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Showing papers on "Piezoelectric motor published in 1994"


Book
27 Jan 1994
TL;DR: The ultrasonic motor, invented in 1980, utilizes the piezoelectric effect in the ultrasonic frequency range to provide the motive force as mentioned in this paper, which has already found applications in camera autofocus mechanisms, medical equipment subject to high magnetic fields, and motorized car accessories.
Abstract: The ultrasonic motor, invented in 1980, utilizes the piezoelectric effect in the ultrasonic frequency range to provide the motive force. (In conventional electric motors the motive force is electromagnetic.) The result is a motor with unusually good low-speed high-torque and power-to-weight characteristics. It has already found applications in camera autofocus mechanisms, medical equipment subject to high magnetic fields, and motorized car accessories. Its applications will increase as designers become more familiar with its unique characteristics. This book is the result of a collaboration between the inventor and an expert in conventional electric motors: the result is an introduction to the general theory presented in a way that links it to conventional motor theory. It will be invaluable both to motor designers and to those who design with and use electric motors as an introduction to this important new invention.

627 citations


Journal ArticleDOI
TL;DR: Passive piezoelectric damping devices are studied in this paper, which are analogous to mechanical damped vibration aborbers, and they can be used to damp the air.
Abstract: Passive piezoelectric damping devices are studied. These devices, consisting of a piezoelectric element and a resonant shunt, are analogous to mechanical damped vibration ab sorbers. In the past, a...

437 citations


PatentDOI
TL;DR: In this paper, a tunable ultrasonic probe includes a body of a first piezoelectric material acoustically coupled in series with another body of another, relaxor ferroelectric material.
Abstract: A tunable ultrasonic probe includes a body of a first piezoelectric material acoustically coupled in series with a body of a second piezoelectric material. The second piezoelectric material has a Curie temperature that is substantially different than that of the first piezoelectric material. Preferably, the first piezoelectric material is a conventional piezoelectric ceramic, such as lead zirconate titanate, while the second piezoelectric material is a relaxor ferroelectric ceramic, such as lead magnesium niobate. At an operating temperature of the probe, the first piezoelectric material has a fixed polarization. In contrast, the second piezoelectric material has a polarization that is variable relative to the fixed polarization of the first piezoelectric material. A preferred novel arrangement of electrodes electrically couples the bodies in parallel with one another. An oscillating voltage for exciting the acoustic signals in the probe is coupled with the electrodes. The polarization of the second piezoelectric material is variably controlled by a bias voltage coupled with the electrodes. In a preferred embodiment, the bias voltage has a reversible electrical polarity for selecting one resonant frequency from a plurality of resonant frequencies of the probe. In another preferred embodiment, the bias voltage source has a variable voltage level for selecting at least one of a plurality of resonant frequencies of the probe.

98 citations


Proceedings ArticleDOI
06 May 1994
TL;DR: In this paper, the Rayleigh-Ritz assumed mode energy method is used to model the distributed piezoceramics and the traveling-wave dynamics of the stator.
Abstract: A piezoelectric rotary ultrasonic motor is modeled for the purpose of predicting, a priori, motor performance as a function of design parameters. The Rayleigh-Ritz assumed mode energy method is used to model the distributed piezoceramics and the traveling-wave dynamics of the stator. Natural frequencies and dynamic modeshapes are obtained for a generally configured motor. Nonlinear normal and tangential interface forces between the rotor and stator are incorporated into the forcing function along with the linear piezoelectric forcing. Given the applied torque, applied axial loading, and piezo drive voltages as inputs to the model, general motor performance measures are obtained--namely speed, input power, output power, and efficiency. The approach presented here provides a general framework for modeling these motors as well as a design tool for optimizing prototypes with the added flexibility of allowing for a wide variety of geometries and materials.

86 citations


Journal ArticleDOI
TL;DR: In this paper, a step-beam model is developed to predict the frequency and mode shape of a uniform flexible beam with surface bonded piezoelectric materials, which includes the inertia and stiffness of the material and bonding layer, and the shear deformation and rotary inertia of the beam.

