In this paper, the finite-element/boundary-element program CAPA is presented, which has been developed by the authors during the last decade. With this software environment we are able to model quite different types of transducers which mostly ask for the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic- mechanical fields. Practical applications in the area of smart structures will demonstrate the applicability of the developed software.

The paper first presents a general purpose finite element based simulation tool for piezoelectric controlled smart structures. In addition to the standard finite elements, this tool contains a number of coupled electromechanical finite elements as well as numerical tools to simulate controlled structures in statics and dynamics. The effectiveness of a smart structure decisively depends on the amount and distribution of active materials across the passive structure and on the controller design. To solve this design problem automatically, a discrete optimization technique and ideas from topology optimization are presented. The control parameters are considered as continuous design variables. Mathematical solution algorithms for non-linear, mixed continuous and discrete-valued optimization techniques are used to solve the optimization problem. As a test example the distribution of piezoelectric wafers over a beam structure is presented. Finally, this paper gives an outlook for new developments in this field.

Recent developments in adaptive composite structures with distributed multifunctional actuators and sensors have attracted significant attention in the research community due to their potential commercial benefits in a wide range of applications such as vibration suppression, shape control and noise attenuation. In this study, composite plate and shell finite element models with electromechanical properties are presented. The adaptive composite consists of a plate or shell structure with piezoelectric actuators either bonded or embedded as a laminate in the structure. Its applications in aircraft internal noise suppression are investigated. The underlying concept consists of stiffening the structure using the distributed electromechanical actuation.

In this paper the design of an optimal controller using discretely placed collocated sensor/actuator pairs to control the vibration of a plate structure is presented. Three- dimensional finite elements are used to model the smart structure containing discrete piezoelectric sensors and actuators by the use of a combination of solid, transition, and shell elements. Since several discrete piezoelectric patches are spatially distributed in the structure to effectively observe and control the vibration of a structure, the system model is thus utilized to design multi-input-multi- output (MIMO) controller. The output feedback controller is then employed to emulate the optimal controller by solving the Riccati equations from modal space model. An optimal controller design for the vibration suppression of a clamped plate is presented for the steady state excitation case. The reduction in the sound pressure level inside an enclosure radiated from this optimally controlled vibrating plate is also estimated.

The focus is on obtaining and identifying optimal distributed- parameter-control equivalent actuation profiles for desired roll maneuvers by a modal synthesis approach. The solution for distributed-parameter-control of an aeroelastic system is developed by synthesis of modal-state-space controllers designed via the globally power optimal Independent Modal- Space Control (IMSC) technique. The desired maneuver (set- point) control performance is achieved by a modal-performance- output synthesis (MPOS) approach. The MPOS approach requires that each independent modal controller be allocated a desired portion of the total desired output performance. In view of this, a modal performance-output allocation optimization problem is also defined, which minimizes a hybrid measure of control power and elastic strain energy of the structure during aeroelastic control. Insight to distributed-parameter- control equivalent actuation solutions are sought by considering the aeroservoelastic interactions among vehicle motion, aerodynamics, structural flexibility and control actuators from the perspective of work-energy, control power, and control loading requirements. The modal synthesis approach is illustrated for a flight vehicle wing design to achieve a 90 deg/sec roll-rate in a Mach 2 flight condition at altitude (20000 ft) via distributed-parameter equivalent actuation. The preliminary results indicate that such a roll-rate maneuver can be accomplished via distributed-parameter actuation with feasible levels of control power, work-energy, and control loadings through eliciting favorable aeroservoelastic interactions.

This paper is concerned with designing an optimum flexible wing structure to enhance roll maneuver capability at high dynamic pressures using embedded actuating system. A wing optimized to minimize the weight, with constraints on strength for symmetric pull up maneuver and constraints on the frequency distribution was used for this study. 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 equilibrium equations were developed for the steady roll maneuver of a wing subjected to aerodynamic loads and actuating forces. Optimal control design approach was used to determine the distribution of actuating forces. The total straing energy was calculated as a measure of power requirement to produce twist and camber, to achieve specified flexible roll rate at different Mach numbers.

