceramics, shape memory metals, and magnetostrictive

materials.

3:1 Fiber-Optic Sensors Background:
The field of fiber-optic sensors is extensive. R.M. Measures, R.D. Turner,
W. D. Hogg, et al, have published fiber-optic sensor papers on strain
detection4, damage detectionl, imbedded sensorss, and the merits and

drawbacks of the various classes of fiber-optic sensorsz. The earliest paper

that investigated imbedded fiber-optic sensors in polymeric composite

materials was done by S.Y. Field and K.H.G. Ashbee in 19726. Other authors

involved in researching strain detection include S.R. Waite, et 317, R. Rogowski,

et 318, and M. Martinellig. Waite, et al, are also active in detecting damage and
fatigue in composites with fiber-optic sensorslo. Pressure and temperature
sensing using fiber—optic sensors has been researched by GE. Hockerll, and
by N. Lagakos and J.A. Buccarolz, and R.W. Griffiths”. Bragg fiber-optic

sensors have been developed by G. Meltz, W.W. Morey and W.H. Glenn”.

The use of fiber-optic sensing of vibrations is treated in a paper by Spillmanls.

In the area of fiber coatings there are papers on a spectrum of potential

applications, from how coatings affect microbending losses, by ER. Urruti
and J.F. Wahll6, to luminescent coated fibers for chemical sensing, by

K. Liu, et a1”. Claus, et al, are also investigating coatings for imbedded

fiber-optic sensors, for the purpose of protecting the sensor during cure and

extending the lifetime of the fiber".

In this thesis work, several varieties of fiber-optic sensors were
investigated, including a Mach-Zehnder interferometric sensor, a Michelson
interferometric sensor, a polarimetric sensor, and a single-ended variation of
the polarimetric sensor. Each of these will be discussed in detail in the body
of the thesis, with regard to both technical explanation and suitability for
meeting the chief purpose of this thesis work.

Ego-Electric Actuators Background:

Several papers by ER Crawley, et al, investigate the use of piezo-

ceramics as actuatorsls'zo. Crawley used piezoceramics to induce strain in

beams to control structural deformations to verify the analytical models that
he developed. Pennwalt Company’s Kynar Piezo FilmTechnical Manual is a

valuable information source on the characteristics of polymeric piezo-electric

films21.

Vibration control is addressed in papers by J.E. Hubbard Jr. and T. Bailey 22,

by Ikegami, et a123, and by A. Baz and S. Pohz". These papers considered
optimal actuator positions, distributed-parameter actuator and control models,
and bonding layer effects for minimizing vibration amplitudes in cantilevered

beams with piezo-electric actuators.

Electro-Rheological Fluids Background:
The primary published work in electro-rheological fluids is in the papers
by M.V. Gandhi and BS. Thompson25'26. A mathematical model for a

cantilevered beam with a viscoelastic layer (as used in the experiments

by Gandhi and Thompson) can be found in a paper by CT. Sun, et a1”. So far,
however, no model exists which also includes the electro-rheological fluid

characteristics.

Other Suitable Actu_ators:
Magnetostrictive materials are being manufactured by companies such as
Edge Technologies and work in a manner analogous to piezoelectric materials,
except the strain is induced by a magnetic field instead of by a voltage field.

Like piezoceramics, magnetostrictive materials are brittle, however, there are

10

less safety concerns since high voltages are not needed.

Shape-Memory alloys are metals that return to a preset, trained shape
from whatever deformed state they are in, as described by material data from
Memory Metals Incorporated, for example. Use of shape-memory metals

as both actuators and sensors has been conducted by authors such as

C.A. Rogers28 and R. Ikegami, et 3123.

B. Principles of Light Waveguides

Optical fibers consist of a very thin core of glass, surrounded by a
cladding of a glass with a slightly lower index of refraction. This fiber is
typically protected further by an acrylate or a polyimide coating, and often
one or more of these fibers are contained within a multi-layered jacket. The
only essential parts for guiding light, however, are the core and the cladding.

The light is guided along the core by internal reflection according to the

well-known Snell’s Law:
n1 * cos(91) = n2 * cos(92) ( 1 )
where n1 and n2 are the indices of refraction of the core and cladding,

and 61 and 92 are the angles of incidence and reflection, respectively.

The light entering the fiber must be within certain angles to pass along
the core. This is termed the Numerical aperture (NA) and varies depending
upon the geometry and material characteristics of the fiber. A multi-mode
fiber has a core large enough (typically 50—100 pm) to allows light to pass
along it in any of several paths. A single-mode fiber has a core small enough
(approximately 8 pm) that light can only travel along one path. This is shown
graphically in figure 1.

One can see from Snell’s Law that where there are bends in the fiber
the light guided along the core is more likely to pass into the cladding due to

the change in the angle at which the light interacts with the core-cladding

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interface. In multimode fibers, bends are sometimes introduced to exploit
this in order to strip higher order modes from the core. In single mode
fibers this loss is wavelength dependent, and may be expressed by
y=10Log[RA(0t+2)/(20t*a)], (2)

where R is the bend radius (several centimeters or less), a is a profile
parameter, A is the index elevation, and a is the core radius.

There are two possible orthogonal polarization states for light passing
through a single-mode fiber. Polarized light may be coupled to the single
mode fiber in a way that excites both polarization states equally. A single
mode fiber with a perfectly circular cross-section will have light propagate
equally in both of these orthogonal modes. If, however, the fiber were
ellipsoid in cross-section instead, the light along one mode would
propagate at a different speed than the light in the other mode, on account of
the difference in path lengths between them. The difference between the effective
refractive indices of these two modes is the birefringence of the fiber. In addition,
the birefringence can be introduced due to perturbations to the fiber, because
strain will alter the fiber cross-sectional geometry. The amount of birefringence
introduced is dependant on the manner in which strain is coupled to the fiber.

For a fiber between two plates, a linear force, f, will introduce a birefringence

[3f=4CSf/(ItrE), (3)

14

where r is the fiber outer radius, E its Young’s modulus, and

C5=0-5kon03(P11'P12X1'Up)-

Here, n() is the average fiber refractive index, “Up is Poisson’s ratio,
p11 and p12 are strain-optical tensor components of the fiber, and k0 = 2.11 / M,

and M is the free Space wavelength.

When forces are distributed over the surface of the fiber instead of point
loading, however, as is the case for fibers imbedded in fibrous composites,
equation (3) may be errant by up to a factor of 8 / It.

For an optical fiber that runs parallel to the fiber direction of the two
composite prepreg plys it is sandwiched between, a more appropriate model

may be that of a fiber pressed into a V-groove of angle 26

flv=2Csf(1-cos25 sin25)/(JtrE). (4)

Equasions (3) through (4) can be found in a paper by SC. Rashlieghzg. An
optical fiber running orthogonally to the fiber direction of the prepreg plys
will experience a series of small kinks, and so will have still a different
birefringence. From this, it is obvious that the birefringence introduced into
a fiber-optic sensor imbedded in a composite structure will vary with the
orientation of the sensor with respect to the adjacent ply fiber directions.

An ideal fiber without flaws such as elliptical or varying cross-section,
material point defects, varying index of refraction, or bends and twists in the

fiber will maintain the initial polarization state introduced to the fiber. Real

15

fibers have imperfections that result in coupling between the two orthogonal
modes. Coupling fiom one polarized mode to the other completely will occur if a

perturbation matches the criterion

IB.-p,|=k+Ak,
where k is the spatial frequency of the perturbation along the length of the
fiber, Ak is the spatial frequency of the length of the fiber, and fix , By are
the propagation constants of the two orthogonal modes. Thus, changes in any
perturbations to the fiber will result in changes in the polarization state of the
light guided by the fiber. Energy is coupled from one mode to another and

hence, the intensity of light passing along a particular mode will change.

