We explore two issues related to metastable systems relevant to shape-memory alloys with highly mobile, complex, and easily transformed microstructure. The first is an approach towards modeling of the system interactions across a wide range of length scales, termed a hierarchy of scales approach. The second relates to possible dynamical principles and, in particular, hysteresis. We suggest that the metastability is governed in the weak topology and evolution is determined by a solution to the Fokker-Planck Equation.

The electrical transport properties of many smart composites and other technologically important materials are dominated by the connectedness, or percolation properties of a particular component. Predicting the critical behavior of such media near their percolation threshold, where one typically obtains the most interesting and useful material properties, is a formidable challenge, and not well understood from a modeling perspective. Here we report on recent mathematical results on lattice and continuum percolation models of these types of materials. In particular, we have found a direct, analytic correspondence between the critical behavior of transport in two component random media around a percolation threshold, and the critical behavior exhibited by phase transitions in statistical mechanics, such as by the magnetization of a ferromagnet around its Curie point. This correspondence has been used to establish that the critical exponents for DC conduction ear a percolation threshold, for both lattice and continuum systems, satisfy the same scaling relations as their counterparts in statistical mechanics. Underlying our correspondence is an integral representation for the effective conductivity, which has exactly the same mathematical form as a corresponding representation for the magnetization of an Ising ferromagnet. The integral representation applies in general to many classical transport coefficients for two component media, and we have used it to obtain rigorous insulator-conductor composites is investigated here, and even when the inclusions are near to touching, the new bounds give a dramatic improvement over the complex versions of the fixed volume fraction and Hashin-Shtrikman bounds found independently by Milton and Bergman in the late 1970's.

Martensitic transformations are shape-deforming phase transitions which can be induced in certain alloys as a result of changes in the imposed strains, stresses or temperatures. The interest in these alloys, which undergo a shape-deforming phase transition form a high temperature phase to a low temperature phase, stems in part from their applicability as elements in active structures. In this paper we focus on the energy transfers that accompany the martensitic phase change. We discuss, in three concrete examples, the ways in which temperature, together with the elastic and dissipated energies, determine the equilibria as well as the quasi-static dynamics in martensites. Thus, in (xi) 1 we consider the pseudoelastic hysteresis in shape- memory wires; our treatment draws from (7, 3). In (xi) 2, on the other hand, we follow and discuss equilibrium configurations in polycrystalline martensitic polycrystals. In (xi) 3, finally, we present some new theoretical computations for certain typical microstructural lengthscales, the twin widths, observed in single- crystalline martensite twinning.

Neural network based controllers for vibration suppression of smart structural systems have been reported in several recent studies. These studies have shown that in addition to conventional controller design methodologies, neural networks offer an effective basis for design and implementation of controllers. With the introduction of neural network chips like the electronically trainable analog neural network (ETANN) chip i80170NX by Intel and the Ni1000 chip by Nestor Corp., stand alone hardware implementation of neural network based controllers is possible. In this paper the capabilities of Intel's ETANN chip to implement linear and nonlinear controllers for smart structural systems have been investigated. A neural network based optimizing controller design methodology that integrates the ETANN chip and its capabilities of on-line adaptation has been developed. Apriori information of the smart structural systems such as actuator/sensor bandwidth limits and control effort limits can be directly accommodated in this method. Simulation studies of the performance of a closed loop time varying linear and nonlinear system has also been presented with and without on-line adaptation.

Two adaptive algorithms that reject narrowband disturbances of unknown frequency are compared. The first is based on an adaptive implementation of the internal model principle. The second is based on a phase-locked loop structure and generates a signal whose magnitude and phase match those of the disturbance. The adaptive internal model principle algorithm provides global stability under ideal conditions, tracks reference inputs, and can stabilize unstable plants. However, the algorithm suffers from convergence and robustness problems in simulations and does not appear to be well-suited to high-order systems or systems with unknown time delays, two situations that are typically encountered in active noise control applications. The algorithm based on the phase-locked loop concept has better convergence and robustness properties and can be applied to aborad range of stable systems. Some prior information is required about the magnitude and frequency of the disturbance and about the frequency response of the plant, however. A real-time implementation of the phase-locked loop scheme in an active noise control task provides a 25 dB reduction of a sinusoidal tone of unknown frequency.

Smart structures include active control elements, hence the integration of structure design with control design in inevitable. This paper provides a step in this integration in order to achieve optimal performance. The approach presented here solves a mixed passive and active control problem with performances characterized by the so-called mixed H₂/H_(infinity ) performances.

Sound radiation from a plate into an acoustic cavity is controlled using patches of active piezoelectric-damping composites (APDC). The APDC, under consideration, consists of piezoelectric fibers embedded across the thickness of a visco-elastic matrix in order to control the compressional damping characteristics of the composite. The effectiveness of the APDC treatments in attenuating the sound radiation from thin plates into cavities is demonstrated theoretically and experimentally. A finite element model (FEM) is developed to describe the dynamic interaction between the plate, the APDC patches and the acoustic cavity. The FEM is used to predict the dynamics of the plate/acoustic cavity and the sound pressure distribution for different control strategies. The predictions of the FEM are validated experimentally using a square aluminum plate whose sides are 29.8 cm and thickness of 0.04 cm. The plate is mounted on a 29.8 cm $ MUL 29.8 cm X 75 cm cavity. The test plate is treated with a single APDC patch placed at the plate center. The patch is 5 cm X 5 cm X 0.03125 cm which is made of 15-25 percent lead zirconate titanate fibers embedded in soft and hard polymeric resin matrices and provided with silver-epoxy electrodes. Vibration and sound pressure level attenuations of about 70 percent are obtained a the plate/cavity first mode of vibration, with a maximum control voltage of 330 volts using a derivative feedback controller. Such attenuations are attributed to the effectiveness of the APDC treatment in increasing the modal damping ratios by about a factor of four over those of conventional passive constrained layer damping treatments. Comparisons between the theoretical predictions of the FEM with the experimental results indicate close agreement between theory and experiments. The obtained results suggest the potential of the APDC treatments in controlling the sound radiation from plates into acoustic cavities. Such potential can be exploited in many critical applications such as cabins of aircrafts and automobiles to ensure quiet environment for the occupants.

