Smart structures are a result of effective integration of control system design and signal processing with the structural systems to maximally utilize the new advances in materials for structures, actuation and sensing to obtain the best performance for the application at hand. The research in smart structures is constantly driving towards attaining self adaptive and diagnostic capabilities that biological systems possess. This has been manifested in the number of successful applications in many areas of engineering such as aerospace, civil and automotive systems. Instrumental in the development of such systems are smart materials such as piezo-electric, shape memory alloys, electrostrictive, magnetostrictive and fiber-optic materials and various composite materials for use as actuators, sensors and structural members. The need for development of control systems that maximally utilize the smart actuators and sensing materials to design highly distributed and highly adaptable controllers has spurred research in the area of smart structural modeling, identification, actuator/sensor design and placement, control systems design such as adaptive and robust controllers with new tools such a neural networks, fuzzy logic, genetic algorithms, linear matrix inequalities and electronics for controller implementation such as analog electronics, micro controllers, digital signal processors (DSPs) and application specific integrated circuits (ASICs) such field programmable gate arrays (FPGAs) and Multichip modules (MCMs) etc. In this paper, we give a brief overview of the state of control in smart structures. Different aspects of the development of smart structures such as applications, technology and theoretical advances especially in the area of control systems design and implementation will be covered.

In this research, a broadband variable passive and semi- active circuit is presented. The detailed procedure to obtain the augmented second order differential equations of motion for an electrical dynamic absorber (shunted circuit) using integrated piezoelectric material are given using Hamilton's principle and the finite element modeling procedure. The effect of the electrical dynamic absorber is shown through frequency response and analysis by varying the capacitance and inductance in the shunted circuit. Modal identification and gain scheduling techniques are also employed to identify each mode of the vibration of the structure. Simulations are implemented using a cantilevered aluminum beam with a PZT-5H (lead zirconate titanate) patch. The simulated results are provided in multiple formats.

An analysis of the solutions for various feedback control laws applied to vibrating cantilever beams is evaluated. The control is carried out via piezoelectric patch sensors and actuators. By considering an integral equation formulation, which is equivalent to the differential equation formulation, the analytical results are investigated. The conversion is accomplished by introducing an explicit Green's Function. The feedback controls implemented include displacement, velocity, acceleration and combinations of these. A numerical comparison of eigenvalues will be presented to illustrate the efficacy of the method and to contrast the effects of the controls. The results presented in the study can be used for benchmarking solutions based on numerical or approximation approaches.

This paper addresses system identification and vibration control of a cantilever fabricated from piezoelectric materials (PZT), and shows how system identification and state estimation can be used to achieve self-maintenance of a self-sensing system. Currently, self-sensing systems that have concurrent actuation and sensing can be made by using a bridge circuit. However, hardware tuning is still needed due to the unstable nature of an imbalanced bridge circuit. This problem becomes serious in the space environment where human beings may not be available to perform the maintenance. A method of achieving self-sensing without a bridge circuit is proposed in this paper. Analysis of the system dynamics indicates that the subsystem corresponding to the bridge circuit for a self-sensing cantilever with PZT can be described as a direct transmission component in the state space expression of the system. This means that the problem of balancing the bridge circuit is equivalent to the system identification and state estimation problem. By performing a simple experiment, a model of the system was identified using the 4SID (SubSpace State Space Identification method). Observer theory can be used to estimate state vectors which include information about the mechanical dynamics. Thus, system stability depends on the estimated value of the state vectors. The system can be stabilized using a state feedback controller such as a LQ controller. The proposed method was verified with experimental results, demonstrating that smart structures can achieve self-maintenance.

A new wavenumber domain sensing method has been developed and applied to feedback controller design for active structural acoustic control. The approach is to minimize the total acoustic power radiated form vibrating structures in the wavenumber domain. If the disturbance spectrum is given, the target wavenumbers in the supersonic domain (i.e., the radiating wavenumbers) can be determined. Then, a state-space model can be found to estimate the magnitude of the supersonic wavenumber components. Once we have a state-space model that can be used for active structural acoustic control, a modern control design paradigm can be applied to minimize the acoustic power radiated from vibrating structures. The new sensing method was numerically validated on a thick-walled cylindrical shell with 55 active composite panels mounted. It is found that the method enables us to systematically find a state-space model for wavenumber components in the supersonic region, and therefore makes it easy to design MIMO LQG controller.

This numerical study presents a detailed optimal control design based on the Rayleigh-Ritz approach for the smart plate-cavity system. Linear quadratic (LQ) theory with output feedback is considered on the basis of the state space model of the system. A vibroacoustic model, which includes a rectangular shaped cavity, enclosed with a five rigid walls and a flexible smart plate with discrete piezoelectric sensor/actuator pairs bonded to its surface. Classical laminated plate theory is used to model the composite plate and electroelastic theory is used model the discrete piezoelectric patches. Eigenfunctions of a clamped-clamped beam are used as the Ritz functions for the panel and the rigid walled cavity modes are used the model the acoustic cavity. The dynamic equations of motion for the coupled smart panel-cavity system are derived using Hamilton's principle. The forcing term due to the cavity acoustic pressure is determined by using virtual work considerations. For the present study, five collocated pairs of sensor/actuator pairs are attached to the plate at a predetermined placement scheme. The performance index considered for the design of the optimal controller includes both the displacement of the panel and the pressure inside the cavity. Numerical simulation is used to predict the reduction in the sound pressure level inside an enclosure radiated from this optimally controlled plate. The Rayleigh-Ritz approach is found to be faster and a more efficient method for designing control system for simple plate-cavity systems when compared to other numerical methods such as the finite element method.

In designing a controller, one way to avoid energy spillover is to use what is called the zero spillover control scheme. Here, this scheme is studied for actively controlling sound fields inside an enclosure with a flexible boundary. Noise is transmitted into the enclosure through the flexible boundary, and piezoceramic patches, which are mounted on the flexible boundary, are used as actuators. Polyvinylidene fluoride sensors are used on the flexible boundary and microphone sensors are used inside and outside the enclosure. The locations of the sensors needed to construct a zero spillover controller are discussed along with other issues.