C. Interferometric Sensors and Interference of Light Principles

The interference of light is a well established property. When two
coherent beams of light interact there results alternating regions of
constructive and destructive interference, leading to fringes of light and dark
bands, respectively. Beams are coherent if they propagate in step, although
they may be out of phase. This interference is described by the superposition
principle. Any changes in the phase of one beam relative to the other result in
a shift in the interference fiinges. A 180 degree change in the relative
difference in phase, for example, will result in a fringe Shift such that the
positions previously occupied by the dark fi'inges are now held by light fringes,
and vice versa. Since the wavelength of coherent sources is extremely short,
(633 nm for a Helium-Neon Laser, for example) the end result is that
extremely small changes in the relative phase can be observed by the Shift
in the macroscopic interference fringes. The interference of two waves is
treated in greater detail below.

The interference of light assumes that light has wave-like nature. A solution

to the differential wave equation has the form
E(x,t) = E0 sin[mt - (kx + 8)] (5)
where E0 is the amplitude of the light, (0 is its angular frequency, k is a

propagation constant, and 8 is an initial phase angle. When two such waves

occupy the same space, the resulting disturbance is a linear superposition of

16

17

the two

E = E01 sin[wt -(kx1 + 81)] + E02 sin[wt - (“2 + 82)] (6)

expanding:

E = E01(sin[wt] cos[kxl + 81] + cos[mt] sin[kxl + 81])
4- E02 (sin[wt] cos[kx2 + 82] + cos[mt] sin[kx2 + 82]) (7)

rearranging:

E = (E01 cos[kxl + 81] + E02 cos[kx2 + 82]) sin[mt]
+ (E01 sin[kxl + 81] + Em sin[kx2 + 82]) cos[wt] . (8)

Next, substitute E0 cos[kx + 8] for the terms in the first set of parentheses
in the above equation, and E0 sin[kx + 8] for the terms in the second set.
E0 cos[kx + E] = E01 cos[kxl + 81] + E02 cos[kx2 + 82] (9)

E0 sin[kx + 8] = E01 sin[kxl + 81] + E02 sin[kx2 + £2] (10)

This substitution is valid, provided the following expressions solving for E0

and [kx + 8] are met:
E0 45012 + E022 + 2 E01 E02 cos{k(X1-X2) + (21 422)] 11[2 (11)

and

E01 sin[kxl + £1] + E02 sin[kxz + 82]
(12)

[kx + 8] =tan'1
cos[kx + 8 ]+ cos[kx + 8
1 1 1 2 2 2

Equation (11) is obtained by squaring and adding equations (9) and (10), and
equation (12) is obtained by dividing equation (10) by equation (9). As long

as equations (11) and (12) are met for E0 and [kx + 8], the summation of the

18

two waves becomes

E = E0 cos[kx + 8] sin[mt] + Bo sin[kx + 8] cos[mt] (13)
or

E = E0 sin[wt + kx + 8] . (14)
A phase difference between the two waves may be introduced in two ways: by
the difference in the initial phase angles, or by a difference in the path length
traversed by the two waves. Coherent waves have 81 - 82 constant, and
equal if emitted in phase, as is the case for two beams from a single source. In
this case, the phase difference 5 is

9 = k("l-"2) = 2“ n("14(2) / 7‘0 (15)

where 10 is the free Space wavelength and n is the index of refraction of the
medium the waves are traveling through. From equation (11), it follows that
when 5 equals an even multiple of It the amplitude of the combined waves
will be at a maximum, and when 5 equals an odd multiple of It the amplitude
of the combined waves will be at a minimum. This is referred to as constructive
and destructive interference, respectively. Since the wavelength of the
source may be very small (633 nm for a HeNe laser, for example), very

minute changes between the path lengths can be detected by the resulting

shift in the fringes.

CI The Fiber-optic Mach-Zehnder Interferometer

Interferometric sensors exploit the principle of the interference of light.

19

Two coherent beams are formed, often by beam splitting. In a fiber-optic
Mach-Zehnder set-up, these beams are coupled into two single mode fibers,
called the reference arm and the sensing arm. Any strain on the fiber
waveguide results in a change in the length of the fiber and, hence, a change in
the path length of the light guided by the fiber. When the sensing arm
experiences strain not seen by the reference arm, there is a relative change in
path length of the light passing along the sensing arm with respect to the
reference arm. This results in a relative phase shift between the two guided
beams, which may be detected by combining the beams and observing the
shift in the fringe pattern. In a Mach-Zehnder this is accomplished by
superimposing the beams as they exit the fibers with the aid of a beam
splitting cube. The resulting fringe pattern falls on a Slitted photodiode, so that
unit-impulse-like signals may be obtained as each bright fringe shifts across
the face of the slit. To improve the strength of this signal, a multiple slit filter
was manufactured to cover the face of the photodiode, and this detector was
positioned such that fringes of the same kind were aligned with each slit

of the multiple slit array (see figure 2).

Since strain is defined as the change in length per unit length, it follows
that the change in path length for light passing through the sensing arm with
respect to the light guided by the reference arm will depend on the difference
between the lengths of these two arms subject to the strain. Hence a fiber-optic

interferometer can approximate point sensing when the difference between

 

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21

the arms is small, or the sensor can integrate the strain over large lengths by
increasing the difference in length between the arms, to the limit imposed by

the coherence length of the light source.

Q The Michelson Fiber-optic Interferometric Senior

The Michelson fiber-optic sensor differs from the Mach-Zehnder in that the
light does not simply exit through the opposite end of the fiber from which it was
coupled. Instead, that end is mirrored to reflect the light guided by the fiber
so the light travels back along the length of the fiber and is decoupled by the
same apparatus that initially coupled it to the fiber. This variation is more
elegant than the Mach-Zehnder since it reuses the coupling apparatus rather
than requiring such devices at both ends of the sensing fiber and the reference
fiber. Also, when imbedding the sensor in a composite structure, the Michelson
sensor requires only two leads, one for each arm of the interferometer, whereas
the Mach-Zehnder requires four, since the far end of the fibers must also be lead
out of the composite to recover the signal. For a cantilevered beam it is
desirable to have all the leads exit from the same end of the beam, so leads
exiting from the free end of the beam are not shaken wildly with the tip
deflections. For the Mach-Zehnder interferometer this requires the sensing and
reference arms to double back, producing twice the inter-ply disturbance to
the composite as the Michelson interferometer, as well as requiring a bend in
the arms of the sensor where they double back. This bend causes a loss in

signal strength since the increase in the angle of incidence of light guided by

22

the fiber results in the loss of some of the light to the cladding. In addition,
there is a minimum bend radius for optical fibers, typically of several
millimeters, therefor the Mach-Zehnder sensor has a minimum width requirement
that the Michelson sensor does not have. Finally, since the light guided in
the Michelson sensor travels the length of the fiber twice, the Michelson is
twice as sensitive as the Mach-lender for the same sensing length of fiber.
The only drawback to the Michelson sensor is the need to apply silver to one end
of the fiber, and this silver can be subject to debonding from the glass fiber.

As long as both arms of an interferometric fiber-optic sensor are subject
to the same disturbances (i.e. temperature changes, vibrations, etc.) in the
region away from the sensing region, the effects of the disturbance will be
negated, since light traveling in each arm will be modified identically. Thus,
there are no changes in the fringe pattern due to these effects, and the sensor is
said to be lead-insensitive. The sensing region is made sensitive by having the
length of the two arms different in the region. For a Mach-Zehnder
interferometer, a loop iS typically made by each arm, with one loop being larger
than the other. The Michelson interferometer, however, simply needs one arm

to be longer than the other since it is single-ended.