The deformation of adaptive composite with active polydomain components has been calculated by finite element modeling (FEM). The average deformation, the distribution of stresses and the elastic energy of the composite as a function of different extent of twinning of the composite active component are calculated. Comparing the results of the FEM with the results of the analytical theory demonstrates the effect of the microstresses on the mechanics of the adaptive composite.

A finite element approach for modeling phase transitions in electro-mechanically coupled material is presented. The approach is applicable to modeling a broad range of material behavior, including repolarizations in ferroelectrics (PZTs) as well as ferroelectric-antiferroelectric phase transitions in electroceramics such as lead lanthanum zirconate stannate titanate. A 3D 4 node hybrid element has been formulated. In addition to nodal displacement and voltage degrees of freedom used in conventional coupled elements, the hybrid element also utilizes internal electric displacement degrees of freedom, resulting in improved numerical efficiency. The elements utilize energy based nonlinear constitutive relations for more accurate representation of material response at high electric fields. The phase/polarization state of each element is represented by internal variable,s which are updated at each simulation step based on a phenomenological mode. The material model has been roughly fitted to response of PZT-5H under free strain conditions. The model reproduces strain and electric displacement hysteresis loops observed in the material. The hybrid finite element model results are demonstrated for a complex geometry with non-uniform fields.

A 3D finite element closed loop model is presented for modeling smart structures to predict the effects of both active and active/passive damping on vibrating structures. A comprehensive finite element formulation is presented that includes a control algorithm to relate the sensor voltage to the actuator voltage in a closed lop. Two control approaches based on charge or voltage as the active control force applied to the actuator are studied in the time and frequency domains. Constant velocity and constant displacement feedback control algorithms are subsequently implemented to investigate vibration controllability of structures. A model superposition in conjunction with direct integration is used in the time domain to overcome the numerical difficulties associated with an unsymmetric active damping matrix. A parametric study considers different types of controller as well as feedback gain. Comparisons are made between active constrained layer damping (ACLD) and purely active damping in the frequency domain. Some design studies are presented which examine the performance of ACLD modeling as a function of gain and viscoelastic materials thickness.

This paper presents an integrated finite element-control methodology for the design/analysis of smart composite structures. The method forms part of an effort to develop an integrated computational tool that includes finite element modeling; control algorithms; and deterministic, fuzzy and probabilistic optimization and integrity assessment of the structures and control systems. The finite element analysis is based on a 20 node thermopiezoelectric composite element for modeling the composite structure with surface bonded piezoelectric sensors and actuators; and control is based on the linear quadratic regulator and the independent modal space control methods. The method has been implemented in a computer code called SMARTCOM. Several example problems have been used to verify various aspects of the formulations and the analysis results from the present study compare well against other numerical or experimental results. Being based on the finite element method, the present formation can be conveniently used for the analysis and design of smart composite structures with complex geometrical configurations and loadings.

A soft PZT was subjected to cyclic loading at its resonance frequency. Both the piezoelectric coefficient, d₃₁, and the transverse coupling coefficient, k₃₁, decreased in a manner consistent with 90 degrees and 180 degrees domain reorientation, with the greatest decrease coinciding with the largest stress and temperature. In contrast, for high loads and temperatures, the elastic compliance, S₁₁^E, and the dielectric constant, K₃₃ decreased in a manner consistent with increased, rather than decreased, alignment of the c-axes.

As in many cases piezoelectric devices are made of PZT, it is our objective to incorporate the nonlinearly coupled electro-mechanical behavior of ferroelectric PZT-ceramics into a finite element tool for reliability analyses. In this paper, we will present a phenomenological model for ferroelectrics which is conceived to be valid for complex electro-mechanical loading histories and simple enough to be implemented with acceptable effort in an FE-code. This has been achieved by introducing irreversible polarization and irreversible strain as internal variables besides stress, strain, electric field and polarization. The internal variables represent the loading history and are governed by ordinary differential equations. Each of these evolution equations is subjected to two loading conditions differing in nature. The first indicates the onset of irreversible change by domain switching, while the second characterizes the maximum amount of possible irreversible change corresponding to a totally switched domain structure. Polarization induced anisotropy is taken into account to the extent deemed necessary. For sake of simplicity, no rate effects are included. The model response to uniaxial electro-mechanical loading histories will be discussed and compared to known experimental results. By bilinear approximation the following characteristic macroscopic phenomena of PZT-ceramics can be represented: dielectric hysteresis, polarization induced piezoelectricity, butterfly hysteresis, ferroelastic hysteresis, mechanical depolarization, field dependent coercitive stress.

The development of ferroelectric ceramics is driven by the needs for functional materials used in a very broad range. The most striking features of ferroelectric ceramics are strong electromechanical coupling effect and the prompt response to applied electric fields. These properties have render ferroelectric ceramics desirable for designing smart actuators for active control applications (Newnham and Ruschau 1996) . The major obstacle in actuator applications of ferroelectric ceramics is the so-called electric fatigue, referring to deterioration, under cyclic electric loading, of macroscopic properties, such as the actuation force or the actuation strain. Experimental observation indicates that fatigued ferroelectric specimens often contain scattered microcracks, i.e., cracks of size comparable to the average grain size which is in the range of 2 '-S-'8for commercial PZT ceramics, the most commonly-used ferroelectric materials in actuator applications. The main thrust of this work is to understand the correlation between cracking at the grain level and deterioration of macroscopic properties.

Tensegrity structures represent a special class of tendon space structures, whose members may simultaneously perform the functions of strength, sensing, actuating and feedback control. Thus, these structures ideally match the definition of smart structures. This paper introduces the concept of controllable tensegrity as a new class of smart structures capable of large displacement. The kinematics and nonlinear dynamics of one element of this class is derived and analyzed. Pre-stressability conditions are given and a particular equilibrium identified. The equations of motion are then linearized about this equilibrium and linear parametric models generated. These are next used for controller design. For control system design some of the tendons are chosen as actuators and some as sensors and a family of dynamic controllers designed such that the control energy is minimized while requiring output variance constraints to be satisfied. Another family of controllers is designed such that the output variance is minimized while requiring input variance constraints to be satisfied. The performances of these controllers are evaluated.