This paper presents recent analytical and experimental research to modify and control low Reynolds number flows over prototypical airfoils associated with micro-air-vehicles. The simplified experimental test geometry consists of a meso-scale piezoceramic actuated flap that undergoes peak amplitude displacements of 40 microns. The flap actuator array is designed to modify separation and reattachment location on the airfoil. The location of the reattachment on the upper surface of the prototypical airfoil is measured by an array of MEM's shear stress sensors located downstream. The focus of this paper is the discussion of the status and applicability of reduced order modeling techniques for the derivation of active feedback flow control strategies for the prototypical active airfoil. Frequently, reduced order models are derived from a library of component fluid modes which serve as the basis for a low dimensional approximation of the nonlinear Navier Stokes equations. The methodology discussed in this paper differs markedly from these approaches. We derive a technique employing multiresolution and wavelet approximations of nonlinear Volterra series that represent the input-output dynamics of the system. The accuracy of the resultant low- dimensional input-output models is validated on a benchmark nonlinear aeroelastic testbed.

We first present a summary of results obtained with a numerical code to perform particle dynamics simulations of magnetorheological (MR) fluids upon application of an external magnetic field. These simulations, for the first time, account fully for all linear (long-range) magnetic interactions and are made feasible by recent developments of the Fast Multipole Method. In addition, we present some numerical and theoretical studies for the overall magnetic response in MR fluids based on nonlinear homogenization theory. We show that these results can be effectively used to study a number of experimental findings such as effective magnetic permeabilities (from the linear through saturation regimes) and response time scales, all of which are of crucial importance in the design of MR fluids.

A ferromagnetic material located into a unidirectional exterior magnetic field vector H_ext takes a new internal magnetization which induces closure domains separated by walls. When the magnetic field vector H_ext varies from a saturated value H_max vector e_x to -H_max vector e_x, we can observe hysterisis phenomenon and motion of the walls. The numerical approximation of these phenomena is difficult since the associated modelization is nonlinear and the magnetization field vector m has to satisfy vector m equals constant. The associate modelization, an efficient minimization algorithm (augmented Lagrangian method) and corresponding results have been presented in the last SPIE meeting. This contribution discusses the coupling between magnetic effects and elastic effects which can be met in magnetostrictive materials.

Designers need advanced tools to tap the full potential of the benefits of giant magnetostrictive materials (GMMs) for advanced commercial, space, and military applications. To overcome the deficiencies in present models, a new magnetostrictive analytical formulation needs to be developed that includes the nonlinearities experienced in advanced device designs. Presented herein are a strategy and approach for developing the needed advanced tools to move magnetostrictive transducer design to much higher levels of performance and effectiveness. Advanced GMM FEM modeling capabilities are being developed by extending and combining leading edge theoretical work in nonlinear constitutive equations and ferromagnetic hysteresis. A nonlinear constitutive model for a GMMs uses a Taylor series expansion of independent variables of stress, magnetization and temperature to obtain a polynomial relation in terms of the Gibbs free energy. Phenomenological justification is used to eliminate some terms. Development of a magnetization based magnetostrictive material model at the macroscopic continuum level will be a novel advancement of the state of the art. The planned hysteresis model is derived from related work on energy-based models which considers the total magnetization as the combination of a reversible and an irreversible component. Because both the constitutive and hysteresis formulations are in terms of the same state variables, integration into a new complete magnetostrictive material description is inherently more feasible. The result will be a validated, fully coupled, 3-dimensional, nonlinear, hysteretic, dynamic thermo-electro- magneto-acousto-mechanical (TEMAM) model of magnetostrictive materials. Development of new finite elements to take advantage of the advanced modeling results is planned. The new capability will provide meaningful performance predictions, parameter sensitivity studies, trade-off studies and design optimizations, thereby enabling next-generation applications at reduced developmental cost.

Magnetostrictive materials often rely on magnetic fields generated through the use of a solenoidal coil. However, the field-generating coil also acts as a source of heat causing thermally induced strains in the magnetostrictive drive element. To insure that the useful magnetostrictive strains are large in comparison with the thermally induced strains, the solenoid may be optimized. This paper presents a simple one dimensional (1-D) magnetic model useful for predicting the magnetic field inside the magnetostrictive drive rod. The advantage of this model is that it can be evaluated very quickly, making it well suited for use in optimization algorithms. A figure of merit is presented that weighs the energy stored in the coil against the power that must be dissipated to maintain the field. With the magnetic model and cost function, the solenoid may be sized to maximize the volume averaged field in the magnetostrictive element per unit of volume averaged dissipated heat in the solenoidal coil. While previous work addressed field/power optimization at the center of air-cored selenoids, the work presented here considers optimization of the average field along a rod of permeable magnetostrictive material. The results indicate that coil quality decreases rapidly if the coil is thinner than optimal, but decreases rather slowly for a thicker than optimal coil.