D. Polarimetric Sensors and Principles of Operation

Polarimetric sensors do not operate on the interference principles that the
interferometric sensors do. Instead, the polarization state of the light that
propagates along the fiber is the property that is of interest. Single mode
optical fiber allows two orthogonal polarization states to propagate
Simultaneously. In an ideal fiber the light carried by each mode throughout
the length of the fiber is the same as the light originally coupled into each of
the modes. However, when imperfections are introduced, due to strain on
the fiber, or non-uniformities in the material of the waveguide, for example,
light may be coupled from one mode to the other. The amount of light that
changes modes depends on the magnitude of the strain and the length of
the fiber subject to the strain.

In a polarimetric sensor, polarized light is coupled into a single mode
fiber, usually so both modes of the fiber are equally excited. The light exiting
the fiber is passed through a polarizer. A polarizer allows light to pass, but
only light whose electric field parallels the orientation of the polarizer. In other
words, only the component of polarized light that has the same orientation as
the polarizer is passed. Thus, the polarizer can be positioned so that it allows
the passage of all of the light from one of the two orthogonal modes of the fiber
and none of the light from the other mode. This allows a photodiode with the
polarizer to detect the change in energy in a mode as light couples in or out of

the mode due to strain on the fiber.

23

24

A model for a polarimetric sensor is presented below, as described by
Spillman and Klinels. Polarized light coupled into a fiber is expressed as
cos 9
Bit) = E0 ’ (16)
sin 9

where 9 is the angle of the polarization with respect to the stress on the

optical fiber. The fiber is modeled as a transformation matrix,
elm/3°05“) -ci(q/2)Sinw

[R] = e-i(q/2)sinw e-i(B/2)oosm ’ (17)
where q is the retardation of the coupled light, 0) is the percentage of light
coupled from on orthogonal polarization mode to the other, and fl is the phase
lag between the two. This phase difference is a function of the orthogonal
radial components of applied stress, 0x and 0y, the length of the fiber subject
to the stress, L, the wavelength of the light, 2», and the strain-optic constant,
Cs, as shown in the following equation:

B=Bo+2nLCs(ox-oy)/x. (18)

In the polarimetric sensor, light exiting the fiber passes through an

analyzing polarizer, which is modeled by

com}! sintp
[S] = , (19)
-8sin1p Econ]!
where 82 is the extinction ratio of the polarizer and 1p is the angle of its

transmission axis. Hence, the output light which falls on the photodiode can

be determined by

Eout = [S] [R] Em- (20)

25

For a polarimetric system where the input polarization angle and the
output polarizer angle are set to 45 degrees, assuming that the output light
is linearly polarized (8: 0) and there is no mode coupling ((0:0) results in
the following expression for the output power:

10m = .5 E02(1-cosj3) . (21)
Thus, the intensity of the light on the photodiode is a function of fl, which in
turn varies with the applied stresses on the optical fiber guiding the light.
Polarimetric sensors are not as sensitive as interferometric sensors. Also,
they are more difficult to localize. The leads can be made insensitive, however,
by using high-birefringent fiber spliced to the fiber in the sensing region".

The polarimetric sensors do hold advantages over interferometric sensors,
however. They do not require a sensing arm, so the number of leads is halved.
This reduces the handling required in assembling the fiber, lowers the chance of
damaging the sensor during manufacture and use, and lowers the intrusiveness
of the sensor when it is imbedded in polymeric composite structures. Like the
Michelson fiber-optic interferometric sensor, the end of a polarimetric sensor
can be mirrored, allowing for a single-ended configuration. This type of
polarimetric sensor only requires one lead. The sensitivity, although lower
than the highly sensitive interferometers, is sufficient for the purposes of
vibration control considered herein.

Finally, and most important from a controls point of view, the signal

is readily usable. The signal varies with strain integrated over the sensing

26

length. Thus, it varies with the displacement of the cantilevered beam,
differing only in phase. For large lengths of fiber subject to strain, however, it
is possible that some of the light coupled out of one polarization state could be
coupled back in; this could result in erroneous frequency values from the sensor,
although this effect was not observed in any of the experiments of this thesis. In
contrast to the polarimetric signal, the signal from an interferometric sensor
is a series of pulses whose fiequency is proportional to the rate of strain. This
requires a program to count the impulses and the spacing between them,
determine from the spacing the cycle length, and calculate the frequency. This
is a difficult task to do accurately, and very difficult to accomplish in the limited
time available for real-time control of vibration.

The polarimetric sensor is a distributed strain sensor - it integrates the
strain over its sensing length. This results in a frequency dependant phase
shift in the polarimetric signal. The polarimetric fiber-optic sensor accurately
measures the frequency of excitation of the structure it monitors, but the phase
of this signal varies between the phase of the acceleration and the phase of the
velocity, as Shown in figures 3-7. This is similar to the phase shift seen in
a displacement sensor signal of an oscillating cantilevered beam when the sensor
is moved from the tip of the beam towards the base of the beam. The phase

shift in the polarimetric sensor varies depending on the sensor length.

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E. Procedure for Imbedding Fiber-Optic Sensors
in a Polymeric Composite Laminate
E.1. Composite Manufacture Process

The composites used in the experiments described in this thesis were
manufactured from AS4 3501-6 prepreg donated by Hercules Inc. This is a
carbon-epoxy prepreg that was assembled by a hand lay-up method. The
first specimens were laid up [(0 / 90)3]s , while other lay-ups used included
[114 / -114]s , [164 / -164]s , and [214 / -214]s . Here, the numbers within the
brackets indicate the individual prepreg ply orientations within the laminate,
the subscripts indicate the number of consecutive plys in a particular orientation,
and the subscript s after the close bracket indicates that the plys within the
bracket are repeated in reverse order in order to assemble a laminate that
is symmetric about its midplane in the thickness direction.

The samples were assembled pending the curing process as shown in
figure 8. The cork walls surrounding the prepreg laminate are present to
prevent the flow of epoxy from the edges, which would result in a fiber volume
fraction that varied with the distance from the edges of the plate. The purpose
of the porous tefion is to allow the flow of epoxy from the laminate to the bleeder
cloth without the cloth becoming attached to the composite. This allows an
even distribution of the remaining epoxy across the cured laminate, although
it will vary somewhat through the thickness of the laminate. The clear release

film keeps the steel plates clean and unattached to the composite material.

32

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This assembly was then placed in a vacuum bag, which was evacuated
and placed into a heat press. The heat press cured the composite plate
at (240 F, 85 psi) for one hour after which the evacuation was stopped, and
then at (350 F, 100 psi) for two more hours, as per the manufacturer’s cure
specifications. The cured composite was then allowed two to four hours to
gradually lose pressure and cool to avoid damage due to thermal shock. The

composite plate was then sectioned into beams using a diamond blade saw.

E.2. Imbedding Fiber-Om: Sensors

Care is required when imbedding fiber-optic sensors in a polymeric
composite laminate because the fibers are apt to break, particularly where the
fiber exits the composite. Also, a fiber coated by the matrix epoxy becomes
brittle and prone to break.

Several steps were taken to protect the fibers. Two lead out methods were
tried: in the first the fiber was lead out of the composite through a pinhole in the
top ply of the laminate a few centimeters from the edge of the laminate, while
in the second the fiber was lead directly out the edge of the laminate. The
first method worked as long as the fiber-optic sensor was imbedded
underneath the top one or two plys of the laminate only. Deeper positions
resulted in sharper bends in the fiber, which resulted in the fiber being broken

when exposed to cure pressures; a more gradual exit angle than a direct

35

normal to the laminate surface would alleviate this difficulty. The second
method (leading the fiber strait out the edge of the composite) was preferred,
since it introduced no unnecessary strains on the sensor during the cure

of the composite. When the fiber was imbedded near the center of the
composite plate (in the thickness direction) rather than the edge, a slice was
made in the cork wall so the fiber would not have to bend around it. The slice
was sealed with tacky tape to prevent the flow of epoxy through the rift. Most
of the sensors were imbedded only one or two plys from the upper surface

of the composite, however. This was to take advantage of the greater bend
radius away from the neutral axis of the laminate, in order to maximize the
strain on the fiber due to bending, so the sensor would be more sensitive.