67 citations


Patent
14 Jun 1994
TL;DR: In this article, an ultrasonic probe including one or more piezoelectric ceramic elements mounted on an acoustically damping support body is used to provide an acoustic coupling between the probe and the support body.
Abstract: An ultrasonic probe including one or more piezoelectric ceramic elements mounted on an acoustically damping support body. Desired acoustic signals are transmitted and received through a front portion of the probe while unwanted acoustic signals are dampened by the support body at the rear portion of the probe. Each element has a respective rear face and a respective piezoelectric ceramic layer integral therewith to provide efficient acoustic coupling between the element and the acoustically damping support body. The respective piezoelectric layer of each element includes shallow grooves disposed on the respective rear face of each piezoelectric element. A groove volume fraction of the piezoelectric layer is selected to control acoustic impedance of the piezoelectric layer so as to provide a desired acoustic impedance match between a bulk acoustic impedance of the element and an acoustic impedance of the acoustically damping support body. Electrodes extend into and contact the grooves, imposing electrical boundary requirements that support a desired electrical field distribution within the element.

62 citations


Journal ArticleDOI
TL;DR: In this article, an active truss structure with piezoelectric sensors and actuators is described, and a linear quadratic Gaussian, second-order, and direct-rate feedback control scheme is designed to suppress the vibrations of the active structure.
Abstract: Embedded piezoelectric devices may be ideally suited for vibration control of space structures, which lack an inertial ground. When subjected to an input voltage, an embedded piezoelectric actuator changes its dimensions, which in turn generates a pair of forces exerted on adjacent structural members. From the direct piezoelectric effect, an embedded piezoelectric transducer generates an electric charge proportional to the structural dynamic response. In this paper, the implementation, testing, and modeling of an active truss structure with piezoelectric sensors and actuators are described. Linear quadratic Gaussian, second-order, and direct-rate feedback control schemes are designed to suppress the vibrations of the active structure. Simulation and test results are presented. It is shown that special model reduction considerations are required to achieve good correlation between test and analysis. Nomenclature The typical symbology for piezoelectric material properties are used in this paper. Except where noted, the piezoelectric variables are with respect to the standard piezoelectric material 1-2-3 Cartesian coordinate frame. The single, or first of the double, subscript denotes the direction of the applied/sensed electrical field. The second subscript represents the direction of the stress/strain in the piezoelectric material. The subscript r represents the radial direction, as measured in a cylindrical coordinate frame. A = cross-sectional area Ac - controller state matrix As - surface area B, BI = input matrix, /th input matrix Bc = controller input matrix

54 citations


Journal ArticleDOI
TL;DR: In this paper, a step-beam model is developed to predict the frequency and mode shape at different piezoelectric sensor/actuator locations in a closed-circuit condition.
Abstract: A stepped beam model is developed to predict analytically the natural frequencies and mode shapes at different piezoelectric sensor/actuator locations The modal solution obtained by including the inertia and stiffness of the surface-bonded piezoelectric materials is applied to investigate the interaction of structure vibration and piezoelectric actuation under closed circuit condition It is shown that a generalized stiffness from electromechanical coupling is induced by the interaction The generalized stiffness is a function of structure mode shapes and piezoelectric sensor/actuator locations, thus either softening or stiffening system stiffness is achievable in closed circuit condition All analytical predictions are validated by modal testing

50 citations


Proceedings ArticleDOI
06 May 1994
TL;DR: In this article, a linear motor operating on the inchworm principle was presented, which achieved a stall load of 26 lb and no-load speed of 1 inch/sec vs the design of 30 lb and 1.3 inch/ sec.
Abstract: Magnetostrictive and piezoelectric materials were used to create a linear motor operating on the inchworm principle. This motor operates at an electrical resonance, switching power internally between inductive and capacitive components. Magnetic coils surrounding the two Terfenol-D rods which drive the inchworm's center expanding element form the inductive component. Piezoelectric stacks that control the end clamping action are the capacitive components. The normal electrical phase relationship between these components provides natural drive timing for the inchworm. The motor direction can be easily reversed by changing the magnetic bias on the Terfenol. A prototype motor was built that achieved a stall load of 26 lb and no-load speed of 1 inch/sec vs the design of 30 lb and 1.3 inch/sec. A new type of power supply that switches power from a dc source was built for the motor. This power supply uses a small number of components to exactly supply the energy used in each inchworm cycle. It tracks the motor circuit resonance and is not affected by frequency shifts.