A brief discussion on systems where simultaneous control of forces and velocities are desirable is given and an example linkage with revolute and prismatic joint is selected for further analysis. The Newton-Euler approach for dynamic system analysis is applied to the example to provide a basis of comparison. Gauge invariant transformations are used to convert the dynamic equations into invariant form suitable for use in a new dynamic system analysis method known as the motion-effort approach. This approach uses constraint elimination techniques based on singular value decompositions to recast the invariant form of dynamic system equations into orthogonal sets of motion and effort equations. Desired motions and constraining efforts are partitioned into ideally obtainable and unobtainable portions which are then used to determine the required actuation. The method is applied to the example system and an analytic estimate to its success is made.

We consider a model arising in structural acoustic problems which is comprised of an acoustic chamber with flexible walls to which piezo-ceramic devices are attached. The deices play the role of actuators and sensors for the model. The mathematical description of the model is governed by a coupled system of partial differential equations involving the wave equation coupled with a nonlinear dynamic shell equation. The main aim is to reduce a pressure/noise in the cabin by the appropriate activation of piezo-ceramic devices. The assumed periodic nature of the disturbance, leads naturally to the formulation of a periodic control problem. This, in turn, is strongly linked to the problem of stabilizability of the original model. Thus, the goal of this paper is to present new results on (i) uniform stabilizability of the structural acoustic model with passive damping applied to the boundary of the acoustic chamber, and (ii) an optimal control problem with 'smart' controls activated by piezo-ceramic patches creating suitable bending moments in the structure. The control algorithm is constructed in a feedback from via a solution of a suitable Riccati type equation. One of our results shows the boundedness of the feedback gains in spite of the strong unboundedness of the control operators. This is due to the 'regularizing' effects of shell dynamics which are partially propagated into the 'hyperbolic' component of the structure.

Using a generally accepted model we present a comprehensive analysis of an Euler-Bernoulli beam with PZT sensor-actuator and pure rate feedback. The emphasis is on the root locus - the dependence of the attainable damping on the feedback gain. There is a critical value of the gain beyond which the damping decreases to zero. We construct the time-domain response using semigroup theory, and show that the eigenfunctions form a Riesz basis, leading to a 'modal' expansion.

In the present investigation, the helicopter blade is modeled as a rotating beam with two degrees of freedom, namely the elastic flatwise bending and torsion. A mathematical model in the frequency domain is developed, incorporating the unsteady aerodynamic loads associated with helicopters in forward flight. The effects of dynamic adaptation of the rot boundary conditions on the beam aeroelastic response are studied. The results suggest that it is possible to control the local dynamic response at particular sections of the beam by varying the frequency and relative phase of the control signal.

The reliable use of piezoelectric ceramics as actuators in smart structures hinges on a fundamental understanding of the fracture process in these materials. However, despite the success of fracture mechanics theories in explaining the cracking behavior of a wide range of engineering materials, the extension of these accepted criteria to piezoelectrics fails to predict even qualitatively their response to combined electrical and mechanical loads. A new fracture criterion is presented here, in which a multiscale point of view is adopted in order to account for a zone of combined mechanical brittleness and electrical ductility near the crack tip. As a starting point for the investigations, we assume that the region of electrical nonlinearity is confined to aline segment ahead of the crack, analogous to the Dugdatle zone of plasticity in metals. This mathematical simplification represents the physical situation in which a distribution of excess electric dipoles is aligned on a finite segment in an otherwise linear piezoelectric solid. By applying this model to both insulated and conducting cracks subjected to far-field loading, we obtain local-scale energy release rates whose dependence on applied tractions and electric fields agrees with the trends observed experimentally. One important feature of the analytical expressions for crack driving force is that they are independent of the strength and size of the nonlinear zone.

The magneto-mechanical properties of Terfenol-D thin films deposited on Si substrates were studied by magnetic and mechanical measurements of film/substrate cantilevers. The (Delta) E effect and mechanical damping of the film were measured simultaneously. The stress in the film was controlled by annealing and deposition at different temperatures as well by the selection of the substrate material below the recrystallization temperature and determined to vary from -500 MPa, compression, in as deposited films to +480 MPa, tension, in annealed films. This paper highlights the magneto-mechanical response of tensioned 1 micrometers nanocrystalline Terfenol-D films on 50 $mUm Si substrates display a pronounced damping maximum at a magnetic field of about 1.5kOe oriented perpendicular to the plane of the film. The phenomenon is critically dependent on the orientation of the magnetic field and is the result of a magneto-mechanical instability in the Terfenol film.

Shape memory alloy (SMA) wires can be embedded in a host material to alter the stiffness or modal response and provide vibration control. The interaction between the embedded SMA and the host material is critical to applications requiring transfer of loads or strain from the wire to the host. Although there has been a significant amount of research dedicated to characterizing and modeling the response of SMA alone, little research has focused on the transformation behavior of embedded SMAs. Photoelastic experiments with SMA wires in polymer matrices had previously provided a qualitative understanding of stress transfer in SMA composites. In the current work, 2D photoelasticity is utilized to quantify the internal stresses induced by the actuation of a thin SMA ribbon in a pure polymer matrix. Through the use of a CCD camera and a frame grabber, photoelastic images are digitally recorded at discrete time increments. Shear stresses induced during the actuation are calculated as a function of time. Computational predictions of shear stress are made using finite element analysis and compared with experimental observations.

We model in this work a thermoelectrically cooled thin SMA layer extensional actuator as a first step towards the design of a high frequency, high force, large strain shape memory alloy (SMA) actuator. The thermoelectric Peltier effect is used to alternately heat/cool the SMA, leading to cyclic phase transformation. The effect of variable actuating load and constant load applied as boundary conditions on the SMA actuator are considered. The frequency response is of interest as also are performance measures like energy conversion efficiency and the energy output per unit volume of active material. based on these measures, the proposed actuator is compared with other various commercially available actuators. The analysis points to the possibility that micron-thick SMA layers, with a low transformation hysteresis and undergoing partial transformation, can deliver frequencies of around 30 Hz at peak stresses of about 145 MPa.

Shape memory allow (SMA) components can affect vibrations of structures through two mechanisms. The stresses in a SMA element that experiences phase transformations, as a result of vibrations, have an effect on the frequency-amplitude characteristics. In addition, a dissipation of energy due to hysteresis in a SMA element can reduce the natural frequency and affect forced vibrations. The present paper illustrates the mathematical foundations of these concepts. The method of solution of the equation of motion of flexible superelastic SMA dampers is discussed. Potential benefits to vibrating structures associated with a hysteresis in superelastic SMA dampers are illustrated. As follows from the results shown in the paper, the effectiveness of superelastic dampers increases with temperature, as long as the latter remains within the range where the martensite formation is possible.