The polymeric composite Specimens were laid up [(0 / 90)3]s , [114 / -114]S ,
[164 / -164]S , and [214 / -214]S . The fiber-optic sensors were oriented in the
zero degree direction in all these cases, so the direction of the sensor varied
with respect to the direction of the carbon fibers in the prepreg plys adjacent to
the sensor. The sensors functioned in each case. The sensitivity of each
sensor varied so much with variables such as how well the laser light was
coupled with the optical fiber, that it was difficult to ascertain what affect the
orientation of the sensor with respect to the prepreg fiber angle had, if any.

Two further precautions taken to improve the survivability of the fiber-
optic sensors are shown in figure 9. First, Kapton film was placed around the

fiber for stress relief in the region where it exited the composite. Second, the

 

 

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37

fiber of each sensor in a laminate was lead out an individual pinhole in the
vacuum bag, leaving only to inches or so of fiber inside the vacuum bag but
not within the laminate. The fibers were lead out individually, because when
they were lead out a common hole, the leads inside the vacuum bag would

lie on top of one another, and when cure pressures were applied the overlapping
fibers broke each other. The exit pinholes were sealed with tacky tape to
preserve the integrity of the vacuum bag. Finally, the portion of the fiber-optic
sensor within the vacuum bag, but not within the laminate, was protected

from embrittlement by the epoxy and other handling stresses by a coating of
general purpose silicone sealant. This was accomplished by applying the
silicone along approximately two inches of the fiber, starting from the end of
the length of the sensor intending to be imbedded, and letting it cure. After
the sensor was sandwiched between the plys of a laminate, the fiber leads
were drawn out through a pinhole in the vacuum bag, before the vacuum bag
was sealed. The fiber was drawn through until stopped by the silicone coated
portion of the lead, and then the pinhole was sealed with tacky tape, which
also held the fiber in position. Only then was the vacuum bag sealed and the
cure begun. A carbon-epoxy composite plate made with imbedded fiber-optic

sensors is shown in figure 10.

E.3. The Effect of Curing on the Fiber-Optic Sergor Performance
The length of fiber protected by the silicone showed some discoloration

after the cure. The acrylate coating of the optical fiber turned brown due to the

 

Figure 10: Fiber-Optic Sn-nwr Imbedded in ("urban—Epoxy Contpmih- PlJlL‘

38

39

heat present in the curing process. The only portion of the fibers thus affected
was the length where the silicone sealant protecting the fiber was thin. Where
the silicone coating surrounded the fiber there appeared no damage. The
fiber within the composite material appeared unharmed as well. This was
ascertained by removing a portion of one fiber from within the composite
and observing it. This portion could be removed because the Kapton film
prevented the bonding of the fiber to the composite roughly one centimeter
in from the edge of the laminate. Although there was discoloration on some
of the imbedded sensors, the sensors still functioned. This indicates that the
core and cladding were undamaged, which is a reasonable result, since glass
has a much higher melting temperature than the acrylate coating.

The signal strength of the imbedded fiber-optic sensor was less than
its surface-bonded counterpart. Again, other variables such as the coupling
efficiency affect this, but the cure process did seem to increase the attenuation
of light passing through the sensor. Nevertheless, a signal sufficiently strong
for the control algorithm to utilize was obtainable from an imbedded,
single-ended, polarimetric fiber-optic sensor in a [114 / -114]Slaid-up

carbon-epoxy cantilevered beam (figure 11).

 

Figure ll: Imbedded Single-Ended Polarimetric Fiber-Optic Sensor Signal

40

F. Actuators
It is important in a smart structure that the actuators are an integral part
of the structure itself. Rather than motors with moving parts, a smart structure
actuator is a more reliable, no maintenance solid state material, preferably with

low power requirements.

F.1. Piezo-Electric Films and Ceramics

Piezo-electric materials produce an electrical charge when they are
deformed, and conversely undergo a change in dimension when exposed to
an electric field. This occurs because deformations change the volume of the
material, and this results in a change in the net charge distribution within the
film from the dipole properties of the film. The effect is a capacitive one, so
induced charges will decay over time. In addition, the material is anisotropic,
with the dipole alignment set by poling during the manufacture of the material.

There are two classes of piezoelectric materials: ceramics (such as BaTiO3)

and polymeric films (polyvinylidene fluoride). The ceramics are stronger electro-
mechanical transmitters than the films and can operate at higher temperatures,

but they are also brittle and more massive. The advantages of the films are
impressive: a dynamic range from 10'8 to 106 psi, a frequency range from

.005 to 109 Hz, a maximum voltage field of 75V/ttm, and a voltage output (for
sensing applications) an order of magnitude greater than the ceramic output
for the same applied force. Also, the film is tough, flexible, lightweight,

moisture insensitive, chemically inert, and inexpensive.

41

42

The stress-free ratio of strain developed to applied field is shown by the
piezoelectric strain constant d. The form of this constant which is of greatest

interest is d31, where the 3 indicates that the axis of the applied electrical

field is in the thickness direction of the piezoelectric material, and the 1 identifies

the axis of induced mechanical strain (or applied stress) as being in the length

direction. For a piezoelectric film, d31 is approximately 23x10'12 C/N, while d31

is 78x10'12 C/N for BaTiO3 piezoceramic, and 110x10'12 C/N for PZT, a lead

zirconate titanate piezoceramic. Thus, the amount of strain developed along

the length of a beam with a piezoelectric actuator is d31 times the field

applied normal to the thickness of the beam. A ceramic produces greater strain
than the film for the same applied field, however, the dielectric strength of the
film (the dielectric strength is the maximum voltage per thickness that the
material can stand without a breakdown in its piezoelectric properties) is 70

times greater than the dielectric strength of piezoceramics”.

Piezoelectric materials have been used extensively in the past in a variety
of fields. Some devices exploiting the piezoelectric effect include sonar
transmitters and receivers, robotic tactile sensors, switches, microphones,
audio Speakers, and fiber-optic modulators.

Both ceramic and polymeric piezoelectric materials can be used in a smart
structure as sensors or actuators of strain. While ceramics have been imbedded
in polymeric composites in experiments, their size and brittleness limits the

strength and compliance of the structure they are incorporated in. Piezoelectric

43

films, on the other hand, are incapable of surviving the composite cure
temperatures, but can be bonded between pre-cured laminates or can be surface
bonded to a structure. Their presence has a much more benign influence on

structures. Also, the use of a distributed actuator such as a piezo-electric

film theoretically allows all modes to be controlled”.

L; Electro-Rheological (ER) Fluids
Electro-rheological fluids consist of polar particulates in a non-conductive
suspension. The dipole associated with the particles may by inherent to the
particle, as in a zeolitic ER fluid, or may be due to molecules of water which
are bound to the particles, as in a starch based ER fluid. These particles have
random positions and orientations within the suspension initially, but in the
presence of a voltage field, the particles form chains as shown in figure 12. This

results in a change in the viscosity of the fluid. Furthermore, the ER fluid can

respond to voltage changes as rapid as 11 kH225.

This effect is utilized by incorporating the ER fluid in a sandwich beam
structure (see figure 13). The upper and lower plates act as electrodes, and so
must be either made of a conductive material, or coated so as to be conductive.
The rubber seal around the sides insulates the electrodes from one another so
a voltage field may be applied and also serves to maintain the integrity of the
structure, scaling in the ER fluid. Although voltages as high as 34 kV per mm
between the electrodes are required, very little power is actually drawn

because ER fluids are activated by a voltage field, so negligible current (about

 

Figure 12: Photomicrograph of ER Fluid at 0.0 kV/mm and at 2.0 kV/mm

44

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45

46

10 uA/cmz) flows between the electrodes.