40 citations


Journal ArticleDOI
TL;DR: In this article, a ZnO piezoelectric sensor was used for detecting force gradients in the noncontact atomic force microscope (AFM) using a transfer matrix.
Abstract: This paper presents a piezoelectric sensor for detecting force gradients in the noncontact atomic force microscope (AFM). To simplify the force gradient detecting system of the noncontact AFM, the direct sensing cantilever with a ZnO piezoelectric film has been developed. The signal related to the vibration amplitude of the cantilever end is measurable by detecting the charge induced by the piezoelectric effect. The gradient of the force between the tip of the vibrating cantilever driven by an external oscillator and the sample modifies the vibration amplitude of the lever, hence inducing a change of the piezoelectric charge signal. We have adapted the transfer matrix method for calculating the change of the piezoelectric charge due to the gradient of the force. The piezo-electric signal trace has been recorded as a function of sample displacement. We have converted the recorded data to force gradients using a transfer matrix.

31 citations


Proceedings ArticleDOI
02 Oct 1994
TL;DR: In this paper, a micro mobile machine for pin-type actuators based on the piezoelectric vibration has been developed, which is composed of four pairs of PPE elements, elastic plate and contact pin to generate the driving force in S-Y plane by transmitting the PPE vibration to the tip of the contact pin with elastic plate bending vibrational mode control.
Abstract: The micro mobile machines for pin-type actuator models based on the piezoelectric vibration have been developed. It is composed of four pairs of piezoelectric sheet elements, elastic plate and contact pin to generate the driving force in S-Y plane by transmitting the piezoelectric vibration to the tip of the contact pin with the elastic plate bending vibrational mode control. In the experiment, the fundamental characteristics of pin-type actuators were measured with the various size, shapes and materials. For example, m o d e l 4 is composed of the elastic metal plate with 26mm(W) X 26mmO) X O.lmm(t) and of the contact pin with 17mm(L) X @ l.llmm, and model-B is a half size of model-A. As a result, the maximum un-loaded driving speed and the starting force with the normal force of 40gf along the X-direction of both models-A and B were found to be 73mm/sec, 5Ogf and 67mm/sec, lO.Ogf, respectively. Although the movability of the S and Y directions was also observed. The miniaturization effect on their performance has not been determined yet, further is now under investigation. Besides, the pin-type actuators have been applied to construct a prototype model of micro mobile machine being of eight pieces of pin-type actuators attached to a machine body. The machine power and control signals are supplied by tlie external driving circuit. Their movements for the forward, backward, rotational and spiral could be performed in 4 36" pipe by controlling tlie each actuaitor vibrational modes.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated some stationary piezoelectric linear motors which could easily be constructed in a flat shape, and the structure, operation principles, and characteristics of such stationary linear motors are described, and moreover, a method to lower the driving voltage of these linear motors is reported.
Abstract: This paper deals with piezoelectric linear motors for driving an optical pickup element of CD-ROM. These linear motors have such merits in that they can be made thin because of their simple construction, and they are suitable for precise positioning owing to their operation principle of using ultrasonic vibrations of essentially very small displacements. We can expect that the input power of these motors will be economized due to their self-position-retention function. Therefore, in order to achieve such linear motors, we have already reported some piezoelectric linear motors of the self-moving type. On the other hand, in this paper, the authors investigated some stationary piezoelectric linear motors which could easily be constructed in a flat shape. Compared with the self-moving piezoelectric linear motors reported previously, the stationary piezoelectric linear motors have the merit that they easily generate a uniform pressing force. In this paper, the structure, operation principles, and characteristics of such stationary linear motors are described, and moreover, a method to lower the driving voltage of these linear motors is reported.

Journal ArticleDOI
TL;DR: In this paper, the authors present an analytical model to predict the model parameters of a dither-motor structure in a ring laser gyroscope in which the piezoelectric sensor and actuator are employed as driving mechanisms to avoid the problem of so-called lock-in effects.
Abstract: The authors present an analytical model to predict the model parameters of a dither-motor structure in a ring laser gyroscope in which the piezoelectric sensor and actuator are employed as driving mechanisms to avoid the problem of so-called lock-in effects It is shown that the natural frequency of a dither motor is strongly influenced by: (1) the inertia and stiffness of piezoelectric elements and bonding layers, (2) the location of piezoelectric elements, and (3) the interaction between structural vibration and piezoelectric actuation Conventionally piezoelectric elements are used for sensor and actuator independently A technique for utilizing each of the piezoelectric elements concurrently for dither rate sensing and dither motion actuation is also developed Experimental results show that the system performance and reliability can be significantly increased by accurately predicting the fundamental structural frequency and by implementing the concurrent sensing/actuating technique