This paper presents a static, temperature dependent constitutive model for polycrystalline relaxor ferroelectrics operating near their diffuse transition temperature. The model assumes that the relaxor material consists of superparaelectric, micro polar regions with a diffuse spectrum of Curie temperatures. A simple Ising model with near neighbor ion interaction represents the thermodynamics of the individual micro polar regions. A random-order dispersion of the B-site ions simulates the distribution of phase transitions. The diffuse micro polar region model predicts two important materials parameters, the saturation polarization and the density of the polar regions, as a function of temperature. A macroscopic model was constructed with these parameters to simulate dielectric and polarization response of the aggregate material. The macroscopic model also accounts for interaction between the micro polar regions. Finally, the predictions made by the model are compared with experimental data obtained by other researchers on lead magnesium niobate (PMN) relaxor ferroelectrics.

Piezoelectric actuators are key components in many smart structures applications. Long term reliability of these actuators becomes increasingly important as research makes the transition to commercial applications. Fracture toughness is a material parameter that measures a material's resistance to crack propagation. This is perhaps, one of the most important parameters for reliable device design. This paper reviews recent work by the authors on fracture behavior of ferroelectric ceramics. Vickers indentation data were used to determine the fracture toughness of a coarse and a fine grained PZT and two compositions of PLZT. R-curve data were obtained for two compositions of PLZT. The R-curve data presented here were generated using four point bend specimens with controlled surface flaws. The R-curve results compare favorably with the Vickers indentation data. A comparison of the R-curves for a ferroelectric composition of PLZT and a quadratic electrostrictive composition of PLZT demonstrate the contribution of domain reorientation to the toughening process.

This paper summarizes a mathematical model for characterizing hysteresis in ferroelectric materials. The model is based on the quantification of energy required to bend and translate domain walls and is developed in two steps. In the first, the underlying anhysteretic polarization is quantified through constitutive equations derived using Boltzmann statistics. Three anhysteretic models are considered including the Langevin and Ising spin relations as well as a third formulation which combines attributes of the other two. Hysteresis is then incorporated through the consideration of domain wall motion and the quantification of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.

In this paper we study on the effects of heat generated from a moving domain boundary during polarization reversals in ferroelectrics. According to the one-dimensional model of ferroelectrics proposed by Kim (1999), there are two heat sources associated with a moving domain boundary: one is from dissipation mechanism on the domain boundary and the other from the entropy difference between two variants across the domain boundary. In order to investigate the effects of heat generation and transfer during polarization reversals we utilize the finite difference algorithm shown in Kim and Abeyaratne (1995). The results of calculation show that it is possible for the specimen temperature to reach as high temperatures as observed in experiments.

In this paper a self-consistent model for the switching of a ferroelectric polycrystal will be presented. We will assume that the polycrystal is made up of spherical grains or crystallites. Each crystallite is made up of two domain types separated by 180 degree domain walls. The linear dielectric properties of the domains are assumed to be isotropic. When the electric field in the crystallite reaches a critical level the domain walls are allowed to sweep through the crystallite. This gradual domain wall motion causes the tangential dielectric permittivity of the crystallite to be transversely isotropic. Each spherical crystallite is given a distinct orientation and embedded in a matrix material. The tangential dielectric permittivity of the matrix is taken to be consistent with the overall averaged incremental response of the crystallites taking into account the constraint or depolarization fields imposed by the matrix. Hysteresis loops and switching surfaces are presented for the polycrystal.

The problem of an isolated crack as well as a crack with a kink in a plane piezoceramic medium is theoretically investigated in this study. The orientation of a crack with respect to the poling direction may be arbitrary. The approaches of Lekhnitskii's complex potentials and distributed dislocation modeling of cracks for elastic solids are extended to formulate the piezoelectric crack problems. For the case of an isolated arbitrarily oriented crack, analytical solutions are obtained for all electroelastic field variables. It is found that a change of crack orientation may alter the trend of toughness variation, and initiate failure along different planes depending on the direction of electrical field. For the case of a kinked crack, it is shown that the problem is reduced to solving three integral equations with the dislocation densities along the kink line as unknowns. The accuracy of the present scheme is confirmed by comparing with the limiting case of elastic solids. The results presented in this study provide important information on electroelastic fields and fracture parameters corresponding to kinked cracks in piezoceramics.