In the area of underwater vehicle design, the development of highly maneuverable vehicles is presently of interest with their design being based on the swimming techniques and anatomic structure of fish; primarily the undulatory body motions, the highly controllable fins and the large aspect ratio lunatic tail. The tailoring and implementation of the accumulated knowledge into biomimetic vehicles is a task of multidisciplinary nature with two of the dominant fields being actuation and hydrodynamic control. Within this framework, we present here our progress towards the development of a type of biomimetic muscle that utilizes shape memory alloy (SMA) technology. The muscle is presently applied to the control of hydrodynamic forces and moments, including thrust generation, on a 2D hydrofoil. The main actuation elements are two sets of thin SMA wires embedded into an elastomeric element that provides the main structural support. Controlled heating and cooling of the two wire sets generates bi-direction bending of the elastomer, which in turn deflects or oscillates the trailing edge of the hydrofoil. The aquatic environment of the hydrofoil lends itself to cooling schemes that utilize the excellent heat transfer properties of water. The modeling of deflected shapes as a function of input current has been carried out using a thermomechanical constitutive model for SMA coupled with the elastic response of the elastomer. An approximate structural analysis model, as well as detailed FEM analysis has been performed and the model predictions are been compared with preliminary experimental measurements.

This study demonstrates the feasibility of developing an integrated assembly of accurate and robust simulation tools for intelligent structures. Limitations of existing numerical models and cost associated with experimental models motivated this research. The emphasis is placed on the incorporation of structural analysis, plant modeling, control algorithm synthesis, optimization and performance evaluation into a single software package. The present paper includes finite element formulation of a coupled electromechanical smart structure with piezoelectric sensors and actuators, implementation of control design and evaluation of candidate control laws on the basis of finite element discretization. The discretized model predicts both mechanical and electrical responses due to the electromechanical loading and generates sensor output equations. An optimal independent modal space control is implemented and a rudimentary finite element-control package is developed to evaluate the performance of candidate control laws.

Modeling of piezoelectric smart structures applied in a cabin noise problem is studied. Cubic shaped acoustic cavity with flat plate which covers one side is taken as the problem. Noise source locates outside of the box and the noise propagates into the interior region through the plate structure. Disk shaped piezoelectric actuators are mounted on the plate and the actuators are excited. The actuators will generate a proper response to reduce the pressure fields at a certain region in the cavity. The plate structure is modeled using finite element method which is based on a combination of 3D piezoelectric, flat shell and transition elements. The transition element connects the 3D and flat shell elements. Acoustic cavity is modeled using modal approach which represents the pressure fields in the cavity, finite element equation for the structure with the influence of acoustic cavity is derived. Once the structure response is found by solving the finite element equation, the pressure fields at the inside of the cavity are recovered directly. Numerical results show the pressure fields at the inside of the cavity are recovered directly. Numerical results show the pressure fields at the inside of the box. No activation results are examined at different frequencies to see the feasibility of the proposed modeling approach. When the actuators are activated, the results of pressure fields inside of the cavity show that the cabin noise at a certain zone inside the cavity can be reduced. Future works to improve cabin noise control performance are addressed.

A finite element model for aeroelasticity analysis of hypersonic panels, using a 9 degree-of-freedom discrete Kirchhoff Theory triangular element along with a 6 d.o.f inplane membrane element, had been developed in authors' previous work, and this model had been sued for the determination of flutter boundary. This paper intends to develop an optimal control strategy to suppress the panel flutter using piezoelectric material as actuators. Two pieces of piezoelectric patches are bonded at the both sides of the panel symmetrically. The actuator pair is assumed such that one laminate contracts, another expands, to create bending control moment. The original finite element model is modified to include the piezoelectric patches' effect. A modal reduction technique is used to reduce the number of modes involved, and to simplify the nonlinearity of the model. A quasi-linear optimal control approach is applied for optimal control design. Numerical result shows that active piezoactuator controller effectively delays the flutter to a relatively higher dynamic pressure.

A mathematical theory of electrical-mechanical modeling for systems governed by piezo-coupled behavior is investigated. To illustrate this new theory, piezo-coupled beams models are developed. The fully coupled energy balance equations, power flow are investigated for this model with a generalized admittance control architecture. The generalized admittance structure of the coupled system enables investigation into the co-dependency of actuator placements, control complexity and system performance.

The feasibility of employing a passive control methodology using piezoelectric actuators to control panel flutter is investigated. An electromechanical panel model containing distributed piezoelectric layers either bonded to the surface or embedded within the structure is used to control flutter. The performance of piezoelectric actuators is dependent on the mass to stiffness ratio, the configuration and placement of the actuators. The physical programming design optimization methodology to calculate the optimal actuator configuration is used. This approach reduces the computational intensity in large design optimization problems and completely eliminates the need for iterative weight setting.

Model predictive control (MPC) is a control method which uses future predicted outputs of a system to determine the inputs to the system. The predictive control methods are well suited for systems where model identification is difficult and expensive or where the parameters of the plant and environment change frequently. All of the predictive control methods are tracking controllers by nature. Most predictive control algorithms have been developed for use in the process control industry for set point tracking. The main advantage of MPC controllers over other tracking controllers is that they can act in advance of the actual time when there is a change in the set point. The use of predictive control for vibration suppression of smart structural systems investigated in this paper. For vibration suppression purposes, the set point of the predictive control is set to zero and the effect of the disturbances on the system performance is to be minimized. Many of the predictive control algorithms do not allow for the system output to substantially depart from its predicted values. However, the predictive controller proposed by Gawronski allow the prediction to converge to the correct value after a disturbance has occurred, even if the disturbance causes the output to oscillate as in the vibrations of smart structures. We have proposed a modification to the predictive control algorithms by incorporating the prescribed degree of stability concept in the design. In order to demonstrate the capabilities of the proposed predictive controllers, we have designed and implemented the controllers on two simple test structures. The experimental closed-loop response of single input/single output and multi-input/multi-output structures is presented in the paper. The response of the predictive control system is compared with that of Linear Quadratic Gaussian controllers. The advantages and limitations of the predictive controllers are discussed in the paper.