Proceedings ArticleDOI
01 Jan 1994
TL;DR: In this article, the characteristics of a hybrid transducer-type ultrasonic motor are summarized as a function of the size and diameter dependence of torque and no-load speed.
Abstract: In this report, the characteristics of a hybrid transducer-type ultrasonic motor are summarized as a function of the size First, the diameter dependence of torque and no-load speed is discussed theoretically Second, it is investigated experimentally by using trial made motors with diameters range from 5 mm to 80 mm Based on the results, the keys to making a much smaller motor as well as a bigger sized one with a giant torque are mentioned

Patent
17 Aug 1994
TL;DR: In this paper, a piezoelectric motor with a progressive waveform distortion at the stator surface is described. But the model is based on biased ceramic rods, where each rod is connected to a stator by a joint.
Abstract: Piezoelectric motor with progressive wave comprising one or more rotors (20, 21), one or more annular stators (27, 28), and two sets of piezoelectric elements (29) distributed on the stator, in permanent contact with the stator and energized by an alternative current with a phase shift of π/2 between the groups so as to generate a progressive waveform distortion at the stator surface. The piezoelectric elements are formed of biased ceramic rods (29) independent of each other and perpendicular to the stator, wherein each rod is connected to said stator by a joint (14).

Patent
30 Mar 1994
TL;DR: In this article, a piezoelectric actuator is driven by continuously applying a pulse voltage or an AC voltage to the actuator, so as to cause it to generate heat.
Abstract: A piezoelectric actuator is driven by continuously applying a pulse voltage or an AC voltage to a piezoelectric element, so as to cause the piezoelectric element to generate heat because of a dielectric loss of the piezoelectric element itself. If the temperature of the piezoelectric element reaches a temperature not less than 15° C., moisture contained in atmosphere is effectively prevented from entering into a resin casing of the piezoelectric actuator enclosing therein the piezoelectric element. Otherwise, moisture condensation or sweating would occur on a surface of the piezoelectric element. Therefore, even if the piezoelectric actuator is used in atmosphere of high humidity, a discharge breakdown will not occur, and reliability is remarkably increased.

Proceedings ArticleDOI
01 Jan 1994
TL;DR: In this paper, a mathematical model of a traveling wave ultrasonic motor with a piezoceramic stator is proposed based on the theory of piezoelectric plates planar vibrations and on physically well-grounded ideas of classic contact mechanics.
Abstract: A consistent mathematical model of a travelling wave ultrasonic motor with a piezoceramic stator is suggested. The model is based on the theory of piezoelectric plates planar vibrations and on physically well-grounded ideas of classic contact mechanics. The theory developed provides an opportunity to calculate the rotor velocity, speed-voltage characteristics, efficiency of energy transformation etc

Journal ArticleDOI
TL;DR: In this article, a same-phase drive-type ultrasonic motor with two degenerate bending vibration modes of a disk was used to investigate the mechanisms for supporting a stator and pressing a rotor.
Abstract: This paper deals with a same-phase drive-type ultrasonic motor, using two degenerate bending vibration modes of a disk Characteristics of the motor are influenced considerably by the mechanisms for supporting a stator and pressing a rotor By investigating these points experimentally, a motor with high efficiency characteristics was realized Moreover, the driving method for improving the transient response of the motor is described

Journal ArticleDOI
TL;DR: In this paper, the elastic force motor (EFM) was used to detect the influence of a point contact force applied on a flexural vibrating plate, which was detected by an integrated piezoelectric sensor.
Abstract: In the last few years, attempts have been made to miniaturize ultrasonic motors by using silicon micromachining techniques. In particular, the motion of small plates or the rotation of lenses using travelling waves on thin piezoelectric activated diaphragms has been observed. We have recently reported on a new micromachined ultrasonic motor called the elastic force motor (EFM). In this new family of motors, the flexure waves of a circular diaphragm are converted to a net torque by elastic tilted legs attached to the rotor. The main interest for this type of micromechanical device is its potential use in microsystems. For this type of application, detection of the angular position of the rotor will be of crucial importance. In this paper, we report on preliminary results of the influence of a point contact force applied on a flexural vibrating plate. Electrical detection of this force by an integrated piezoelectric sensor is also described.