This paper proposes a new space telescope design in which the classical truss structure of the telescope is replaced by a tensegrity structure. A tensegrity structure is a prestressed structure whose structural shape is guaranteed by the interaction between elastic members in tension (tendons) and a set of rigid members (bars). A nonlinear dynamical model of a two stage tensegrity telescope is derived. Static analysis is performed for tensegrity telescopes composed of two stages. The performance specifications for the control system are formulated in terms of the peak value (L_(infinity ) norm) of the pointing and alignment errors. The control system is designed to minimize a certain upper bound on this peak value subject to a peak value constraint on the external disturbances. Evaluations of the design are performed through numerical simulations of the closed loop system.

Although there is a mature and continually growing body of knowledge concerning the ways in which the dynamics of fluids and solids depend on characteristic length scales, current theories governing control design do not take explicit account of length scales. Recent research has demonstrated the need to take such considerations into account in designing control systems for smart materials and smart structures in which the goal is to employ small-scale actuators and sensors with characteristic length scales in the micron to millimeter range. For many applications, sensors and actuators will need to be separated by considerable distances (in terms of characteristic length scales). Closed loop feedback designs in this setting may involve communications delays, and both the communications channels and the sensors themselves will typically be relatively noisy. Hence traditional approaches to the design of feedback control laws need to be rethought and modified to work effectively in the noisy, nonlinear, bandlimited world of microelectromechanical systems (MEMS). This paper discusses one approach to a robust, length-scale respecting theory of control based on oscillatory actuation. It includes a brief outline of recent developments in the control of mechanical systems using oscillatory actuation, emphasizing the dependence on characteristic length scales. The principal applications with which we are working are micro-pendulum designs, micro-piston actuators for deformable mirrors as well as micro-valves for the control of fluid- structure boundary layer control.

This paper presents a hybrid actuator scheme to actively control the end-point position of a two-link flexible manipulator. A highly nonlinear system model including inertial effects is established using Lagrange's equation associated with assumed mode method. Control scheme consists of four different actuators; two servo-motors at the hubs and two piezoceramics bonded to the surfaces of the flexible links. Two sliding hyperplanes which have time varying parameters are designed for two servo-motors. The surface gradients of the hyperplanes are determined by pole assignment technique to guarantee the stability on the hyperplanes themselves. The sliding mode controllers corresponding to the hyperplanes are then synthesized on the basis of sliding mode conditions. During the motion, undesirable oscillations caused by the torques based on the rigid link dynamics are actively suppressed by applying feedback control voltages to the piezoceramic actuators. Consequently, desired tip motion is achieved. In order to demonstrate the effectiveness of the proposed methodology experiments are performed for the regulating and tracking control problem.

This paper presents a statistical approach to the controller design process for structural systems represented by uncertain models. The plant model uncertainty is here accounted for in terms of first- and second-order statistics of uncertain parameters. The basic idea is to make the closed-loop system stability as robust as possible to statistical variations of uncertain plant model parameters. First, an approximate expression for the root variance of an uncertain polynomial is derived as a function of second-order statistics of the polynomial coefficients. The expression is specialized to the case of an SISO closed-loop system characteristic polynomial, where the uncertainty is due to statistical variability of model parameters. Uncertainty cost functions intended to represent the uncertainty of the closed-loop pole locations are then constructed. By parameterizing the set of controllers that yield a desired characteristic polynomial, the uncertainty cost function minimization is converted into a constrained optimization problem. This scheme is illustrated with an SISO seismic control system previously studied in the literature. By comparing the predicted closed-loop pole variance to numerical results obtained from Monte Carlo simulations, it is concluded that the expression developed here provides excellent approximation, with the advantage of being an analytical expression that is suitable for use in multi-objective optimization design algorithms.

Flextensional transducers consist of a piezoceramic (or a stack of piezoceramics) connected to a flexible mechanical structure that converts and amplifies the output displacement of the piezoceramic. Among the applications, they can be used as actuators and sonars. The transducer performance in these application depends on the distribution of mass, stiffness, and flexibility in the coupling structure domain, which is related to the coupling structure topology. By designing other types of coupling structures connected to the piezoceramic, we can obtain new types of flextensional transducers with enhanced performance for a desired application. In this work, we extended the method for designing flextensional transducers in static and low-frequency applications to dynamic applications by introducing the inertia effect in the optimization problem. The method applies topology optimization technique based on the homogenization design method, which consists of finding the optimal material distribution in a perforated design domain with infinite microscale voids. The problem is posed as the design of a flexible structure coupled to the piezoceramic that produces high output displacements in a specified point of the domain and direction, in a specified frequency. Therefore, it consists of designing a flexible structure with a specified mode shape in a desired resonance frequency. As a result, designs of flextensional transducers are presented.