We present some theoretical and experimental results related to the problem of developing active systems for the control of flexural waves in beams. Two types of feedforward control systems were implemented in the Laboratory. The first system was an implementation of an ideal compensator which modifies the reflection matrix at the boundary of a beam to generate a perfect anechoic termination. The transfer functions for the compensator were identified using an optimum sensor arrangement, with the disturbance waves generated with a shaker attached midways along the span of the beam, and the secondary waves generated by means of two PZT actuator pairs located near the active boundary. For the second system the filtered-X-LMS algorithm (XLMS) was used to adaptively identify the parameters of a compensator. We show how, under certain conditions, the XLMS algorithm converges to the structure of the ideal compensator. We also show how the parameters of the adaptive compensator, as well as the parameters of the plants, can be identified using an estimate of the reflected waves provided by an observer using measurements from a compact array of sensors. We report experimental results in which good attenuation levels were achieved over a wide frequency band.

Dielectric hysteresis in piezoceramic transducers can degrade their performance in structural vibration control applications. Different hysteresis models have been applied to piezoelectric transducers, including those based on Preisach, Jiles-Atherton and Ishlinskii concepts. Relationships between these and other models, new experimental identification schemes and multi-term describing function representations of some of them are reviewed. Then, system equations that incorporate the hysteretic behavior are formulated for two pedagogical smart structural systems: a passively shunted / actively driven PZT wafer on (1) a simply supported thin plate and (2) a simply supported thin beam. The effect of PZT hysteresis on optimized passive and hybrid vibration control strategies is evaluated.

Hysteresis in smart materials hinders the wider applicability of such materials in actuators. In this paper, a systematic approach for coping with hysteresis is presented. The method is illustrated through the example of controlling a commercially available magnetostrictive actuator. We utilize the low-dimensional model for the magnetostrictive actuator that was developed in earlier work. For low frequency inputs, the model approximates to a rate-independent hysteresis operator, with current as its input and magnetization as its output. Magnetostrictive strain is proportional to the square of the magnetization. In this paper, we use a classical Preisach operator for the rate-independent hysteresis operator. In this paper, we present the results of experiments conducted on a commercial magnetostrictive actuator, the purpose of which was the control of the displacement/strain output. A constrained least-squares algorithm is employed to identify a discrete approximation to the Preisach measure. We then discuss a nonlinear inversion algorithm for the resulting Preisach operator, based on the theory of strictly-increasing operators. This algorithm yields a control input signal to produce a desired magnetostrictive response. The effectiveness of the inversion scheme is demonstrated via an open-loop trajectory tracking experiment.

The design process of engineering smart structures requires a virtual overall model, which includes the main functional parts such as the passive structure, the actuators and sensors as well as the control algorithm. The objective of the paper is to pre-sent such a design concept for vibration suppression of thin-walled shell structures controlled by piezoelectric wafers and fi-bers. This concept is based on a recently developed finite element package for the simulation of multi-physics problems. At first a rough design of actuator and sensor distributions is estimated which is based on the controllability and observabilty indices. Then the Matlab/Simulink software tool is used for controller design. From the finite element model all required data and information are transferred to Matlab/Simulink via a data exchange interface. After having designed the controller the result in form of the controller matrices or as C-codes can be transferred back into the finite element simulation package. Within the finite element code the controlled structural behavior can be studied under different disturbances. The structural design can be improved in an iterative way, e.g. by changing the actuator and sensor positions based on a sensitivity analy-sis. As an example an actively controlled smart plate structure is designed and tested to demonstrate the proposed procedure.

When transient temperature is measured by thermocouples, the result is largely influenced by thermocouple's dynamic performance. This problem is encountered in measuring flame temperature fluctuation by using of fine wire thermocouple. Because the heat transfer coefficient mostly depends upon the gas temperature and flow speed, the time constant of fine wire thermocouple is not equal in different temperature ranges. The time constant calibrated in low temperature is not valid in this kind of measurement. Typically frequency of fluctuation in flame is less than 7KHz. The fine wire thermocouple often has to be compensated to meet this working frequency band. The compensation range is determined by its time constant in high temperature. High temperature step source with sharp rise is needed in dynamic calibrating this kind of fine wire thermocouples. A dynamic calibration system based on a set of rocket engine and different propellant is introduced to study the dynamic performance of the thermocouples. This set of rocket engine is designed to have same nozzle exhaust Mach number. Different engines with different propellant provide different high temperature step sources. Experiment is conducted in rocket engine static state experiment laboratory. The position of thermocouple is determined according to numerical simulation results. Dynamic modeling and compensation methods are introduced to process the calibration results.

We derive a Kth order (K = 0,1,2,3...) Piezoelectric plate theory from a 3D mixed variational principle. The balance laws, constitutive relations and the boundary conditions are deduced. The application of the theory is illustrated by analyzing the cylindrical bending deformations of a cantilever PZT5A plate loaded on the top and/or bottom surfaces by a uniformly distributed charge density. We also ascertain deformations of the plate for different values of the angle between the poling direction and the normal to the midsurface of the plate.

An analytical model of the pseudoelasticity of shape memory alloys (SMA) has been developed and validated using tensile test results performed with various kinds of shape memory alloy samples. However, the analytical approach is limited to conventional samples submitted to an uniaxial stress state. Therefore, a numerical model has been developed, which is more suitable for the adaptive structure modeling. To this end, the SMA behavior laws have been implemented in the finite element code ATILA. The validation of the numerical model has been achieved by comparing the finite element results with the experimental ones.

This paper reports our work on the applications of fiber Bragg grating-based strain sensors for the vibration tests and mode analysis on concrete structures. The arrayed fiber grating strain sensors, which were wavelength-division-multiplexed along the fibers, were attached onto the reinforced bars (rebars) before concrete was poured in to form a 5.5m long, 0.3m wide, 0.15m deep reinforced concrete beam. The embedded sensors will provide quasi-distributed real-time dynamic strain information along the length of the beam. For verification with the FBG strain sensors, some electrical accelerometers were also placed on the top surface of the concrete beam. All the data from FBG sensors and electrical accelerometers were recorded and analyzed by a computer. In the experiments, a hammer and an electrical shaker were used to excite the structure. The experimental results obtained with the FBG sensors show good consistency with the theoretical analysis.

We have developed a numerical simulation scheme for magnetostrictive transducers, which is based on the magnetic vector potential formulation. Therewith, magneto-dynamic problems including eddy currents can be treated and the restriction to magnetostatic problems is eliminated. Furthermore, the full coupling of magnetic and mechanical systems including magnetically induced mechanical strains and permeability changes due to mechanical stresses is taken into account. As an application, we will present numerical simulations for a magnetostrictive rod actuator and compare these results with measured data.