Journal ArticleDOI
TL;DR: In this article, an in-phase drive-type ultrasonic motor using two degenerate bending vibration modes of a disk was used as a clock signal for the stepping drive, which was realized using an open-loop control system without a rotary encoder as an angular displacement sensor.
Abstract: A stepping drive method that does not use an extra clock signal source for a self-oscillation-type ultrasonic motor is described. The motor used here is an in-phase drive-type ultrasonic motor using two degenerate bending vibration modes of a disk. The output electrical signals caused on a self-oscillation are used as a clock signal for the stepping drive. An angular displacement at every step is realized using an open-loop control system without a rotary encoder as an angular displacement sensor. In order to eliminate the deviation of angular displacement at every step, a multitooth rotor was used. As a result, stable stepping drive of an ultrasonic motor was realized.


Proceedings Article
01 Jan 1994
TL;DR: In this paper, a two-coordinate ultrasonic linear motor based on the superposition of longitudinal vibrations of rod-shaped rectangular resonators is presented, which is capable of bidimensional nanometric step displacements with travel range in the centimeter range.
Abstract: A new concept of a two-coordinate ultrasonic linear motor, based on the superposition of longitudinal vibrations of rod-shaped rectangular resonators, is presented. The new motor is capable of bidimensional nanometric step displacements with travel range in the centimeter range. Controlled linear motion with steps of less than 10 nm is demonstrated. We compare the influence of the friction pair materials on motor output characteristics. CVD-diamond, alumina ceramics and case-hardened steel were used as friction pair materials. Wear and surface microtopography were measured by Atomic Force Microscopy (AFM). Strong ultrasound influence on wear and deformation of the friction pair materials was found

Patent
20 Sep 1994
TL;DR: In this paper, the shape of a piezoelectric element in a composite body has the thickness and the area of an electrode surface of specified values or below to provide a speaker which is excellent flat up to a high frequency band with less distortion.
Abstract: PURPOSE: To provide a speaker which is excellent flat up to a high frequency bandwith less distortion by making the shape of a piezoelectric element in a composite piezoelectric body have the thickness and the area of an electrode surface of specified values or below CONSTITUTION: The electric signal transmitted from a sound signal source is guided by a lead wire 6 and voltage is impressed on a piezoelectric element 3 by an electrode 5 The piezoelectric element 3 is warped in its thcikness direction and a composite piezoelectric body 2 vibrates in its thickness direction This vibration transmits as sound and it works as a speaker In this case, in an object in which composite material composed of flexible resin and a fine piezoelectric elements is made a sheet shape and the electrode 5 is provided on the upper and lower surfaces, the thickness of the piezoelectric element 3 is defined as 02mm or below and the area of the electrode surface is defined as 4mm or below This is the reason why the amplitude in the thickness direction of the composite piezoelectric body 2 itself becoms too large at the time of producing sound in a high frequency range when the thickness is thicker than 02mm or the composite piezoelectric body 2 itself is thicker than 02mm and the follow-up ability for the sound signal is degraded

PatentDOI
Thomas H. Tichy1
TL;DR: In this paper, a piezoelectric transducer is mounted on a single post to achieve maximum resonation from the transducers, which is achieved by mounting the transdrone within a housing, which has essentially the same geometry as the bender.
Abstract: A piezoelectric transducer (100) may be achieved by mounting a piezoelectric bender (101) within a housing (102). Maximum resonation may be obtained by mounting the piezoelectric bender (101) on a single post (103). The housing (102) is constructed to have essentially the same geometry as the piezoelectric bender (101) and is separated by a predetermined distance (104). This predetermined distance (104) provides an acoustic impedance such that sound may resonate from the transducer.