In this paper, a design approach for controlling a composite plate structure subject to aeroelastic loading using piezoelectric actuators and sensors is presented. The nature of the sensing variables is exploited and accommodated in the control design algorithm. The controller is a feedback controller that uses various measurements related to motion variables such as accelerations, velocities and displacements. Proposed controller designs in this paper are based on equivalent first order state-space baseline design gains that use existing control system design software. The proposed method provides different norms for controller gains, thereby allowing more flexibility in gain magnitudes and selection of sensors and still meet the time response specifications.

The goal of this paper is to examine the use of covariance control to directly design reduced-order multi-objective controllers for gust alleviation using adaptive materials as the control effector. It will use piezoelectric actuators as control effectors in a finite element model of a full-size wing model. More precisely, the finite element model is of the F-16 Agile Falcon/Active Flexible Wing that is modified to use piezoelectric actuators as control effectors. The paper will also examine the interacting roles of important control design constraints and objectives for designing an aeroservoelastic system. The paper will also present some results of multiobjective control design for the model, illustrating the benefits and complexity of modern practical control design for aeroservoelastic systems that use adaptive materials for actuation.

We consider a mathematical model of the noise reduction problem, which couples tow hyperbolic equations: the wave equation in the interior - which describes the unwanted acoustic waves - and a Kirchoff equation - which models the vibrations of the elastic wall. In past models, the elastic wall was modeled by an Euleri-Bernoulli equation with Kelvin-Voight damping. Our main result is a sharp regularity result, in two dual versions, of the resulting system of two coupled hyperbolic PDE's. With this regularity results established, one can then invoke a wealth of abstract results on optimal control problems, min-max game theory. The proof of the main result is based on combining technical results.

By adding a function of memory fading for past observation data to the Kalman filter which has often been used as a time marching identification algorithm we developed an adaptive Kalman filter scheme. The rate of memory fading was defined by a forgetting factor multiplying to pre- information term at each time step. In order to track fast variation in the system parameters the value of forgetting factor should be small. On the other hand, to remove the random noise from the signal, the number of sample points used at any time should be large enough, that is, the large value of forgetting factor should be used. There is, therefore, a trade-off between the time-tracking ability and the noise sensitivity of the identification. The Akaike- Bayes Information Criteria was applied to determine the optimal forgetting factor. Applications of the newly developed identification algorithm to a multi-degree of structural system with non-stationary dynamic characteristic worked out well.

The boundary element method is applied to problems of 3D piezoelectricity. The continuum equations for the mechanical and electrical behavior are combined into one governing equation for piezoelectricity. A single boundary integral equation is developed from this combined filed equation and the Green's solution for a piezoelectric medium. The Green's function and its derivatives are derived using the Radon transform, and the resulting solution is represented by a line integral which is evaluated numerically using standard Gaussian quadrature. The boundary integral equation is discretized using 8-node quadrilateral elements resulting in a matrix system of equations. The solution of the boundary problem for piezoelectric materials consists of elastic displacements, tractions, electric potentials and normal charge flux densities. The field solutions can be obtained once all boundary values have been determined. The accuracy of this piezoelectric boundary element method is illustrated with two numerical examples. The first involves a unit cube of material with an applied mechanical load. The second example consists of a spherical hole in an infinite piezoelectric body loaded by a unit traction on its boundary. Comparisons are made to the analytical solution for the cube and axisymmetric finite element results for the spherical hole. The boundary element method is shown to be an accurate solution procedure for general 3D piezoelectric materials problems.

Boundary element methods are attractive tools in the analysis of complex coupled problems. This method has been used in several engineering disciplines as a computationally efficient and versatile technique. Three boundary element methods that can be used to analyze linear electroelastic response of piezoelectric materials are presented in this paper. The three methods described in this paper are identified as the direct boundary element method, fictitious stress-electric charge method and the indirect boundary element method. The formulation of the three methods is discussed. Closed form solutions for the kernel functions appearing in the integral equations are also presented for the 2D case. The methods can be extended to 3D problems involving piecewise nonhomogeneous piezoelectric materials.

Disturbances attenuation, typically up to 200 Hz, onboard satellites is a key issue for advanced optical space systems with stringent spatial and temporal resolution requirements. Under ESA contract, Matra Marconi Space has conducted an ambitious proof-of-concept programme aiming at designing and demonstrating through prototypes and test innovative active vibration damping systems. In particular, a centralized anti-phase control (APC) system operating on distributed sensors and actuators to compensate stationary harmonic disturbances has been breadboarded and tested. The APC algorithm involves three major functions: (i) extraction of the harmonics signal by synchronous demodulation, (ii) identification of the complex gains between sensors and actuators using a recursive least squares algorithm, and (iii) anti-phase computation. The control algorithm has been implemented on a real-time test bench based on a fast DSP computer. The experiment has been performed on an engineering model of a representative space platform, namely MARCOTS. The measured performances, i.e. harmonic rejection at the controlled frequencies, range from 20 to 40 dB and are consistent with predictions from numerical simulations. Finally, a major advantage of the APC algorithm is intrinsic robustness to actuator failures, without performance impact for a single failure and 10 dB degradation for a double failure.

Shape memory alloy (SMA) actuators can be heated quickly using electrical resistance heating. However, the slow cooling of the SMA actuator limits the actuation frequency. Therefore, the current research was undertaken to increase the actuation frequency by making a SMA heat pipe. The heat pipe is a hollow NiTi SMA cylinder partially filled with a wick and water. The condenser end of the pipe is maintained at 5C. The evaporator was cycled between a temperature below Ms and above As by adding electrical current when necessary. A pipe partially filled with water cycled faster than both a dry pipe and a fully filled pipe. Thus, the heat pipe allows for faster cycling of SMA actuators with no need for complicated or moving parts. However, the heat pipe works best with a constant temperature difference between the evaporator and the condenser, whereas the SMA must cycle. Therefore, the heat pipe is best suited to SMA materials with a small difference between the Mf and the Af temperatures.

Uniaxial deformation of an adaptive material which can change its microstructure due to a phase transformation is considered. At fixed temperature and fixed surface displacement the phase transformation results in an equilibrium two-phase mixture. A typical equilibrium two- phase microstructure of an initial and a product phase is an alteration of the plane-parallel layers of the phases with a special crystallographic orientation of interfaces between layers. The relative fractions of the phases are determined by the external conditions. The two-phase free energy is a non-convex function of constrained strain. Therefore, the stress-strain relation at displacement controlled deformation of the transforming two-phase mixture is characterized by a negative Young's modulus. If deformation proceeds under stress control, a hysteretic stress-strain curve on loading and unloading should be observed instead of a negative stress-strain slope.