In practice, when the beam is affixed in a cantilevered fashion, the
activation of the ER fluid has two effects: the natural frequencies of the beam
are raised due to the stiffening effect of the particulate chains, and the internal
damping is increased due to the additional energy dissipation necessary to
deform or break the chains. This is shown in figure 14. The magnitude of these
two effects is dependant on the strength of the applied voltage field, up to a
maximum achievable effect (figure 15). Both of these effects can be combined
to reduce the amplitude of vibrations in the beam for a given applied excitation
of the beam. The magnitude of the fiequency shift is, however, dependant on the
magnitude of the shear strain that the beam experiences. Larger shear strains
exceed the yield stress of the chains, and when the chains are broken they have
no stiffening effect. There is still a damping increase when the beam deformation
is large because the chain structures continuously reform and energy is
dissipated to break them. This vibration amplitude dependence for three
voltage levels can be seen in the frequency response curves of figures 16-18.

F.3. Shape Memory Metals, Magneto-Strictive
Materials, and Other Potential Actuators
In addition to ER fluids and piezoelectric materials, potential classes

of actuators for smart materials include shape-memory alloys and magneto-

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strictive materials.

Shape memory metals can be trained to ‘remember’ a certain shape or
configuration, such as a spring trained to remember an extended position, or
a wire trained as a semicircular curve. When the device is heated beyond a

preset critical temperature, it returns to its trained shape, regardless of how

it has been deformed (up to strains as high as 8%“). Thus, the heated
spring will expand to its remembered position, and the deformed wire will
return to its curved configuration. Were similar wires to be incorporated
in a composite structure, it would allow the structure to alter its shape or
dimensions as required.

The earliest shape memory metals were NiTi alloys developed at the
Naval Ordinance Laboratory in the 1960’s, but since then better copper-based
memory metals have been engineered. These metals may be heated by joule
heating, or by external heating elements. Unfortunately, the response time of
these materials is not fast enough for their use in active vibration reduction except
for low frequency vibrations. Experimental work has been performed on low

frequency vibration reduction in shape memory metal reinforced composite

23

cantilevered beams and in mode alteration by shape memory metals

incorporated in composite panels for the purpose of noise reduction”.

Magneto-strictive materials are very much like piezo electric materials,
except they change their dimensions when subjected to a magnetic field

instead of a voltage field. Like piezo-electric ceramics, magneto-strictive

53

materials are brittle. Because they are so weak in tension, magneto-strictive
actuators usually need to be operated in compression. When compressed the
material is less susceptible to breakage and in addition produces significantly
more output. The magneto-strictive material has an order of magnitude greater

output than a piezoceramic material, up to approximately 2,000 parts per

million”. Unfortunately, the hardware required to keep the actuator in
compression detracts from its appeal for smart material applications.

More ductile alloys exhibiting magneto-strictive properties do exist,
however, these are typically much weaker actuators.

Since magneto-strictive materials are activated by a magnetic field, the
dangers of a high voltage field are eliminated. The magnetic field is typically
induced by current passing through a wire coil around the actuator. The need
for this coil is an additional drawback when considering magneto-strictive
materials as potential smart actuators, especially in comparison to the simple,

low-mass sputtered metal electrodes required by piezoelectric actuators.

G. Control Algorithms

One of the requirements of a Class II smart material is the ability to send
appropriate control signals to the actuators of the structure based on the
input signals received from the sensors of the structure. This calls for a
control algorithm, which is ultimately to be encoded on a single chip within
the structure. For experimental research and development purposes, however,

a programmable personal computer with digital-to-analog signal processing
capabilities is more appropriate and versatile.

There are many possible control algorithms, from a look-up table approach
to adaptive neural networks, and the advance of control intelligence is what
will advance Class H smart materials into Class III smart materials once the
imbedded actuator and sensor challenges are answered. The control method
chosen will depend on the actual actuating system or systems present. In this
thesis work, three control approaches were considered: two for use with beams
with ER fluids and one for beams with piezoelectric actuators. These programs
do not feature the most advanced control theories, but are adequately efiicient
for the demonstration of significant vibration reduction in smart structures.

The first method of control for ER fluid equipped beams uses a look-up
table based on the frequency response curves of the beam at various voltages. The
program calculates the frequency at which the beam is vibrating, and then applies
the correct voltage, which results in the lowest amplitude of vibration at that

particular frequency. If the excitation frequency shifts to a value where a different

54

55

voltage will reduce the magnitude of the vibration, the program will output that
new voltage level. Thus, the bottommost curve of the various frequency
response curves in figure 15 is followed. The program determines the correct
voltage level to output for a given frequency by consulting a look-up table. Each
particular beam must be characterized by specific frequency response curves at
various voltage levels in order to set the correct values in the look-up table

in the program for that beam.

The second control program for ER fluid equipped beams is a more robust
version of the first in that the beam need not be characterized nor the program
adjusted prior to its use. This program scans the beam by applying different
voltage levels in steps from zero to a specified maximum voltage and finds
the voltage at which the vibrational amplitude of the beam is at a minimum. It
keeps that voltage level applied until a change in the amplitude is detected,
corresponding to a change in the forcing parameters, whereupon it initiates the
scanning sequence again (see figure 19). Although this program will minimize
the vibration levels in a beam of unknown characteristics, it does not reduce
vibrations as quickly as the first control program when the forcing frequency
is altered because the scan sequence requires a finite amount of time at each
voltage increment for the beam to respond, so that an accurate assessment of
the optimal voltage level for minimum vibration amplitudes may be found.

A different control method is necessary for beams equipped with piezo-

electric actuators. These beams do not reduce vibrations by shifting the

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natural frequencies of the beam away from the excitation frequency as ER
fluid equipped beams do, but rather reduce vibration by forcing the beam in
opposition to the perturbing force. This requires an algorithm that will have
the piezoelectric film (or ceramic) actuate at the same frequency as the sensed
excitation frequency but out of phase with the beam velocity.

This algorithm does not work well with distributed polarimetric fiber-optic
sensors because of the frequency dependent phase shift associated with them.
Possibly a look-up table and output delay loop could be used to correct for the
lag, but this is a cumbersome solution. In the case where the polarimetric
fiber-optic sensor has a sensing length such that the signal is close to
180 degrees opposed to the velocity signal at the fundamental frequency,
then this closed-100p control can dramatically reduce forced vibrations at this
resonance. Note, however, that this frequency dependant phase shift is of
no concern for the control of ER fluid equipped beams where phase information
is not required, only the frequency. It is also important to point out that the
fiber-optic sensors need no insulation from the high voltage fields present in
ER beams because the optical fibers do not conduct electricity. Therefore, no
special precautions need to be taken to protect the sensing and signal processing
equipment, which is not the case for strain gauges and most other conventional

SCDSOI'S.

H. Experimental Program
M
The experimental program goals included the development and comparison
of interferometric and polarimetric fiber-optic sensors (including single-ended
leads and imbedded variations), the assembly and characterization of ER fluid
and piezoelectric actuator equipped beams, and the integration of the above
sensors and actuators with control algorithms for the purpose of vibration

reduction in prototype Class 11 smart materials.