Patent
05 Jul 1994
TL;DR: In this article, a broadband ultrasonic transducer has a layer of piezoelectric material sandwiched between respective layers of backing and matching material, where the piezelectric element is coupled to a pair of electrical terminals, across which a varying voltage is produced.
Abstract: A broadband ultrasonic transducer has a layer of piezoelectric material sandwiched between respective layers of backing and matching material. The piezoelectric element is coupled to a pair of electrical terminals, across which a varying voltage is produced. The piezoelectric layer has a structure such that in response to the varying voltage, a forward-propagating wave emanating from its back surface does not destructively interfere with a forward-propagating wave emanating from its front surface when the frequency of the waves is an even multiple of the half-wave frequency of the particular piezoelectric layer. This effect can be attained by roughening the back surface of the piezoelectric layer or by spatially varying the piezoelectric coupling in the thickness direction in a portion of the piezoelectric layer which is proximate to the back surface.


Patent
11 May 1994
TL;DR: In this paper, the authors proposed a method to detect a pressure applied to the surface of a living body by a piezoelectric transducer unit and automatically control the pressure in a ultrasonic bone evaluating apparatus for measuring an acoustic velocity in a bone using ultrasonic waves.
Abstract: PURPOSE:To detect a pressure applied to the surface of a living body by a piezoelectric transducer unit and automatically control the pressure in a ultrasonic bone evaluating apparatus for measuring an acoustic velocity in a bone using ultrasonic waves. CONSTITUTION:Arms 10 and 12 are provided with piezoelectric transducer units 18 and 20. The arms 10 and 12 are moved close to each other so that the piezoelectric transducer units 18 and 20 are pressed against the surface of a living body. In this instance, pressure sensors 26 and 28 installed in the piezoelectric transducer units 18 and 20 detect the pressures applied. On the basis of the detected pressures, a controller 30 regulates the driving of the arms 10 and 12 so that the pressures become appropriate.

Patent
03 Feb 1994
TL;DR: In this paper, a distribution network of electric signals in a piezoelectric or ultrasonic waves motor, is produced by depositing electrodes of conductive material on one face of a strip in dielectric material, that on the other face of the strip conductive tracks are deposited according to an interconnection diagram, designed beforehand to supply the piezelectric elements with proper voltage.
Abstract: A distribution network of electric signals in a piezoelectric or ultrasonic waves motor, is produced by depositing electrodes of conductive material on one face of a strip in dielectric material, that on the other face of the strip conductive tracks are deposited according to an interconnection diagram, designed beforehand to supply the piezoelectric elements with proper voltage. Drillings are made through the strip between the conductive tracks and the electrodes, and through plating or deposit of conducting material, these drillings are made conductive.

Proceedings ArticleDOI
25 Jan 1994
TL;DR: In this article, the rotation speed of an ultrasonic flexure wave type micromotor has been regulated using piezoelectric detection of the rotating stress field induced by the contact force between the stator and the rotor.
Abstract: The rotation speed of an ultrasonic flexure wave type micromotor has been regulated using piezoelectric detection of the rotating stress field induced by the contact force between the stator and the rotor. The regulation principle proposed is to insert the motor as a Voltage Controlled Oscillator in a Phase Lock Loop circuit. In normal operation, the rotation speed of the motor will be locked to an external control frequency. In addition, the number of rotor revolutions can be obtained on a counter for specific applications. With this configuration, quasi-synchronous or step-like operations are possible, increasing considerably the application field of such devices. This technique can be applied to a miniaturized version of the Elastic Force Motor (EFM) using a batch processed silicon micromachined stator with a patterned active piezoelectric layer. Based on this principle, future hybrid EFM associated with a low power, single chip control unit will provide a low cost actuator for mechanical microsystems.

Proceedings ArticleDOI
13 Sep 1994
TL;DR: In this paper, a closed form solution is obtained for a given displacement assumption, based on a power series technique, to study the stress distribution that is generated in the interaction between a simple (plate) structure and a piezoelectric actuator.
Abstract: Recently piezoelectric materials have been used as actuators or sensors in some simple adaptive structures. Thin polarized piezoceramics were bonded to the top and bottom surfaces of simple plate-like passive structures. The piezoelectric layers work as actuators or sensors by means of the converse of the direct piezoelectric effect. In both cases the interaction mechanism between the active layer and the passive structure plays a fundamental role in the response of the overall structure [1,2,3]. Aim of the present paper is to study the stress distribution that is generated in the interaction between a simple (plate) structure and a piezoelectric actuator. A closed form solution is obtained for a given displacement assumption, based on a power series technique. The displacement form allows the interlaminar stress continuity at the interfaces between the actuator layer and the structure [4].© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.