The problem of impact damage detection in composite structures using piezoceramic sensors is addressed. Piezoceramic sensors are bonded on the composite specimen and used in a passive mode to acquire the strain data from dropweight impact tests. The paper is focused on the comparative study of various signal processing techniques which can extract features related to different impact energy levels associated with different types of damage. The analysis includes time, frequency and wavelet domain features. The results show the potential of the methods fo impact damage identification.

Recent years have shown considerable progress on the problem of determining the optimal type, number and location of sensors in engineering structures. The aim of this paper is to give an overview of different methodologies which can be used to position integrated sensors for structural damage detection. The focus is on combinatorial optimization, neural network and information theory. A simple example which illustrates the ideas is presented. This involves piezoceramic sensor location for impact damage detection in composite structures. Although, the example presented in the paper is related to piezoceramic sensors and damage detection, the methods shown are generic and can be used to solve any sensor/actuator location problem in smart structures.

TiNi/CFRP composites were fabricated by hot-pressing in the temperature range of 130-180 degree(s)C, by controlling the applied pressure. The TiNi wires were embedded as an 1mm interval into the center of CFRP layers and CFRP host materials were stacked as 0, 30, 60 and 90 degrees configuration on tensile direction, respectively. The stress-strain curve and tensile strength of composites strongly depends on stacking direction of carbon fibers. The tensile strength of TiNi/CFRP composites with stacking direction of 0 and 90 degrees configuration are about 1.2GPa and 50MPa, respectively. The microstructural properties of TiNi/CFRP composites were observed by SEM. Pore and/or voids were found to congregate near the embedded TiNi wire and they increased in proportion to stacking direction of carbon fibers. Larger pores and interfacial crack were also observed at interface between TiNi wires and epoxy resin. Furthermore, the fracture behavior was studied by an AE technique during tensile test, to analyze the fracture process. The effects of surface treatment of TiNi wire by acid etching to improve the interfacial bonding strength between TiNi wire and epoxy matrix are also investigated. The average interfacial bonding strength of the TiNi wire embedded in CFRP matrix was evaluated by pull out test. It was confirmed that surface treatment of TiNi wire by acid etching improved the interfacial bonding strength. Acid etching by HF+HNO₃ mixed solution significantly increased the interfacial bonding strength. The damage recovery effect of SMA in specimen was successfully confirmed by heating above 70 degree(s)C.

Pseudo-wavelets were proposed for system identification of linear systems to determine their natural frequencies and modal damping ratios. The approach provides excellent results for single-degree-of-freedom (SDOF) oscillators but significant errors might be observed for multiple-degree-of- freedom (MDOF) systems due to interference between different modes if the pseudo-wavelet transform (PWT) is directly applied. IN this paper a truncated pseudo-wavelet transform was employed to improve the accuracy for MDOF systems. A peak of the Fourier amplitude spectrum of the response was located and truncated in its neighborhood to isolate the peak. The frequency amplitude response function of a linear SDOF system was selected as the pseudo-wavelet. A truncated pseudo-wavelet transform was performed and its maximum value was located on a contour map of the PWT coefficients. The associated frequency and bandwidth of the MDOF system may be identified by the matching values of the scale and shift parameters. The methodology is illustrated for linear MDOF systems to identify their system parameters and good estimates were obtained. Noise effects were discussed. The approach can be applied for structural health monitoring. Change in system parameters using any two segments of response data may suggest occurrence of structural damages.

This study presents results from experimental validation of a recently developed model for predicting the thermomechanical behavior of shape memory alloy hybrid composite (SMAHC) structures, composite structures with an embedded SMA constituent. The model captures the material nonlinearity of the material system with temperature and is capable of modeling constrained, restrained, or free recovery behavior from experimental measurement of fundamental engineering properties. A brief description of the model and analysis procedures is given, followed by an overview of a parallel effort to fabricate and characterize the material system of SMAHC specimens. Static and dynamic experimental configurations for the SMAHC specimens are described and experimental results for thermal post-buckling and random response are presented. Excellent agreement is achieved between the measured and predicted results, fully validating the theoretical model for constrained recovery behavior of SMAHC structures.

The dynamics of intelligent actuators utilized in vibration control of flexible structures may exhibit nonlinear behavior under extreme environments and/or prolonged/repeated usage. When transitions to nonlinearities are not accounted for in the controller design, they might compromise controller performance and even destabilize the very system they are designed to control. A novel approach that addresses the issue of actuator nonlinearities is presented here. Specifically, the actuators considered are those that at some initial period exhibit linear behavior and enter a nonlinear regime thereafter. The method studied here only utilizes these actuators while on their linear behavior by proposing an optimal activation sequence of these actuators. At a given time interval of fixed length, only a single actuator is activated while the remaining ones are kept dormant. The reason is to ensure that at each time instance, a single actuator with linear dynamics is active. When the active actuator is about to become nonlinear, then the algorithm switches to and activates the next available actuator in an optimal fashion. The optimality of switching is with respect to the minimal cost of an associated LQR performance index that corresponds to each actuator. In the proposed algorithm, a control logic is incorporated that only selects the next actuator to be activated from the set of the remaining actuators that are considered healthy(linear); an example of this would be SMA actuators that had enough time to cool down and thus when activated again can exhibit linear dynamics.

A state-switched device is conceptually capable of instantaneously changing its mass, stiffness, or damping. Such a device will exhibit different dynamical response properties (modes and resonance frequencies) depending on its current state. A state-switched vibration absorber exploits the state-switching concept for the purposes of enhanced vibration suppression. Between each state switch, it is fundamentally a passive vibration absorber, but one which exhibits a different tuning frequency for each possible state. A state-switched vibration absorber therefore has a greater effective bandwidth than a classical passive absorber. This paper considers the role of damping in the state-switching concept for a simple one-degree of freedom system and for a two-degree of freedom system. Certain values of damping in the system improve performance, while other values hinder the performance of the state-switched absorber, as compared to classical absorbers. The predicted performance of the system also depends upon the particular damping model used, such as proportional, viscous, or modal damping. Damping values also affect the frequency of switch events that occur during the response of the system. In general, a state-switched absorber with optimized damping is more effective at vibration suppression as compared to a classical vibration absorber with optimized damping.