Compliant mechanisms are devices which utilize elastic deformation to emulate the behavior of conventional rigid mechanisms. Structural optimization techniques represent a relatively new approach for automating topology synthesis of compliant mechanisms. A cantilever beam model is presented in order to examine the solution behavior of various objective functions intended for compliant mechanism optimization. The model reveals that objective functions which attempt to simultaneously maximize the flexibility and stiffness of a compliant mechanism can be formulated such that they are not well-bounded. Topology optimization problems using these types of objective functions may exhibit heightened convergence sensitivity with respect to the lower design variable bound. The cantilever beam model is also used to develop a new objective function based on maximizing the energy throughput of a compliant mechanism pushing against an external spring. The objective function shows a well-bounded solution to the simple beam model and consequently exhibits more robust optimization convergence. A simple numerical example is given which demonstrates the heightened robustness of the formulation.

In this paper we state the homogenized model of a periodic electro-piezo-mechanical thin shells. The electrical network is including resistive devices, tension sources, current sources and voltage to voltage amplifiers. It is distributed evenly on the surface of the shell. The model derivation is based on a two-scale convergence which is based on the two- scale transform introduced by T. Arbogast, J. Douglas and U. Hornung. The present work is based on some results of two- scale convergence of gradients which leads to the same results than the usual two-scale convergence introduced by G. Allaire. We apply these results and those introduced in the framework of M. Lenczner and G. Senouci-Bereksi for the electrical network, to derive the two-dimensional electro-piezo- mechanical thin shell model applying Reisner-Mindlin kinematic.

Adaptive structures optimal design problems and solution methods are presented and discussed for the cases of shape control and active damping. A general method to solve simultaneously optimal placement and control problems for active damping applications is outlined. This method is based on a finite element structural model and on the calculation of the closed-loop system poles. Numerical results are given to illustrate this method for the case of a beam with collocated PZT sensor/actuator pair and a direct velocity feedback controller.

In this paper we present results on numerical studies of the martensitic-austenitic phase transition mechanism in a large shape-memory-alloy rod. Three groups of experiments are reported. They include results on stress- and temperature- induced phase transformations as well as the analysis of the hysteresis phenomenon. All computational experiments are presented for Cu-based structures.

Numerical implementation of solid-solid phase transformation modeling with a Gibbs function is presented with particular emphasis on computational efficiency. The phase transformation model is outlined first, followed by a discussion of the proposed constrained integration method. Numerical tests are then presented demonstrating the characteristic accuracy of the method under both mechanical and thermal loads.

In this article we propose a material model for the representation of shape memory behavior based on a phenomenological thermoviscoplasticity theory. The constitutive model is thermodynamically consistent in the sense of its compatibility with the Clausius-Duhem inequality as a special formulation of the 2nd law of thermodynamics. Numerical solutions of the constitutive equations for isothermal and nonisothermal strain and stress processes demonstrate that the behavior of these materials, namely the one- and two-way shape memory effect, the pseudoelasticity and the pseudoplasticity as well as the transition region between pseudoelasticity and pseudoplasticity, is depicted as observed.

Integration of controllers with smart structural system require the controllers to consume less power and to be small in hardware size. These requirements pose as limits on the control input and the order of the controllers. Use of reduced order model of the plant in the controller design can cause spill over problems in the closed loop system due to possible excitation of the unmodeled dynamics. In this paper we present the design of output feedback robust controllers for smart structures in the presence of control input limits considering unmodeled dynamics as additive uncertainty in the design. The performance requirements for the design are specified as regional pole placement constraints on the closed loop poles. Formulation of this multi-objective design problem in terms of matrix inequalities resulted in a feasibility problem involving bilinear matrix inequalities (BLMIs) in the unknown variables. To facilitate the solution of this feasibility problem, a change of variables is used to convert these BLMIs into linear matrix inequalities (LMIs) which can be readily solved by the use of available tools. Finally, this design procedure is applied on an experimental smart structure and the results are presented.