Layer composites containing adaptive polydomain components are considered. Polydomain structures can be result of constrained phase transformation. Polydomain structures consist of periodically alternating layers of different phases or differently oriented domains of product phase. The domain interface movement enables an additional mode of deformation. The theory predicts unusual physic and mechanical properties of composites, particularly, considerable decrease of the effective elastic moduli of composites, nonlinear stress-strain relations, critical behavior at decreasing thickness of an active layer. For ferroelectric or ferromagnetic polydomain components superelasticity can be governed and stiffed by the bias electric or magnetic field.

A general formulation for coupled thermomechanical shape memory alloys is presented in the context of the finite element method. AN internal variable formalism is adopted for the evolution of the martensite fraction at the microstructural level. In particular the response of material under partial loading/unloading conditions at various temperature ranges is modeled. An isothermal fractional-step method is utilized for the solution of the coupled problem, in which the development and implementation of the mechanical and thermal parts of the problem are discussed. In this report our attention is restricted to the area of geometrically linear quasi-static problems. Specifically, we investigate the proposed formulation in the setting of a truss element and show its extension to multiple dimensions. Representative numerical simulations of full and partial load cycles show favorable performance of the formulation, for all admissible regions in stress- temperature space.

We obtain a simple model for the eletromechanical motion of a linear piezoelectric rod with quasi-static domain switching. We start from the 3D linear piezoelasticity and by using suitable mechanical internal constraints and electrical semi-inverse hypotheses, we arrive at a 1D enthalpy functional. By using standard variational techniques then we get 1D equations of motion for extension and bending which show the coupling between the mechanical and electrical properties of the material.

The problems of the mathematical modeling and dynamical behavior of rotating blades carrying a tip mass and incorporating adaptive capabilities are considered. The blade is modeled as a thin-walled beam which encompasses features such as the anisotropy, transverse shear, secondary warping and includes the centrifugal and Coriolis force fields. In addition, the adaptive capabilities provided by a system of piezoactuators bonded or embedded into the structure are also implemented. Based on the converse piezoelectric effect, the piezoactuators produce a localized strain field in response to an applied voltage, and as a result, an adaptive change of the dynamic response characteristics is obtained. A combined feedback control law relating the piezoelectrically induced bending moment at the beam tip with the kinematical response quantities appropriately selected is used, and its beneficial effects upon the closed-loop eigenvibration characteristics are highlighted.

This paper presents an exact solution for the stresses in an infinite shape memory alloy plate with a circular hole subjected to biaxial tensile stresses applied at infinity. The solution obtained by assumption of plane stress is based on the 2D version of the Tanaka constitutive law for shape memory materials. The plate is in the austenitic phase, prior to the application of external stresses. However, as a result of tensile loading, stress-induced martensite forms, beginning from the boundary of the hole and extending into the interior, as the load continues to increase. Therefore, in general case, the plate consists of there annular regions: the inner region of pure martensite, the intermediate region where martensite and austenite coexist, and the outer region of pure austenite. The boundaries between these annular regions can be found as functions of the external stress. Two methods of solution are presented. The first is a closed-form approach based on a replacement of the actual distribution of the martensitic fraction by a piece-wise constant function of the radial coordinate. The second method results in an exact solution obtained by assumption that the ratio between the radial and circumferential stresses in the region where austenite and martensite coexist is governed by the same relationship as that in the encompassing regions of pure austenite and pure martensite.

The vibrational and dynamic response control of cantilevers carrying externally mounted stores is investigated. The cantilevered structure is modeled as a thin-walled beam of arbitrary cross-section and incorporates a number of non- classical effects such as transverse shear, secondary warping, anisotropy of constituent materials and heterogeneity of the construction. The control is carried out via a dynamic bending moment applied at the tip of the structure. A feedback control law relating the boundary moment with one of the kinematical variables characterizing the response of the beam is implemented, and its results upon the closed-loop eigenfrequencies and dynamic response are highlighted. The obtained numerical results emphasize the efficiency of this control methodology to enhance, without weight penalties, vibrational and dynamic response behavior and inhibit and even suppress the occurrence of the resonance phenomenon.

We study dynamic deformations of a neo-Hookean composite plate with PZT sensors and actuators bonded to its top and bottom surfaces. The constitutive relation for the PZT is taken to be linear in the Green-Lagrange strain tensor but quadratic in the driving voltage. It is shown that a simple feedback algorithm suffices to control the deformations of the plate.

The accurate control of a system that exhibits hysteresis requires a control strategy that incorporates some form of compensation for the hysteresis. One approach is to develop a compensator based on an inverse hysteresis operator. If this can be accomplished, the composite operation will produce a linear relationship between the input and output. Thus, an open loop control can be developed in which the inverse operation adjusts the system input to compensate for the hysteresis in the physical system. One difficulty lies in developing a model of the hysteresis for which an inverse operator can be obtained. In this work, a system with hysteresis in modeled by a classical Preisach model. We show that in the case of certain bivariate distributions, a closed-form formula for the inverse operator can be obtained. The concept is illustrated by a computer simulation.

The mechanical behavior of shape memory alloys (SMA) can be separated into two distinct categories: the shape memory effect and the superelastic effect. When loaded, the superelastic SMA undergoes a stress-induced martensitic transformation that will result in a large recoverable strain. Upon unloading, the undergoes a large hysteresis loop that makes the superelastic SMA an excellent candidate for strain energy absorption. This large strain energy absorption capability has been used to improve the impact tolerance of composites in related work. It is to further understand this strain energy absorption capability in composites that a 1D model to evaluate the energy absorption of superelastic shape memory alloy under bending and tension loading is developed using the Euler-Bernoulli beam theory. This theoretical model gives quantitative relations between the martensite fraction, the applied load, and the strain energy absorbed in the SMA. As expected, the superelastic SMA as demonstrated a very high strain energy absorption capability, demonstrating the advantage of using superelastic SMA to absorb strain energy. The closed form solution of the strain energy absorption capability of SMA bars provides a useful tool in the design of energy dissipation applications of superelastic SMA.

A model using energy balance is proposed to describe the volume fraction of martensitic transformations.It is found that in the absence of external stress, the volume fraction of martensite (xi) in the forward austenite-to-martensite transformation is proportional to the undercooling and inversely proportional to a linear function of the instantaneous temperature T. Similarly, for the reverse transformation from martensite to austenite, (xi) is proportional to and inversely proportional to a linear function of T. The results obtained from this model are in good agreement with experimental results.