Piezoelectric multilayer actuators combine the advantages of large deflections, fast response time and, accurate repeatability. By using cofired multilayer structures deflections up to several microns in the case of stacked actuators and several millimeters for transducers operating in bending mode can be achieved. The high driving levels, however, lead to nonlinearities mainly caused by the ferroelectric hysteresis of the piezoceramic material. For an improved design of these complex transducers finite element analysis of the complete system is utilized. We have established a calculation scheme, now allowing full 3D-modeling of a piezoceramic multilayer actuator taking the nonlinear material behavior into account. The hysteretic effects caused by ferroelectricity are modeled using a macroscopic Preisach model describing the actual state of polarization. Furthermore, dependencies of the material parameters on the electric field strength and the mechanical stresses are considered by the implemented constitutive relation. Therewith, the calculation scheme allows the precise numerical analysis of a complex multilayered stack actuator.

This paper summarizes techniques for quantifying the displacements generated in THUNDER actuators in response to applied voltages for a variety of boundary conditions and exogenous loads. The PDE models for the actuators are constructed in two steps. In the first, previously developed theory quantifying thermal and electrostatic strains is employed to model the actuator shapes which result from the manufacturing process and subsequent repoling. Newtonian principles are then employed to develop PDE models which quantify displacements in the actuator due to voltage inputs to the piezoceramic patch. For this analysis, drive levels are assumed to be moderate so that linear piezoelectric relations can be employed. Finite element methods for discretizing the models are developed and the performance of the discretized models are illustrated through comparison with experimental data.

Possibility of passive piezoelectric damping based on a new shunting parameter estimation method is studied using finite element analysis. Piezoelectric device with shunt electronic elements, for example, inductor and resistor, are normally used for passive piezoelectric damping to achieve damping near resonance of the target structure. The key in implementation of such an electronic damping is to tune the shunt parameters accurately. The adopted tuning method is based electrical impedance that is found at piezoelectric device and the optimal criterion for maximizing dissipated energy at the shunt circuit. Full three dimensional finite element model is used for piezoelectric devices with cantilever plate structure and shunt electronic circuit is taken into account in the model. Electrical impedance is calculated at the piezoelectric device, which represents the structural behavior in terms of electrical field, and equivalent electrical circuit parameters for the first mode are extracted using PRAP(Piezoelectric Resonance Analysis Program). After the shunt circuit is connected to the equivalent circuit for the first mode, the shunt parameters are optimally decided based on the maximizing dissipated energy criterion. A cantilever beam example is taken to demonstrate the piezoelectric damping in the finite element simulation. Less than 10 dB vibration reduction at the tip of the beam is achieved by the piezoelectric damping. When the electrical potential at the shunted electrode is simulated nearly 80 Volt was found at the first resonance frequency. The dissipated electrical power ratio with respect to the mechanical input power is calculated from this electrical voltage, and it was found to be 0.39, which is close to the energy ratio found from the electromechanical coupling coefficient of the piezoelectric patch. Since this tuning method is based on electrical impedance calculated at piezoelectric device, multi-mode passive piezoelectric damping can be implemented for arbitrary shaped structures.

The low order controller has many advantages such as simple hardware implementation and high reliability and is very important for the successful integration of controllers with smart structures. Designing a controller with robustness to different uncertainties ins mart structure always leads to a high order controller. In this paper, two low order controller design methods are proposed. One method is to design a low order controller based on the reduced plant model. The model error between the full order model and reduced order model is considered as an additive uncertainty in the controller design to reduce the spill-over effect. Another method, controller reduction, is to find a low order controller by reducing the full order controller. The effect of the controller reduction on the system performance is taken into account by selecting a maximum allowable controller reduction error for preserving the performance. The full order controller can be synthesized to provide optimal performance or maximum allowable controller reduction error. Linear matrix inequalities (LMIs) are utilized in those methods to design the low order controllers. The variations of structural parameters, natural frequencies and damping ratios are considered in the controller design as parametric uncertainties.

This paper presents a study of a distributed arrangement of double PVDF actuator/sensor pairs bonded on a cantilever beam for the control of vibration at the tip. The arrangement of a single PVDF actuator/sensor pair, in practice, is known to be non-minimum phase due to coupling between in-plane motion and out-of-plane motion. This means that a single pair arrangement does not have the conventional driving-point collocated system property. The stability and performance of the arrangement are limited by finite feedback gains, which can be used with direct velocity feedback control. A double pair arrangement using four layers of PVDF has thus been suggested to overcome this problem. Theoretically, when both the actuator pair and the sensor pair are working out-of-phase, then the response becomes minimum phase since in-plane motion cannot be excited or detected. A smart beam with double PVDF actuator/sensor pairs has been implemented. A triangular shaped actuator/sensor pair was bonded on each side of the beam. The initial experimental measurements with individual pairs of transducers showed a good reciprocity and a strong coupling between out-of-plane and in-plane responses. All the four layers have then been used as out-of-phase actuators and sensors to attempt to measure only the out-of-plane response. However, in practice, this compensation method was found not to discriminate against the in-plane response, due to the direct coupling between the actuation and sensing transducers due to their finite thickness and compliance. Therefore, the four layers smart beam does not have a minimum phase property. A new arrangement of actuator/sensor pair for in-plane compensation is then suggested and discussed.

This paper provides an account of a student research project conducted under the sponsoring of the National Science Foundation (NSF) program on Research Experience for Undergraduates (REU) in Mechatronics and Smart Strictures in the summer of 2000. The objective of the research is to design and test a stand-alone controller for a vibration isolation/suppression system. The design specification for the control system is to suppress the vibrations induced by the external disturbances by at least fiver times and hence to achieve vibration isolation. Piezo-electric sensors and actuators are utilized for suppression of unwanted vibrations. Various steps such as modeling of the system, controller design, simulation, closed-loop testing using d- Space rapid prototyping system, and analog control implementation are discussed in the paper. Procedures for data collection, the trade-offs carried out in the design, and analog controller implementation issues are also presented in the paper. The performances of various controllers are compared. The experiences of an undergraduate student are summarized in the conclusion of the paper.

A technique of deforming a flexible wing to hold the airplane in a steady pull-up maneuver with required load factor at high dynamic pressures is examined. Rather than using an elevator system for pull-up, symmetric elastic twist and camber is determined to achieve the required pitching moment for increase in the angle of attack and change in the pitch rate to generate the required lift forces for pull-up maneuver. The elastic twist and camber is achieved by providing a system of actuating elements distributed within the internal substructure of the wing to provide control forces. The modal approach is used to develop equilibrium equations for the steady pull-up maneuver of a wing subjected to aerodynamic loads and the actuating forces. The distribution of actuating forces required to achieve specified load factor was determined by using an iterative procedure in conjunction with an optimal control design approach. Here, a full-scale flexible realistic wing is considered for the assessment of strain energy as a measure of the necessary power required to produce the symmetric twist and camber deformation to achieve the required lift forces. Subsonic and supersonic design conditions are investigated.