H.2. Experimental Procedures

The configurations of the various sensors on cantilevered beams are shown
in figure 20, while the optical set-ups for the interferometric and polarimetric
fiber-optic sensors are shown in figures 21 and 22, respectively. Note in
figure 20 that the Mach-Zehnder interferometer has two fiber loops bonded to
the beam. The shorter loop is the reference arm of the interferometer. It is
positioned adjacent to the sensing arm in order that the leads both experience
the same perturbations. This makes the leads insensitive, leaving only the
additional length of the sensing arm sensitive to strain. For this reason, this
configuration was chosen over the separate arm configuration of figure 21. To
integrate the strain over a length instead of only at a point, it is only necessary
to increase the length of the sensing loop with respect to the reference loop,
up to the limit imposed by the coherence length of the laser (typically on the

order of 25 cm for HeNe lasers).

58

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A variety of optical fibers were used in manufacturing the various
sensors, but Corning Flexcor single-mode fiber #50633.126 with CPC3 coating
was used more than any other kind of fiber. The CPC3 coating is an acrylate
coating with a 250 um outer diameter. The acrylate coating does not withstand
cure temperatures as well as special polyimide coatings, but it was found
that the sensors with the acrylate coating imbedded within carbon-epoxy
laminae still functioned adequately after undergoing the cure process.

None of the imbedded sensors survived the cure process intact before the
protective measures described previously were taken. Of the fibers imbedded
with protective measures, roughly 75% were functional. The dysfunctional
fibers were for the most part those fibers exhibiting coating damage due to
an incomplete coating of silicone sealant.

To ensure coherence in the interferometric sensors, light from a single
Helium-Neon laser source is split via a beam-splitting cube into two beams
with (nearly) half the power each of the source beam. The light is coupled into
the single-mode optical fiber arms of the interferometer using two Newport
M-F-lOlS Precision Single Mode Fiber Couplers. The light emitted from the
exiting end of the two fibers is recombined using a second beam-splitting cube.
The ends of the fibers must be aligned in order to obtain the optical fringes
formed by the interference of the two exit beams. The fringe pattern falls on
a slit in front of photodiode, so that an impulse signal is obtained as each bright

fringe shifts across the face of the slit. To improve the strength of this signal, a

63

multiple slit filter was manufactured to cover the face of the photodiode and
positioned so that fringes of the same kind were aligned with each slit of the
multiple slit array (see figure 2). Thus, as the fringes shift, several bright
fringes align with the slits and shine onto the photodiode instead of only
one. This results in a signal similar to the one in figure 23.

As an improvement on this sensor, a Michelson interferometric sensor
was developed by silvering the ends of the fibers used as the arms of the
interferometer. This reduced the complexity of the sensor in three ways. First,
only two leads into the sensing region are required, so the amount of fiber needed

is reduced, the potential for breakage is lowered, and there is less intrusion to
the structure. Second, no loops are now required for the leads to enter the
beam from the same end, so the required width of the sensor is drastically
reduced, and there is no more light loss due to the bend. Third, the reflected
light exits out the same apparatus which originally coupled it through the fourth
side of the beam-splitting cube; and so the alignment for obtaining fringes is
automatically accomplished, and one less beam-splitting cube is needed.

When the Michelson sensor was surface-bonded to a cantilevered beam,
three fibers were positioned with different lengths. This was to allow any two
of the leads to be used as a Michelson interferometer, in case any one of the
leads was defective in some way. If all three leads worked properly, then the
three different combinations would allow for comparisons of fringe patterns and

sensor sensitivity between sensors with different sensing lengths.

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Both of the above interferometric sensors produced fringes, and with the
aforementioned slitted photodiode discernible signals were received. For the
purpose of real-time control of vibrations, however, the signals produced by
the interferometric sensors were not readily useful. The number of fringes
passing by a slit is proportional to the magnitude of the strain, while the rate
at which the fringes pass is proportional to the rate of strain. A control program
would need to find the beginning and end of a cycle from the relative spacing
between the fringes, then calculate the frequency from the number of fringes in
the cycle and the length of time of the cycle. Unfortunately, this spacing varies
with strain and rate of strain. This would be a diflicult task to accomplish in
real-time.

In contrast, the signal from a polarimetric fiber-optic sensor is a sinusoidal
response with the same frequency as the forcing frequency, resulting in a
signal easily used by control algorithms. The polarimetric sensor, although
less sensitive than the interferometric sensor, did produce a signal sufficiently
clear for use. For these two reasons, the research into interferometric fiber-optic
sensors for vibrational control purposes was dropped in favor of polarimetric
fiber-optic sensors. Figure 24 shows one carbon-epoxy composite beam with
two surface-bonded single-ended polarimetric fiber-optic sensors (top), and
two carbon-epoxy composite beams with imbedded single-ended polarimetric
fiber-optic sensors. All surface-bonded fiber-optic sensors were attached to
aluminium or carbon-epoxy composite beams using a commercial superglue.

Beams with piezo-electric film actuators were assembled by adhering the

 

Figure 24: Surface- Bonded and Imbedded Fiber-Optic Sensor Equipped
Carbon-Epoxy Composite Beams.

66

67

actuator to the beam with a commercial superglue. The silvered portions of the
actuators were 15.5 cm long, not counting the leads, and 19 mm wide, but the
film itself was 1.5 mm wider along each side than the electrodes. Each actuator
was positioned so that the end with the leads was approximately one centimeter
from where the clamp held each beam. Piezo-electric actuators were used on
both aluminum beams and carbon-epoxy composite beams. These beams, as
well as the ER fluid beams, were insulated from the clamping fixture to avoid
grounding high voltages into the Ling Dynamic Shaker.

Both hydrophilic and hydrophobic electro-rheological fluids were mixed
for incorporation into beams. A variety of particulate to fluid mass rations were
mixed in each case. Although both varieties exhibited changes in viscosity
with voltage, those beams incorporating hydrophilic ER fluids exhibited
superior breadths of performance, and the results presented in this thesis are
from hydrophilic ER fluid beams only.

The beams containing electro-rheological fluids consist of the fluid,
contained by a rubber seal sandwiched between two plates (fig 13). The
plates act as electrodes and must either be made of a conductive material
or coated with one. The beams used in this work had aluminum plates, although
carbon-epoxy composite plate beams had been investigated in previous
studies as well. The beams were assembled using RTV silicone for the
sealant. This manufacturing of ER beams follows the procedures described by

Gandhi, Thompson, and Choi in reference 25.

68

The optical experimental set-up for the polarimetric sensor equipped smart
beam is shown in figure 22, and the rest of the equipment is shown in figure 25
and pictured in figure 26. The ER fluid or piezo-electric film equipped
cantilevered beam is excited by the Ling Dynamic V411 Shaker, which is
controlled through a Hafler P500 Variable Amplifier by a Wavetek Model 275
Arbitrary Function Generator. The strain in the beam is coupled to the fiber
sensor. From the optical set-up, the photodiode signal is conditioned by a
Wavetek 432 Signal Filter and then converted into a digital signal by a
Keithley DAS-20 D/A Board as input for one of the control algorithms run on
a Zenith 2386-25 Personal Computer. The program control signal is converted
by the Keithley board and Amplified by a Trek 609C-6 Voltage Amplifier on
the way to activating the ER fluid or piezo-electric film to reduce vibrations in
the beam. An accelerometer signal conditioned by a B&K 2635 Charge
Amplifier and a displacement signal from a non-contacting Kaman KD-2400
Proximator are lead to a Hewlett-Packard 3S66OA Dynamic Signal Analyzer
for comparison with the fiber-optic sensor signal. These two sensors are also
used with the signal analyzer to obtain the frequency response curves
required by the look-up table control program. The results are plotted using

the HP Colorpro Plotter.