Photoelastic model material with shape memory effect and molding processes of the material is developed in this research. Matrix and fiber of the photoelastic model material developed in this research are respectively epoxy resin and wire of Ti₅₀Ni₅₀ shape memory alloy. It is called Ti₅₀Ni₅₀ shape memory alloy fiber epoxy composite. It is assured that Ti₅₀Ni₅₀ SMA-FEC is satisfied with the requirements of photoelastic model material and can be used as photoelastic model material and can be used as photoelastic model material. The maximum recovering strain of Ti₅₀Ni₅₀ SMA-FEC is occurred at 80 degrees in any prestrain of Ti₅₀Ni₅₀ shape memory alloy wire fiber and in any fiber volume ratio. Recovering strain is increased with the increment of the prestrain and the fiber volume ratio.

Control of longitudinal vibration and wave in a cantilevered beam is studied in this paper. The algorithm of the control system is based on the concept of active attenuation, the traveling wave of the structural response can be annihilated by a control wave of opposite signature. Experimental results showed that the longitudinal vibration and wave have been substability suppressed in a beam.

This paper presents robust vibration and position tracking control of a flexible smart structure featuring a piezoceramic actuator. A cantilever beam structure with a surface-bonded piezoceramic actuator is proposed, and its governing equation of motion and associated boundary conditions are derived from Hamilton's principle. The transfer function from control input voltage to output displacement is then established in Laplace domain in order to formulate a robust controller using the quantitative feedback theory (QFT). A robust QFT compensator is designed on the basis of a stability criterion which prescribes a bound on the peak value of an M-contour in the Nichols chart. In the formulation of the compensator, disturbance rejection specification and tracking performance bounds are specified to guarantee the robustness of the system to plant uncertainties and external disturbances. A prefilter is also designed for the improvement of step and sinusoidal tracking control performances. Vibration and position tracking control performances are evaluated through computer simulation and experimental implementation in order to demonstrate the efficiency and robustness of the proposed control methodology.

Following the theory of linear piezoelectricity, we consider the dynamic bending of a cracked composite plate with attached piezoelectric polyvinylidene fluoride layers subjected to electric field loading and incident flexural waves. The input waves are generated by a combination of bending moments applied to the plate edge causing the plates to vibrate in the transverse direction, and the electric field and the poling direction are perpendicular to the plate surfaces. Fourier transforms are used to reduce the mixed boundary value problem to the solution of a pair of dual integral equations. The integral equations are further reduce to a Fredholm integral equation of the second kind. Numerical results are given for the dynamic moment intensity factor versus frequency for several values of the electric field and the geometrical parameters.

Piezoelectric stack actuators have been used in structural acoustic controls, and active vibration isolation systems. In recent tests of heavy duty vibration isolation systems, it has been found that piezoelectric stack actuators under large loadings and high driving voltages can produce substantial heat to cause failure. This paper presents preliminary results of a research effort that was set out to investigate the heat production and thermal effects on the actuator performance In the paper, a general constitutive formulation of piezoelectric materials is presented starting from the first law of thermal dynamics. the constitutive equations involve thermoelastic, pyroelectric and, of course, piezoelectric effect. A variational principle based on Oden's approach is then developed. As a special case, the equations of motion for a circular multilayer stack piezoelectric actuator are derived from the variational principle. Numerical results of blocked force and free stroke of the actuator are presented in the paper. The effects of various parameters on these two common specifications of solid state actuators are studied.

The accuracy of stabilized, turreted gun systems like the 120mm gun on the M1A2 Abrams tank and the 30mm gun on the Apache helicopter are limited by, among other things, structural flexure of the gun barrel and support structure. An advanced actuation system based on piezoelectric translators and an optical fiber strain sensing system are described in conjunction with a rapid prototyping workstation for the design of distributed parameter control systems to actively minimize the effects of vibrations caused by traversing rough terrain or weapon firing.

Material interfaces are commonly encountered in the fabrication of smart structural elements. Common examples are electrode-actuator-host material interfaces. Interface behavior is a very critical issue in the development of a reliable smart structure technology. This study presents a set of analytical solutions that can be used in the computational fracture mechanics analysis of interface cracks in electronic materials and in smart structural elements. Exact solutions for 2D governing equations of piezoelectric and ideal elastic media are used. Shear and opening dislocations are modeled as discontinuities in the displacements at a piezoelectric-elastic interface. The interface is assumed to be electrically insulated. Closed form solutions are developed for stress and electric fields in a bi-material system. These solutions can be used in the analysis of interface fracture problems involving smart structural elements by applying the displacement discontinuity method.

Nonlinear modeling and control methods can be used to increase the usable range of operation of Terfenol-D. Presently, in dynamic applications the usable range of Terfenol-D is often limited to approximately 850ppm. This limitation is imposed by harmonic distortion, spurious vibration, and/or tracking error considerations. These nonlinear effects are due to large variations in the magnetoelastic parameters and hysteresis. The preliminary results of this program indicate that a large performance advantage may be gained through proper control of the nonlinearities. As an example, a recently designed reaction mass actuator that weighs 1.125lbm can produce peak forces as high as 125lbf. However, to limit the open-loop total harmonic distortion to less than 2 percent requires that peak forces be limited to roughly 65lbf. To determine the magnetoelastic parameters, quasi-static experiments were performed with a specially designed apparatus. The research included modeling and simulation based on the static nonlinear magnetoelastic equations. Under assumptions of quasi-static magnetoelastic behavior, a fourth-order linear model was extended with the static nonlinearities. The model is compared with preliminary experiments. These types of models will allow nonlinear control strategies to be developed for Terfenol-D based actuators, thus extending the harmonic-free operating range.

Experiments based on the compact tension geometry are applied to a relaxer composition of lead lanthanum zirconate titanate. This composition is transparent, and displays electro-optical and piezo-optical coupling. A standard photo-stress arrangement gives a direct view of electric field and stress concentrations. Electric field is observed to cause cracks to close. This is consistent with earlier predictions of a negative energy release rate.