A study of the vibrational control of adaptive doubly- tapered cantilevered beams, simulating an aircraft wing, exposed to time-dependent external pulses is presented. Whereas the beam structure encompasses non-classical properties such as transverse shear, anisotropy and heterogeneity of their constituent materials, the active control capabilities are based upon the implementation of the adaptive materials technology. Herein, the adaptive feature is achieved through the converse piezoelectric effect that consists of the generation of localized strains in response to an applied voltage. Piezoactuators in the form of patches or spread allover the beam span are considered. The active control involves the dynamic response to arbitrary time-dependent external pulses. The closed-loop dynamic response time histories are obtained via the use of the piezoelectrically induced boundary moment control, and through the implementation of a modified bang- bang control strategy that involves a maximum value constraint imposed on the input voltage. Numerical simulations emphasizing the performance of the adopted control strategies intended to contain and even reduce to zero the response quantities when time unfolds are presented, and pertinent conclusions are outlined.

A study on the dynamic structural coupling behaviors of a laminated composite beam with an embedded piezo-ceramic (PZT) layer is presented in this paper. The composite structure under investigation is a three-layer laminate with anti-symmetric configuration, which leads to an extension-twisting structural coupling. Due to this coupling effect, when an electric filed is applied to the PZT layer, the actuated in-plane deformation can result in torsional motion. During the course of this study, both experimental investigation and computational modeling were performed. The longitudinal and out-of-plane displacements of the laminate were measured by three optical sensors. An interesting phase shift among the applied voltage, the in-plane deformation, and the twisting angle was observed at the resonant frequency of the first torsional mode. Such behavior was also confirmed by computational modeling. Further investigations by harmonic analysis were performed as well in the present study. The results from computational analysis revealed more features of structural dynamics of the concerned anti-symmetric laminate.

The primary objective of this study is to develop a more accurate research and design tool than those in the currently available literature for active constrained layer damping treatments applied in bending. A five layer beam finite element model is presented that includes bonding layer strain energy and extends current finite element models for Euler-Bernoulli beams with segmented active constrained layer damping treatments. Active constrained layer damping utilizes modern piezoelectric materials as the constraining layer for these types of damping treatments. Preliminary studies have confirmed that strains in the bonding layers can have a significant effect on damping ratios at the fundamental modal frequency, especially when relatively thin compliant piezo materials are used for constraining layers. Previous researchers that have developed three layer finite element models assumed perfect no-slip adhesion between adjacent surfaces of the beam, viscoelastic layer, and constraining layer. In certain instances this can contribute to reduced accuracy when predicting damping. The effectiveness of the finite element model is validated experimentally for both active and passive constraining layers. The damping is represented using an elastic displacement fields (ADF) to model the frequency dependent stiffness and damping properties in viscoelastic materials as developed by Lesieutre and Bianchini.

The concept of smart structures, such as piezoelectric laminates, has received a great deal of attention recently as an alternative to conventional techniques. These advanced structures can be designed to actively react to disturbance forces in order to maintain structural integrity while maintaining, or even improving, the level of performance. Great potential can be found in advanced aerospace structural applications. However, the introduction of smart devices inevitably perturb the local values of the field variables and nucleate damage such as debonding and delamination at the interface of piezoelectric devices and the host structure due to stress concentration. The layerwise characteristics of the laminates make the determination of stress and strain distribution a challenging problem. Conventionally, classical lamination theory has been extended to smart laminated structures which ignores transverse shear effects'3. A higher order theory was proposed and applied by Chattopadhyay et al.4'5 in the analysis oflaminated structures to address transverse shear effects without shear correction factors. The theory proved to be successful in global analysis for thick structures and smart structures. However, it fails to provide continuous distribution of transverse shear stresses. This implies that the theory is not sufficient in predicting local information regarding stress and strain distributions which is critical in the analysis of structural failure. The multifield characteristics of piezoelectric structures make the analysis even more complex, particularly in the presence of thermal effects as dictated by specific missions. A typical environment is represented by a solar flux of 1350W/m2 as vehicles move from shadow to sunlight. Some research in the field of smart structural modeling in the presence of thermal effects has been reported610. However, oneway coupling that only considers the effect of a known field on another field is used in these works. The bi-way coupling between piezoelectric and mechanical fields was included in the hybrid plate theory developed by Mitchell and Reddy3. A coupled thermal-piezoelectric-mechanical (t-p-m) model was developed by Chattopadhyay et al.1113 to address the bi-way coupling issues associated with smart composites under thermal loads. Their work indicates that the effects of bi-way coupling on structural deformation increase with the thickness of piezoelectric device. However, an equivalent single layer approach is used, and therefore the localized interlaminar characteristics cannot be addressed accurately by this theory. The present paper aims at the investigation of interlaminar stress distribution in laminated shell structures using coupled thermal-piezoelectric-mechanical model. The goal is to develop a theory that is capable of providing sufficient accuracy while guaranteeing computational efficiency compared to other layerwise theories. To maintain local accuracy of stress and strain distributions, the trial displacement field is assumed using zigzag functions and C0 continuity through the entire laminate thickness accommodating zigzag in-plane warping and interlaminar transverse shear stress continuity. The continuity conditions of inplane displacement and transverse shear stress fields as well as traction free boundary conditions are applied to reduce the number of primary structural variables. The temperature and electrical fields are assumed using higher order functions. These descriptions can satisfy surface boundary conditions of heat flux and electrical potential. The mathematical model is implemented using finite element technique. The case of cylindrical bending and spherical composite shell structures with piezoelectric patches are investigated. The analysis of stress distributions under electrical and thermoelectrical loading is performed and numerical results are presented.

The anisoparametric three-node MIN6 shallow shell element is extended for modeling Macro-fiber Composite/Active Fiber Composites (MFC/AFC) actuators for active vibration and acoustic control of curved and flat panels. The recently developed MFC/AFC actuators exhibit enhanced performance, they are anisotropic and highly conformable as compared to traditional monolithic isotropic piezoceramic actuators. The extended MIN6 shell element formulation includes embedded or surface bonded MFC/AFC laminae. The fully coupled electrical-structural formulation is general and is able to handle arbitrary doubly curved laminated composite and isotropic shell structures. A square and a triangular cantilever isotropic plates are modeled using the MIN6 elements to demonstrate the anisotropic actuation of a surface bonded MFC actuator for coupled bending and twisting plate motions. Steady state bending and twisting modal amplitudes of the cantilever square and triangular plates with MFC actuator are compared with the plate's modal amplitudes with traditional PZT 5A actuator. Frequency Response Function (FRF) for the square plate with MFC and PZT 5A are also compared.