Piezoelectric devices represent an important new group of actuators and senors for active vibration control systems. Indeed, this technology allows to construct spatially distributed devices. A mathematical model of a multilayered piezoelectric plate, which takes hysteresis and polarization of the piezoelectric laminae into account, is presented. Passive control for Lagrangian systems is used to derive a class of stabilizing control laws, which are based on the collocation of sensors and actuators. Therefore, the design of the spatial distribution of the sensors/actuators is considered as a part of the controller synthesis.

While PZT exhibits only mild nonlinear response at low voltage levels, it is well-known that the response can be profoundly nonlinear at high field strengths. Moreover, the use of mechanical linkages and structural design to amplify the stroke of PZT-based actuation likewise can couple with this material nonlinearity to yield a structural level nonlinearity that is non-negligible. In this paper, we investigate such a nonlinear response in a PZT actuated trailing edge flap attached to a scaled helicopter rotor blade. While the example studied in this paper is quite specific, the methodology derived is generally applicable. We extend the recent results of [18,19] for the derivation of closed loop control for active material actuated devices. In this technique, a compensator derived from an offline identification of a Krasnoselski-Pokrovski hysteresis operator is cascaded with the plant. We show that the methodology is well-posed for the class of problems under consideration; we derive closed loop stability and robustness conditions that can be associated with the prediction error in the identified hysteresis operator. We study the performance of our methodology in numerical examples and discuss relevant experimental results.

Dynamic behaviors of a 1-story and 4-story steel structures subject to multi-dimensional ground motion excitations were experimentally investigated by using a shaking table. Linear and nonlinear structural responses were obtained as observation data for the identification. Dynamics characteristics of the model structures were identified using the adaptive H_(infinity ) filter, which was developed for identifying structural systems with non-stationary dynamic characteristics by adding the function of memory fading (forgetting factor) for past observation data to the H_(infinity ) filter. Identification results show that the H_(infinity ) filtering technique are very efficient for identifying linear and nonlinear structural systems. Especially, the nonlinear behavior of the model can be traced effectively.

In this work the control of vibration in an elastic plate, by piezoelectric transducers, is considered. The model of the plate is that presented in ]2]. An approximation of the optimal controller by a derivative partial operator is given. It is based on a development in series of the Riccati operator with respect to the reverse of the stiffness. Its implementation in term of distributed analog electronic circuits, is developed. Numerical simulations, obtained by the coupling of Finite Elements code and a circuit simulator, Alecsis, are presented. To improve the preceding result an iterative algorithm of approximation of the optimal controller, being able to be implemented by an electronic circuit, is developed. The algorithm is inspired by the approach of [4].

This paper is concerned with flexural vibrations of smart beams. Layers made of piezoelectric material are used to perform a distributed sensing of strains. In the present contribution, special emphasis is given to the sensor shaping problem, which can be stated as follows: Seek a shape function of the distributed sensor such that a mechanical interpretation of the sensor output is possible, e.g. to interpret the output as deflection, or as a slope. The scope of the present contribution is to find a class of easy to obtain analytic solutions of this inverse problem, and to present an experimental verification. Within the context of the Bernoulli-Euler beam theory, sensor equations are derived taking into account the coupling of mechanical and electrical fields. The principle of virtual work is then applied to derive integral equations for the structural deformations e.g. deflection, slope, curvature. Comparing these integral equations, the above sensor shaping problem is solved. Beams with different boundary conditions are considered. Furthermore, shape functions responsible for non-uniqueness of the shaping problem are derived. These nilpotent solutions may be added to the above derived solution of the sensor shaping problem without influencing the measured sensor signal. The analytical results of the sensor shaping problem are realized in a series of experiments for a cantilever beam, without and including a redundant support. Deflections measured by the new type of distributed piezoelectric sensor are compared to laser based distance measurements. Excellent coincidence between these measurements is found.

In this work, refined finite element models based on higher order displacement fields have been developed to study the mechanical and electrical behavior of laminated composite plate structures with embedded and/or surface bonded piezoelectric actuators and sensors. Sensitivity analysis and optimization techniques are also applied in order to maximize the piezoelectric actuator efficiency, improve the structural performance and/or minimize the weight of the structure. To show the performance of the proposed models several illustrative and simple examples are presented.

The electrical and mechanical field distributions inside the layers of a piezolaminate beam are calculated when excited by a harmonic load or electric potential applied on the surface of the laminate. The Fourier series solution approach is used to solve the electroelasticity problem and the electrical and mechanical field distributions are estimated at frequencies away and close to the natural frequency of the laminate. Numerical results are computed for a single piezoelectric layer and a three layered piezoelectric laminate under cylindrical bending vibration. Our results indicate that the approximations made in many papers dealing with laminated piezoelectric beams are unjustified especially close to structural resonance frequencies at which control of vibration is most often desired.

Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite shell structures. A new mixed multi- field laminate theory is developed which combines 'single layer' assumptions for the displacements along with layerwise fields for the electric potential and temperature. This laminate theory is formulated using curvilinear coordinates and is based on the principles of linear thermopiezoelectricity. The mechanics has the inherent capability to explicitly model both the active and sensory responses of piezoelectric composite shells in thermal environments. Finite element equations are derived and implemented for an eight-noded shell element. Numerical studies are conducted to investigate both the sensory and active responses of piezoelectric composite shell structures subjected to thermal loads. Results for a cantilevered plate with an attached piezoelectric layer are compared with corresponding results from a commercial finite element code and a previously developed program. Additional studies are conducted on a cylindrical shell with an attached piezoelectric layer to demonstrate capabilities to achieve thermal shape control on curved piezoelectric structures.

The paper discusses feedback control strategies for the reduction of helicopter vibration using a trailing edge flap located at the outer part of the rotor blades. The problem of reducing rotor-induced vibration is considered as a disturbance rejection control problem where robust servomechanism control is applied in combination with optimal constant output feedback. This control scheme is examined in the view of limitations in the transient performance by investigating the zeros of the multivariable system. Local control strategies in the rotating system are developed for active damping enhancement. Simulations are presented based on a BO105 helicopter.

The problems of the mathematical modeling and dynamical response of thin-walled beam structures including a number of non-classical features and incorporating adaptive capabilities are considered. The theory of thin-walled beams as considered in this study encompasses non-classical features such as anisotropy, transverse shear and secondary warping, whereas the adaptive capabilities are provided by a system of piezoelectric devices whose sensing and actuating functions are combined and which are bonded or embedded into the host structure. The synergistic implications of the application of both tailoring and collocated sensing-actuating capabilities upon the closed-loop dynamic response are presented and pertinent conclusions are outlined.

A study of optimal vibration control of aircraft wings carrying externally mounted stores and exposed to blast loading is presented. The wing structure is modeled as a thin- walled beam of closed cross-section contour, and a number of non-classical features such as transverse shear, secondary warping, and anisotropy of the constituent materials are included. The wing structure can carry underwing and/or tip stores. The control is achieved via the use of actuating and sensing capabilities provided by piezoelectric devices which are bonded or embedded into the host structure. The cases of piezoactuators spread over the entire span of the structure, or in the form of a patch are considered, and issues related with the influence of patch location and size upon the vibration control efficiency of wings carrying external stores are discussed. Other issues related with the minimization of the required input power and of those generated by the inclusion/discard in the quadratic performance index of time- dependent external excitations are also addressed.

This paper describes a general technique to analyze the radiation impedance and actuator power efficiency of an active structure. Using a modal expansion of the structural vibration, the sound power is conveniently expressed as an integration over the surface of the planar structure. Integrating the finite element analysis into the numerical integral makes this technique applicable to any complex geometrical planar structure under arbitrary boundary conditions. As an example, this technique is applied to study of an actuator driving circular plate with an elastic support, which could be used to simulate a rigid piston. The radiation impedance and power efficiency of this active structure are studied using eigenvalue decomposition. Using general eigenvalue decomposition, the efficiency of air acoustic arrays are also analyzed. A dynamic model of the actuator is introduced to above studies by taking into account the coupling of the actuator and its host structure. Numerical results demonstrate that the radiation impedance of rigid-body motion is comparable to the analytical solution of a baffled rigid piston. Power efficiency studies demonstrate that one or two actuators will generate high efficiency when the rigid- body modes are dominant and more actuators are needed to improve the efficiency if the flexible modes are dominant. The efficiency is related to the structure impedance. A relatively soft actuator will generate a higher efficiency at low frequencies and low efficiency at higher frequencies. In contrast, a relatively stiff actuator will have a moderate efficiency at higher frequencies.

Modeling of piezoelectric smart structures including absorbing material was studied for cabin noise problems. The finite element method which uses a combination of three dimensional piezoelectric, flat shell and transition finite elements is adopted to model the piezoelectric active structure. The acoustic pressure in the cubic shaped cavity is represented in terms of modes of the cavity and the absorbing material is modeled using surface acoustic impedance. Finally, the effect of the cavity pressure is introduced in the finite element equations. The simulation result of sound pressure in the cavity is compared with an experiment and they show a good agreement. The cavity pressure is reduced in a wide frequency range except the resonance frequencies of the plate by applying absorbing material. It can be concluded that the piezoelectric smart structures with absorbing materials can be a creative technology for cabin noise problems.