H.3. Results and Accomplishments
Throughout the experiments, several interesting phenomena were

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71

polarimetric fiber-optic sensor signal mentioned previously, and documented
in figures 3-7. Discussed earlier are the characteristics of an ER fluid
equipped beam. The beams experience an increase in their damping factor
and a shift in their natural frequencies when voltage is applied to the fluid
(see figure 14) as the voltage causes the suspended particles to align in

chains (fig 12). Furthermore, as shown in figures 16-18, the shift in the natural
frequencies of the beam with applied voltage is reduced by large shear strains.
Large strains in the beam break the particulate chains of the ER fluid resulting
in the negation of the stiffening effect of the fluid on the beam. The damping,
though, remains higher in an activated beam even when large strains are
present because of the additional energy loss required to continuously break
the particulate chains.

In figures 27 and 28 the signal from a single-ended surface-bonded
polarimetric fiber-optic sensor is compared with the displacement signal from
a non-contacting displacement sensor located at the tip of a 19.5 cm long
cantilevered carbon-epoxy composite beam which is being forced at its first
fundamental natural frequency (41.2 Hz) with a tip displacement of 1 mm. In
the first figure, the Wavetek model 432 Signal Filter only acts as a DC cut-off
and signal gain. While in the second figure, the filter low-pass is set to
110 Hz. The improvement in the signal arises from the elimination of the noise
from the overhead lights, which operate at 120 Hz. This source of noise results

from the use of bulk optics in the experiment. The use of bulk beam splitters,

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couplers, etc., is convenient for laboratory use where a variety of optical
configurations are examined, but in practice these elements in smart
structures would be replaced by all fiber couplers, pigtailed sources, etc. Thus
ambient light noise terms will not be problematic in applied fiber-optic sensor
systems. When the polarimetric fiber-optic sensor signal strength is small,
due to very small vibrations, inadequate coupling of light to the fiber, or other
reasons, the 60 Hz line noise in the support hardware can become significant
enough to warrant filtering out as well.

To show an alternative use for the polarimetric signal, the HP 35660A
Signal Analyzer was used to determine the frequency response curve of a
carbon-epoxy composite cantilevered beam using first a conventional
non-contacting displacement sensor located at the tip of the beam and then
the signal from a polarimetric fiber-optic sensor. The two results are shown
in figure 29. The vertical displacement of the fiber-optic sensor signal is an
indication that the relative strength of the signal is less than the proximeter
signal strength. The proximeter signal strength is a function of its proximity
to the vibrating surface and of the reflectivety of the surface, and so it is limited
to a location where the vibrating surface will not strike the proximeter but
close enough for a clear signal. The polarimetric fiber-optic sensor, on the
other hand, is located on or within the vibrating surface and so need not be
repositioned each time the magnitude of the vibration changes. The figure
clearly shows that the results using the fiber-optic sensor are as informative

as the results using the displacement sensor.

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Figure 30 is a photograph showing the beam tip velocity signal and the
phase-based control algorithm output in response to the signal. This control
is a ‘bang-bang’ actuation, where the actuator (in this case a piezo-electric
polymeric film) forces the beam it is bonded to in opposition to the actual
vibrational mode of the beam in order to reduce the magnitude of the vibration
of the beam. As mentioned previously, the phase relation between the
polarimetric fiber-optic sensor signal and the tip deflection varies depending
on the length of the sensor and the frequency of vibration. When this length is
adjusted so that it is nearly 180 degrees out of phase with the tip velocity of
the beam when the beam is excited at its fundamental frequency, the
polarimetric fiber-optic sensor can then be used for piezo-electric actuator
control of first mode forced vibrations, which are the most necessary to control
in cantilevered beams. As shown in figure 31, the magnitude of the forced
vibration is reduced by a factor of five using this method. The piezo-electric
film was operated at 750 V, well below its maximum operating voltage of 2 kV.

Scanning control of beams incorporating electro-rheological fluids works
on beams of unknown frequency characteristics by applying different voltage
levels long enough to ascertain whether the magnitude of vibrations is
improving or worsening in comparison with the other voltage levels, and then
settling on the best available voltage level until conditions worsen (due to a
change in the excitation frequency, for example). This is shown working in

figure 19.

 

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Better control is possible when beam characteristics are known, through
the use of a look-up table control approach. The frequency response curves in
figure 14 show the change in the magnitude of the vibration of the beam with
the change in the forcing frequency for an ER beam at 0.0 kV/mm and the
same beam at 2.0 kV/mm. From the figure, it can be seen that the vibration
will be less when the voltage is at 2.0 kV/mm when the forcing frequency is
less than 24 Hz, but between 24 Hz and 124 Hz the magnitude is less with
0.0 kV/mm, and so on. Intermediate voltage levels can lower the vibration
magnitude at narrow frequency bands (as evident from figure 15) but compared
to the ‘on/off’ method any improvements are only incremental.

The results of using the look-up table approach with ER fluid equipped
beams are presented in bar graph form in figure 32. This figure compares
the response of the beam with no applied voltage, constant gain voltage, and
closed-loop control using polarimetric fiber-optic sensors and, for comparison,
a non-contacting displacement sensor. The closed loop reduces the vibration
magnitude on the constant applied voltage by over 50% at some frequencies

and reduces the vibration magnitude over no applied voltage by over 95%.

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80

CONCLUSIONS

Based on the results presented in this thesis, a number of conclusions
may be drawn. Based on a review of the field, there is considerable research
involving a wide variety of fiber-optic sensors and their incorporation into
polymeric composite materials, but the description of methods undertaken to
protect fibers during the cure process has been scant. The methods described
herein represent a collection of and an improvement on the processes described
previously.

Another innovation was the design of a fixture with several slits to allow
several alike fringes to fall simultaneously upon a photodiode, which improved
the signal strength in Mach-Zehnder and Michelson interferometric fiber-optic
sensors.

Also, it was found that although standard, acrylate coated optical
fibers are less durable at withstanding the cure temperatures than polyimide
coated fibers, imbedded fiber-optic sensors composed of acrylate coated fibers
did still function after undergoing the cure process. Thus, although sensors
using specially coated fibers may have improved sensitivity and reduced
impact on the composite structure when imbedded, fiber-optic sensors with
standard coatings are suitable for imbedding in composite structures, as well
as being less expensive and more available at the present time.

Another finding of interest was the dependance of the phase of the

polarimetric sensor signal on the frequency of excitation of the beam the

81

82

sensor monitored. The phase offset differed for sensors of different lengths,
and as a result, the use of the polarimetric signal was difficult for phase-based
control methods. Also of interest was the reduction of the ER fluid effect with
increasing shear strain as vibration amplitudes increased.

In addition to fiber-optic sensor research, there are many publications
on the topic of vibration control with either ceramic or polymeric piezo-electric
actuators, as well as some research on other actuators, such as electro-rheological
fluids, shape memory alloys, and magnetostrictive materials. There have not,
however, been many publications that bring such actuators together with
fiber-optic sensors imbedded in polymeric composites and vibration control
algorithms. This accomplishment is the subject of this thesis, and it is hoped
that this will encourage further steps in the integration of diverse fields for
the development of smart structures.

Forced vibrations in a cantilever beam with ER fluid were reduced over
various forcing frequencies by as much as 95% using a surface-bonded
polarimetric fiber-optic signal to a controller utilizing a look-up table control
program. Similarly, forced vibrations at resonance in a carbon-epoxy beam
with an imbedded single-ended polarimetric sensor and surface-bonded

polymeric piezo-electric actuator were reduced by a factor of five.

RECOMMENDATIONS

There is much work yet to be done to bring the systems described
herein from the laboratory to practical applications in industry. One step
in this process is the extension of the technology to two dimensions, where
sensors and actuators are applied to to plates, for example. This involves
more complex control schemes, and actuator placement is more complicated
as well. This step is already in its initial stages of development by the
authors.

Another step in this process is the packaging of the ’smart structure’ as
a unit to allow installation by non-specialized personnel. This includes
the assembly of preformed panels or other structures, with the sensors and
sensors and actuators already incorporated. For example, the fiber sensors
can be imbedded with pigtailed ends, for a simple mechanical connection to
signal processing equipment.