In hard disk drive (HDD), and important issue related to increased storage density is the tribological problem of the head/disk interface. The conventional head gimbal assembly (HGA) of the HDD is contact start/stop (CSS) mode which results in wear particles and debris. This may cause a serious problem for read/write function. In this work, we propose a new type of suspension featuring shape memory alloy (SMA) actuator in order to prevent the friction between the slider and the dksi. As a first step, a finite element analysis is undertaken to investigate modal characteristics of the proposed SMA-HGA. Using the principal modal parameters such as natural frequency, a control system model is established and sliding mode control algorithm to achieve non-contact start/stop (Non-CSS) mode is formulated. The control principle for accomplishing the Non-CSS mode is briefly discussed as follows. The control input is employed to SMA actuator before the disk rotates, and disconnected when the angular velocity of the disk is fully developed to have a certain flying height. In order to demonstrate the effectiveness of the proposed control system, one of conventional HGA is modified to integrate the SMA actuator. The control algorithm is experimentally realized and controlled motions for Non-CSS mode are presented in time domain.

We investigate theoretically and experimentally the performance of linear and nonlinear vibration absorbers to suppress high-amplitude vibrations of twin-tailed fighter aircraft when subjected to a primary resonance excitation. The tail section used in the experiments is a 1/16 dynamically scaled model fo the F-15 tail assembly. Both techniques (linear and nonlinear) are based on introducing an absorber and coupling it with the tails through a sensor and an actuator, where the control signals ae either linear or quadratic. For both cases, we develop the equations governing the response of the closed-loop system and use the method of multiple scales to obtain an approximate solution. We investigated both control strategies by studying their steady-state characteristics. In addition, we compare the power requirements of both techniques and show that the linear tuned vibration absorber uses less power than the nonlinear absorber.

The topic of the present contribution in an experimental verification of the active control of flexural vibrations of smart beams. The spatial distribution of the piezoelectric actuator is determined in such a way that deformations induced by assigned forces with a given spacewise distribution and an arbitrary but known time-evolution are exactly eliminated by the piezoelectric actuation. In the present paper, the theoretical solution of this dynamic shape control problem is first derived from an electromechanically coupled theory in a three dimensional setting, where we make use of the theorem of work expended, and from Graffi's theorem. This more general formulation is specialized to the case of beams, where the kinematic hypothesis of Bernoulli-Euler and a uni-axial stress state are assumed, and the direct piezoelectric effect is neglected. We thus re-derive some results for beams published by our group in earlier contributions. It has been found that if the piezoelectric actuator shape-function is chosen as the spanwise distribution of the quasi-static bending moment due to assigned transverse forces, and if additionally the time-evolution of the applied electrical potential difference is chosen to be identical to the negative time-evolution of the assigned forces, the beam deflections due to these forces are exactly eliminated by the piezoelectric actuation. In the present paper, the validity of this theoretical solution is studied in an experimental set-up. As a result of the performed experiments, the elimination of force-induced vibrations of smart beams by shaped piezoelectric actuators is demonstrated for various time-evolutions of exciting single forces. The obtained experimental results give evidence for the validity of the presented theoretical solution of the dynamic shape control problem.

The actively controlled smart structures should have robust stability and robust performance when structural parameters vary in a reasonable range. In this paper, the parametric uncertainty is defined in a framework of quadratic inequality constraint. This representation of uncertainty can effectively reduce the conservatism. A generalized balanced truncation method for continuous uncertain system represented by linear fractional transformation is presented. The model reduction method can keep the uncertainty information of the full order system in the reduced order model for robust controller design. Linear matrix inequality (LMI) conditions are given for designing a robust output feedback controller to assign the poles of closed-loop uncertain system in a constrained conic sector subregion under the input limits and unmodeled dynamics. The proposed method is demonstrated using an experimental smart structure system.

Electrostrictive materials have been widely studied for the last decade with the view of integrating them in smart structures. Many three-dimensional finite element models have then been elaborated to simulate these structures behavior but no two-dimensional models have been presented up to now. The aim of this article is thus to set out the elaboration of a thin plate electrostrictive finite element for PMN-PT type ceramics used as actuators. This element is developed for dynamic purposes and thus takes into account phenomena induced by applying to the patch a cycling electric field. The finite element formulation is based on electromechanical constitutive equations derived in a previous paper, mechanical and electrical considerations and direct a priori plate assumptions. The electrostrictive finite element is here derived using techniques inspired from a piezoelectric finite element. This method has the particular property of reducing the initial electromechanical problem to a purely mechanical problem based on a modified elastic constitutive law. The electrical unknowns are then explicitly derived from the mechanical displacements. This method considerably simplifies the resolution of the problem since classical finite elements for laminated plates can be used to model the electrostrictive plate with a modified constitutive law.

The experimental observations in single crystals determine the local behavior of a martensite plate via nucleation, intrinsic thermoelasticity/pseudoelasticity, interface friction, growth and interaction with neighbor plates until coalescence. The thermomechanical behavior of a great group of martensite plates of the same variant in a single crystal can be established via the plate average behavior. The Clausius-Clapeyron equation is the link between force (or stress) and temperature. Starting from the experimental analysis a representative model (time independent) can be constructed. After an identification of the mean values, the hysteresis cycle and the internal loops can be predicted. Avoiding the classical fatigue effects, an evaluation of the time effects is realized. The characteristic of the local evolution associated to the coexistence among the phases and, also, the time and temperature actions related to the long time permanence in parent phase are ascertained.

Based on Brinson's one-dimensional constitutive relation for shape memory alloy (SMA), the kinetic equations for phase transformation are refined in this work in the following aspects: (1) Of both the martensite to austenite transformation and the reverse procedure, the start and finish temperatures of phase transformation for detwinned martensite is differentiated from those for twinned martensite. Different transformation parameters are introduced for the two variants of martensite. (2) The zone of the conversion from twinned martensite to detwinned martensite is extended to the austenite finish temperature A_f. Numerical simulations are conducted for (1) stress- strain relation of tensile loading and unloading under constant temperature; (2) strain-temperature relation of heating and cooling under constant stress; (3) stress- temperature relation for heating and cooling under fully restrained condition. All results obtained give good descriptions of thermo-mechanical behavior of SMA.