This paper presents a method for predicting the power consumption of piezoelectric actuators utilized for active vibration control Analytical developments and experimental test show that the maximum power required to control a structure using surface-bonded piezoelectric actuators is independent of the dynamics between the piezoelectric actuator and the host structure. The results demonstrate that for a perfectly-controlled system, the power consumption is a function of the quantity and type of piezoelectric actuators and the voltage and frequency of the control law output signal. Furthermore, as control effectiveness decreases, the power consumption of the piezoelectric actuators decreases. In addition, experimental results revealed a nonlinear behavior in the material properties of piezoelectric actuators. The material nonlinearity displayed a significant increase in capacitance with an increase in excitation voltage. Tests show that if the nonlinearity of the capacitance was accounted for, a conservative estimate of the power can easily be determined.

A problem of local field for 2D regular and weakly non- regular arrays of bi-anisotropic particles is considered. Such arrays are excited by an incident plane electromagnetic wave. The local field is formed by incident wave and by all the particles besides an arbitrary chosen particle under consideration which can be named as zero-particle. For infinite or very large arrays we can express the local fields with only tow vector complex values which are to be defined in frames of the separate problem of an exciting and scattering by such grids. But the equations relating electric and magnetic dipole moments of zero-particle with an incident wave field are that we find in this paper. Since these moments can be easily related with the surface density of electric and magnetic moments averaged on the grid surface the equations under consideration are analogues with the known local field formulae in theories of 3D media. Our relations are given by several dyadics which are named below as key dyadics.

The electromagnetic excitation of 2D array of bianisotropic particles by plane waves is considered. The array is assumed to be infinite and the particles to be small compared with the wavelength so that the dipole approximation is available. The electromagnetic interaction between tall the particles is taken into account analytically. Two kinds of bianisotropic particles: chiral particles and omega particles are analyzed. Both the electric and magnetic moments of each particle are related to each other and depend on the local field. Therefore, the standard approach used in the theory of scanning antenna arrays cannot be applied. The analytical model under consideration allows to express the electric and magnetic moments induced in each particle through incident wave field amplitudes. These relations are dyadic ones.

The fabrication of conducting polymer - silver-polymer electrolyte composite materials is described. Discs of these materials mounted in a coaxial test fixture exhibit rapid and reversible changes in their microwave impedance when small electric fields are applied across them. The effect of the concentration of conducting polymer on the cyclic voltammetry and microwave characteristics of the composites is discussed. Comparison of the cyclic voltammetry and microwave results has shown that changes in the gradients of the cyclic voltammograms coincide with large changes in microwave reflectivity. The results are consistent with the conducting polymer being switched from an insulating to a conducting state when the fields are applied. The reverse change occurs when the field is removed. Microwave coaxial line measurements for annular samples are presented and an equivalent network model comprising a parallel resistor and capacitor has been fitted to the measured data. Scanning electron microscopy studies on both the cycled and uncycled composites are presented and the results suggest that during cycling, the silver metal dissolves and is then re- precipitated.

The differential equations and boundary conditions describing the vibrations and stability of superconducting elastic plates in the external magnetic field were obtained. The effective numerical method is proposed for the solution of Neumann external problem The concrete problems of vibration and stability of superconducting rectangular plates were solved. The possibility of loss of static and dynamic stability under the influence of external longitudinal magnetic field was proved.

In present paper the problem of surface magnetoacoustic waves propagation taking into account the rotational motion of particles of the body is discussed. The medium is considered to be ferromagnetic and to be situated in external homogeneous magnetic field. Directions of the external magnetic field and magnetic spin coincide and are parallel to the free surface of the semi-space. It is shown that interaction between surface magnetoacoustic Rayleigh wave and SH waves is missing in the discussed problem. The dispersion equation for the coupled surface magnetoelastic waves is derived.

Active vibration control is using increasingly large numbers of sensors and actuators to achieve ever-improving results in the control of distributed systems. As the number of actuators and sensor increases, computational effort for control purposes increases. As the number of actuators and sensors grows, so too does the frequency range over which it is sensible to attempt active control and the time available for control calculations is therefore shrinking. Notwithstanding the remarkable rate at which processor speeds continue to increase, it is evident that full multi- input multi-output control cannot continue to be applied for increasing numbers of sensors and actuators. The requirements for every actuator to have an amplifier and every sensor to have signal conditioning is also very demanding. This paper addresses the issue of how best to implement the controller and estimator in smaller sensor/actuator groups and to determine the optimum topology, or grouping, of the sensors and actuators. The demands of both the control and the parameter estimation are addressed, and the implementation of modal control and selective sensitivity estimation algorithms are described.

Distributed piezoelectric sensor and actuator have been designed for efficient vibration control of a cantilevered beam. Both PZT and PVDF are used in this study, the former as an actuator and the latter as a sensor for our integrated structure. For the PZT actuator, the position and size have been optimized. Optimal electrode shape of the PVDF sensor has been determined. For multi-mode vibration control, we have used two PZT actuators and a PVDF sensor. Electrode shading of PVDF is more powerful for modal force adjustment than the sizing and positioning of PZT. Finite element method is used to model the structure that includes the PZT actuator and the PVDF sensor. By deciding on or off of each PZT segment, the length and the location of the PZT actuator are optimized. Considering both of the host structure and the optimized actuators, it is designed that the active electrode width of PVDF sensor along the span of the beam. Actuator design is based on the criterion of minimizing the closed-loop system energy under a given initial condition. Sensor is designed to minimize the observation spill-over. Modal control forces for the residual modes have been minimized during the sensor design. Genetic algorithm, which is suitable for this kind of discrete problems, has been utilized for optimization. Discreet LQG control law has been applied to the integrated structure for real time vibration control. Performance of the sensor, the actuator, and the integrated smart structure has been demonstrated by experiments.

We study the behavior of several organizations for a market based distributed control of unstable physical systems and show how a hierarchical organization is a reasonable compromise between rapid local responses with simple communication and the use of global knowledge. We also introduce a new control organization, the multihierarchy, and show that is uses less power than a hierarchy in achieving stability. The multihierarchy also has a position invariant response that can control disturbances at the appropriate scale and location.

Piezoelectric actuators are particularly suitable for integration into 'smart structures.' A basic understanding of the electro-mechanical properties of piezoactuators is required to develop high-performance 'smart structure' applications. The high mechanical and electric load on the actuators is typical of these applications, but very little data material is as yet available here. This contribution presents suitable measurement methodologies and systems for the application-oriented characterization of piezoelectric high-load actuators, and the results are discussed.