Furthermore, the simple control algorithms used thus far could easily
be replaced by more efficient programs, and eventually even adaptive neural
networks could be used. Also, it would be best if the control software and
hardware could be incorporated onto a dedicated integrated microchip, once
specific control methods have been selected.

In addition, health monitoring of the structures may be accomplished with
networks of strength-tailored fibers in the same structure where vibration

control is accomplished. The initial research in this direction has already been

83

84

accomplishedl, but the health monitoring still needs to be tied in with
other smart materials aspects.

Also, research into cure monitoring needs to be further developed than
its current level in order to produce consistent, fully polymerized materials.
This cure monitoring of polymeric composites may be accomplished, at least in
part, with the same imbedded sensors which are to sense vibrational strains during
the structure’s post-cure service, although both pressure and temperature

require monitoring. This advance has been at least partially accomplished

according to the most recent issue of the NASA Tech Briefs”.
With these advancements and the research already accomplished the
age of smart materials is just ahead, where the structures we build begin to

look after themselves.

LIST OF REFERENCES

LIST OF REFERENCES

. Measures, R.M. "Fibre Optic Sensors - The Key to Smart Structures, "
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. Turner, R.D., T. Valis, W.D. Hogg, and RM. Measures. "Fiber-Optic
Strain Sensors for Smart Structures," Joumat of Intengent MateriaB,
Systems, art-{Structures Vol. 1, pp. 26-49, January (1990).

. Claus, R., C. DiFrancia, J.W. Hellgeth, and T.C. Ward. "Structure [Property
Correlations of Several Polyimide Optical Fiber Coatings for Embedding

in an Epoxy Matrix," flier Optic Smart Structures art-{561:5 II, pp. 505-12,
SPIE Vol. 1170 (1989).

. Hogg, W.D., R.D. Turner, and RM. Measures. "Polarimetric Fibre Optic
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. Valis, T., E. Tapanes, and RM. Measures. "Localized Fiber Optic Strain
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. Field, S.Y., and K.H.G. Ashbee. "Weathering of Fiber Reinforced Plastics:
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. Rogowski, R., M. Holben Jr., J. Heyman, and P. Sullivan. "A Method for
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. Martinelli, M., "The Dynamic Behavior of a Single-Mode Optical Fiber
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10. Waite, S.R. "Use of Embedded Optical Fibre for Early Fatigue Damage

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86

11. Hocker, G.B. "Fiber-Optic Sensing of Pressure and Temperature,"
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12. Lagakos, N ., and J.A. Bucaro. "Pressure Desensitization of Optical
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13. Griffiths, R.W., and G.W. Nelson. "Recent and Current Developments in
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14. Meltz, G., W.W. Morey, and W.H. Glenn. "Formation of Bragg Gratings

in Optical Fibers by a Transverse Holographic Method," Optics Letters,
14:823-825 (1989).

15. W.B. Spillman, Jr., and ER. Kline. "Fiber-Optic Vibration Sensors for
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16. Urruti, ER, and J.F. Wahl. "Coatings Affect Fiber Performance in Smart
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17. Liu, K., M. Digonnet, K. Fesler, B.Y. Kim, and HJ. Shaw. "Superflourescent
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18. Crawley, ER, and J. de Luis. "Use of Piezoelectric Actuators as Elements of
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20. Crawley, et al. "Development of Piezoceramic Technology for Applications
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21. Kynar Technical Manual, Pennwalt Corporation.

22. J.E. Hubbard, Jr., and T. Bailey. "Distributed Piezoelectric-Polymer Active
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W, Vol. 8, pp. 605-11 (1985).

23. Ikegami, R., D.G. Wilson, J.R. Anderson, and GI. Julien. "Active Vibration
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87

24. Baz, A., and S. Poh. "Performance of an Active Control System with Piezo-
electric Actuators," JoumanfSoun-{muf’Vifir-ttion, 126(2), pp. 327-43 (1988).

25. Gandhi, M.V., B.S. Thompson, and SB. Choi. "A New Generation of
Innovative Ultra-Advanced Intelligent Composite Materials Featuring
Electro-Rheological Fluids: An Experimental Investigation," Jouma! of
Composite Meter-ids, Vol. 23, pp. 1232-55 (1989).

26. Gandhi, M.V., and BS. Thompson. "A New Generation of Ultra-Advanced
Intelligent Composite Materials Featuring Electra-Rheological Fluids,"
Intelligent Materials and Structures Laboratory, Michigan State University.

27. Sun, C.T., B.V. Sankar, and VS. Rao. "Damping and Vibration Control of
Unidirectional Composite Laminates Using Add-On Viscoelastic
Materials," JoumafofSounJanJ'l/ifimtion, 139(2), pp. 277-87 (1990).

28. Rogers, C.A., C.R. Fuller, and C. Liang. "Active Control of Sound Radiation
from Panels Using Embedded Shape Memory Alloy Fibers," JournaI of
SoundmtJ'J/ifimtton, 136(1), pp. 164-70 (1990).

29. Rashleigh, S.C. "Origins and Control of Polarization Effects in Single-Mode
Fibers, " Jaw-rut! of Lyfitw-we Teclinotogy, Vol. LT-l, No. 2, pp. 312-31,
June (1983).

30. Burke, SE, and Hubbard, J .E. Jr. "Distributed Parameter Control Design
for Vibrating Beams Using Generalized Functions," Charles Stark Draper
Laboratory, Cambridge, MA.

31. Memory Metals informational booklet, Memory Metals Inc., 1985.

32. Rogers, C.A. "Novel Design Concepts Utilizing Shape Memory Alloy
Reinforced Composites, " TroceeJi-vgs of tfie American Society for
Composites, Third Technical Conference, Seattle, WA, pp. 719-31 (1988).

33. NASA Tech Briefs, p. 66 January (1990).

1.

10.

11.

Genergl References

Allard, F.C., ed. Fiber Optics Handbook For Epgineemnd Scientists,
New York, McGraw-I-Iill Publishing Co. (1990).

 

Daly, J.C., ed. Fiber Optics, Florida, CRC Press, Inc. (1984).
Hecht, E. thics, Massachusetts, Addison-Wesley Publishing Co. (1987).

Waite, SR, and G.N. Sage. "The Failure of Optical Fibres Embedded in
Composite Materials, " Composites, pp.288-94, July (1988).

. Wiencko, J .A., R.O. Claus, and RE. Rogers. "Embedded Optical Fiber

Sensors for Intelligent Aerospace Structures," Sensors 3?" Troceed'irys,
pp. 257-62 (1987).

Paipetis, SA, and P. Grootenhuis. "The Dynamic Properties of Fibre
Reinforced Viscoelastic Composites," Fiber Science and Technology,
Vol 12, pp. 353-76 (1979).

Application Manual for the Design of Etrema Terfenol-Dtm Magnetostrictive
Transducers, Edge Technologies, Inc., prepared by J .L. Butler (1988).

Kashyap, R., and BK. N ayar. "An All Single-Mode Fiber Michelson
Interferometer Sensor," Joanna! of Lylitw-we ‘I’ecfitwbgy, Vol. LT-l, No. 4,
December (1983).

Thompson, B.S., C.Y. Lee, and M.V. Gandhi, Intelligent Materials and
Structures Laboratory research results.

Claus, R.O., B.S. Jackson, and KD. Bennett. "Non Destructive Testing
of Composite Materials by OTDR in Imbedded Optical Fibres,"
Troceed'bgs, STII: Int. Synposiwn, San Diego, August (1985).

Rogers, A]. "Distributed Optical-Fibre Sensors," Journal of Tliysics I):
flppEe-I’Pliysics, Vol. 19, pp. 2237-55 (1986).

IES

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