The model of a polymeric bar, which is connected in series with a shape memory alloy (SMA) wire, is analyzed. Both the polymeric bar and SMA are exposed to a transient temperature field. The thermo-viscoelastic theory for thermoheologically simple material is applied to the polymeric bar. Brinson's one-dimensional constitutive law is employed for the analysis of SMA. The fundamental equation governing the behavior of the combined structure is obtained. Results of stress (strain)-time relation and stress (strain)-temperature relation in SMA are obtained. It is found that the results from thermo-viscoelastic analysis coincide well with those of thermo-elastic and visco-elastic analyses only within low temperature range, however, notable discrepancy occurs when temperature is close to the glass transformation temperature of the polymer. Besides, the effects of polymeric material parameters on the actuating force of SMA are also discussed.

This paper focuses on the development of partial inverse compensation techniques for linear control design in systems employing magnetostrictive transducers operating in nonlinear and hysteretic regimes. At low drive levels, linear models can be used to characterize strains and forces generated by magnetostrictive transducers with reasonable accuracy. However, at the moderate to high drive levels where transducer performance is optimal, inherent constitutive nonlinearities and hysteresis must be accommodated to achieve the accuracy and speed requirements for high performance applications. Appropriate nonlinear and hysteretic modeling techniques are reviewed and an inverse compensator based on the nonlinear kernel of the model is developed. The performance of the technique is illustrated through numerical examples.

A model has been developed in MATLAB to design a new active, steerable end-effector. The end-effector design consists of a number of bimorph actuator sections in series with each active layer being individually controlled. Each section may behave as either a bimorph or a unimorph actuator, where in the case of unimorph one of the active layers is passive. By varying the strength and direction of the electric field across each section, a prescribed overall shape can be achieved to allow the user to steer the device. The focus of ths paper is on the model of the end-effector using electroactive polymer (EAP) materials. In the EAP model, the experimental data for the electrostrictive P(VDF-TrFE) copolymer is used to model the non-linear relationship between the electric field and the induced strain. Due to the large deflections achievable with the EAP, a pseudo rigid-body model for large deflections beams is also used. The behavior of piezoelectric ceramic is compared to that of electro-active polymer (EAP). The target application for this steerable device is a small-scale smart surgical instrument for minimally invasive surgery.

Vibration and stability feedback control of a robotic manipulator modeled as a cantilevered thin-walled beam carrying a spinning rotor at its tip are investigated. The control is achieved via incorporation of adaptive capabilities that are provided by a system of piezoactuators bonded or embedded into the master structure. Based on converse piezoelectric effect, the piezoactuators produce a localized strain field in response to an applied voltage, and as a result, an adaptive change of vibrational and stability response characteristics is obtained. A feedback control law relating the piezoelectrically induced bending moments at the beam tip with the kinematical response quantities appropriately selected is used, and the beneficial effects of this control methodology upon the closed-loop eigenvibration characteristics and stability boundaries are highlighted. The cantilevered structure modeled as a thin-walled beam, and built-up from a composite material, encompasses on-classical features, such as anisotropy, transverse shear and secondary warping, and in this context a special ply-angle configuration inducing a structural coupling between flapping-lagging transverse shear is implemented. It is also shown that the directionality property of the material of the host structure used in conjunction with piezoelectric strain actuation capability, yields a dramatic enhancement of both the vibrational and stability behavior of the considered structural system.

Piezoelectric motors consist essentially of a coupling structure actuated by two or more piezoceramics excited with different phases. The actuated piezoceramics deform the coupling structure which moves due to friction over a fixed structure, called stator. The motor performance is related to the displacement generated by the motor in the moving direction and clamping force between the coupling structure and stator. Both quantities depend on the distribution of flexibility and stiffness in the coupling structure domain, which is related to coupling structure topology. By designing other types of coupling structures connected to the piezoceramics, novel types of piezoelectric motors with enhanced performance can be obtained. In this work, topology optimization is applied to design piezoelectric motors. Topology optimization is a general computer design method applied to design optimal structural topology that improves a specified objective function in according to some constraints. The optimization problem is posed as the design of a flexible structure coupled to the piezoceramics that maximizes the output displacement and clamping force in a specified point of the domain and direction. The design of a quasi-static inchworm-type piezoelectric motor is presented to illustrate the implementation of the method.

A piezoelectric traveling-wave motor model has been developed with parameters entirely related to physical properties. The approach is well-rooted in the formulation suggested earlier by Hagood and McFarland, but several model improvements have been integrated in an effort to realize an accurate model suited for automated design optimization. Additional model considerations include a flexible rotor model and a hysteretic stick-slip friction contact model which replace the previous assumptions of a rigid rotor and pure slip. The most notable contribution has been the use of lossy (complex) material properties to account for inherent material losses, supplanting the use of non-physical damping coefficients. The model is partly formulated in the frequency domain, and by representing the modal states and forces as Fourier series expansions and retaining higher harmonic terms, it has been generalized to account for non-ideal traveling-wave excitation. Needing to simulate the hysteretic contact model in the time domain, a mixed-domain solution procedure has been implemented to maintain some of the computational efficiency of frequency domain analysis. A preliminary validation study has demonstrated excellent correlation between simulation results and experimental data for a commercial motor.

This paper deals with a fully coupled assumed strain solid element that can be used for simultaneous moiling of thin sensors and actuators. To solve fully coupled field problems, electric potential is regarded as a nodal degree of freedom in addition to three translations in an eighteen node assumed strain solid element. Therefore, the induced electric potential can be calculated for a prescribed deformation or an applied load. Since the original assumed strain solid element is free of locking, the element can be used to analyze behavior of very thin actuators without locking. Numerical examples, such as a typical bimorph actuator/sensor beam problem shows that the present element can handle fully coupled problems. Using the solid element, we have analyzed the actuation performance of THUNDER and compared the result with measured data. The comparison shows that the numerical estimation agrees well with measured displacement for simply supported boundary condition. It is also found that a particular combination of materials for layers and curvature of THUNDER improve actuation displacement.

This paper introduces a model for a vibration control system in which spatially etched Polyvinylidene Fluoride (PVDF) was utilized to implement uniform damping control on a distributed system. Uniform damping node control (UDNC) theory states that near optimal vibration control can be achieved when the following criteria are met: all modes are damped at the same exponential decay rate, the open loop and closed loop natural frequencies of the structure are identical, and the closed loop modal shapes are identical to the open loop modal shapes. To help accomplish this, in a system with N modes participating in a response, sensor/actuator pairs are placed at the nodes of the N+1 mode. Spatially shaded PVDF actuators are distributed actuators that produce pseudo discrete forces due to the special weighting applied to the etched electrodes. The system was implemented using a spring steel cantilevered beam and spatially etched PVDF actuators which were placed according to nodal control theory (NCT). When given the set of gains that are attributed to UDNC, the modes de-couple, reducing spillover. This experiment marks the first time that distributed control techniques such as uniform damping control were realized in a discrete fashion by utilizing spatially shaded piezoelectric actuators.

The design of active structures requires numerous design tasks to be performed. One of these is the placement of the sensors and actuators. For complex structures this leads to a complicated optimization process. In this paper, an analytical method to evaluate the effectiveness of the position of one or more actuators respectively sensors will be presented. It is based on a modal description of the system and the differential equations of motion. Subsequently a genetic and a search algorithm are used to find the optimal locations for piezoceramic patches. This is done for one actuator on a flat rectangular plate as a benchmark test, where the optimization results are compared to a complete search of all possible locations. In a second case two active elements are positioned to obtain the optimal locations for the control of the first eight eigenmodes. This represents a case where the complete enumeration of the search space is infeasible. A comparison of the tested optimization methods and the proposal of a procedure for optimal placement of active elements will conclude the paper.

Recent work investigating the use of Lamb-wave propagation to detect and localize damage in composite structures has produced some very encouraging results. Lamb-waves are launched form piezoceramic actuators and the resulting signals are recorded at piezoceramic sensors at various locations on the structure. When damage is introduced into the structure, the Lamb-wave will be modified in some potentially complicated matter. The extent of this modification will be dependent upon the proximity of the damage location to the relevant actuator/sensor path. The purpose of this paper is to propose a strategy for the location of piezoceramic actuators and sensors so as to provide optimum damage detection coverage of the structure. The method used is a differential evolution algorithm constructed so as to minimize a cost function based on either an angular of Lamb-wave propagation distance approach. More complicated effects such as attenuation, edge reflection, orientation of fibers in the structure may be taken into account using this approach. Known trouble spots in the structure may also be given greater priority in a straightforward manner and also components known to cause propagation problems, such as stringers or riveted joints, can be accommodated.

The problems of bending and vibrations of transversely - polarized thin piezoelectric cantilever plates are considered. The classical theory of thin plates is assumed to be valid concerning the stress-strain state of the plate. Upon the electric field no hypotheses are taken. It is only assumed that the potential of the electric field can be expressed as a sum of symmetric and asymmetric functions with respect to the transverse coordinate. In general case the problems of generalized plane stress state and the bending problem are coupled through electric boundary conditions. However, under certain electric boundary conditions the equations of generalized plane stress state together with the asymmetric part of the potential of the field are separated from those of the bending problem with the symmetric part of the electrostatic potential. The bending problem of the cantilever plate is considered when arbitrary electrostatic potential is given on the facial surfaces of the plate. The problem is solved also for different cases of electrostatic potential. The results are compared with those obtained by solving the problem with a certain hypothesis for the electric field potential. The planar and transverse vibrations of the plate are studied, under periodically varying in time electrostatic potential, given on the facial surfaces of the plate.

Efficiency in high speed mechanism can be further increased by use of lightweight construction. But quite often these structures have the drawback of being susceptible to vibrations. This can be overcome by applying the technology of smart structures. Here distributed actuators and sensors made from piezoceramic (PZT) material are capable to actively reduce the unwelcome vibrations if implemented within a control loop. For the optimal design of such kind of mechanism up-to-date simulation tools have to be developed further. To simulate the dynamic behavior of lightweight structures undergoing large motions the multibody approach is a suitable tool. The necessary parameters in the equations of motion for the flexible body can be calculated from the output of a finite element code. The large number of variables from the finite element model have to be reduced to only a few generalized coordinates. Therefore a modal reduction is applied in combination with the introduction of a moving frame of reference. Beyond this technique so called active modes are introduced to represent the impact of the active strain by the PZT patches. These active modes combined with natural modes represent the body deformation within the multibody model.

Template regularization embeds the problem of class separability. In the machine vision perspective, this problem is critical when a textural classification procedure is applied to non-stationary pattern mosaic images. These applications often present low accuracy performance due to disturbance of the classifiers produced by exogenous or endogenous signal regularity perturbations. Natural scene imaging, where the images present certain degree of homogeneity in terms of texture element size or shape (primitives) shows a variety of behaviors, especially varying the preferential spatial directionality. The space-time image pattern characterization is only solved if classification procedures are designed considering the most robust tools within a parallel and hardware perspective. The results to be compared in this paper are obtained using a framework based on multi-resolution, frame and hypothesis approach. Two strategies for the bank of Gabor filters applications are considered: adaptive strategy using the KL transform and fix configuration strategy. The regularization under discussion is accomplished in the pyramid building system instance. The filterings are steering Gaussians controlled by free parameters which are adjusted in accordance with a feedback process driven by hints obtained from sequence of frames interaction functionals pos-processed in the training process and including classification of training set samples as examples. Besides these adjustments there is continuous input data sensitive adaptiveness. The experimental result assessments are focused on two basic issues: Bhattacharyya distance as pattern characterization feature and the combination of KL transform as feature selection and adaptive criterion with the regularization of the pattern Bhattacharyya distance functional (BDF) behavior, using the BDF state separability and symmetry as the main indicators of an optimum framework parameter configuration.

Advances in smart materials and structures technology, especially in applications of Shape Memory Alloys (SMA) as actuators and vibration isolation devices require understanding of the nonlinear hysteretic response found in SMAs. SMA hysteresis can be modeled either through constitutive models based on physical material parameters or through models based on system identification. In this work, a simplified material model for the pseudoelastic response of SMAs is presented, suitable for vibration isolation applications. Response obtained from the simplified model is compared with the response obtained from an existing thermodynamic constitutive SMA model and the results from the two models are found to match well. The computation time required by the simplified model was approximately seven times faster compared with the thermodynamic constitutive model. The simplified model is utilized to simulate a single degree of freedom mass-SMA system where the SMA acts as a passive vibration isolation device, showing a substantial reduction in displacement transmissibility.