A coupled finite element/boundary element method is developed for the fully coupled structural/acoustic/piezoelectric system. This approach uses the dual reciprocity boundary element method to describe time dependent acoustic field and the finite element to structures and piezoelectric materials. A time-domain formulation of the coupled method is obtained. Based on the coupled time domain formulation, linear quadratic regulator and a feedforward controller are applied to reduce the acoustic pressure transmitted into a cavity through a composite plate using embedded piezoelectric actuators. The controls of interior acoustic fields due to excitations at different frequencies are investigated, transmission losses and deflection of the plates of the controlled and uncontrolled systems are presented.

Active Noise Control has been an area of research interest in the recent decades with the goal of providing reduced noise levels in automobile and aircraft enclosures. Although digital controllers are adaptable and efficient, they lack the simplicity of analog controllers due to the requirement of a computer, D/A and A/D boards. Analog controllers on the other hand can be designed to be compact using current IC technology and hence are relatively very cheap. The following paper studies the application of an analog robust controller to abate the noise radiated into a non-reverberant wooden enclosure by a clamped aluminum plate. Since only the odd-odd modes radiate efficiently, a SISO robust analog controller was designed and built inexpensively for a piezoelectric actuator and accelerometer sensor placed at the center of the plate. A reduction of 17 dB is observed when the panel is excited at its fundamental frequency, the dominant radiating mode. When the plate is excited with narrowband noise (40 - 316 Hz), the controller reduces the noise levels in the enclosure by 9 dB. The experimental results agree well with the controller simulation carried out using MATLAB.

This paper presents a methodology to suppress the vibration of thin rectangular plate clamped all edges. Intelligent materials such as the piezoelectric ceramic are used as actuators and sensors. The experimental modeling technique, i.e., the state-space frequency domain identification, is introduced to model the complex shaped structures bonded with noncollocated actuators/sensors. This method is much free from the Multi-Input Multi-Output (MIMO) model order problem caused at the digital implementation and also reduces distortion of the signal. In control scheme, the adaptive feedforward with feedback control algorithm is adopted since it is robust for both the transient and persistent external disturbances. The adaptive feedforward control uses the well known Multiple filtered-x LMS (least mean square) algorithm. The MIMO error path dynamics is controlled by the feedback loop which is constructed by multivariable digital LQG (Linear Quadratic Gaussian) controller composed of the regulator and Kalman filter. Experiment results demonstrate the effective reduction of the vibration label and the robustness for both the transient and persistent external disturbances.

Vibration damping through phase transformation is one major area of application of shape memory alloys in smart systems and structures. The authors of this study have shown in earlier publications, how damping of vibrating rods can be accomplished. Phase transformation due to heating/cooling is the tool for vibration damping in the past and present work. Here, an elastic, polycrystalline rod is considered, which is initially at rest, and from the time t equals 0 on dynamically loaded. The loading function (pressure in the dependence on time) is in the simplest cases rectangular or bell-shaped. Special cases exist, which are equivalent to the release waves discussed in earlier papers. Heating/cooling is performed at the fixed end of the -- after the impact -- freely vibrating rod. This causes phase transformation on some parts of the rod according to the stress-temperature diagram. Thus, the governing equations are the heat conduction equation, the stress wave equation, the kinetic law to describe the phase transformation, and finally the constitutive law as well as a condition to ensure maximal damping. An integral equation algorithm is adapted to the impact problem for the numerical simulation. Results are provided for different impact types and heating/cooling histories. These show the decrease of the energy divided by the impact energy depending on time.

The paper presents a methodology for evaluating the effective stiffness of unidirectional composite materials with shape memory alloy (SMA) fibers in the presence of matrix cracks. The solution is obtained for the case where SMA fibers in the intact composite are in the austenitic phase. However, elevated stresses in the sections of SMA fibers adjacent to the crack planes cause the martensitic transformation affecting the stiffness of the material. The solution has to account for thermal residual stresses in SMA and 'ordinary' fibers and in the matrix. The order of magnitude of these stresses is calculated in the paper for two representative composite systems. As follows from the numerical examples, thermal residual stresses in the SMA fibers increase proportionally to their volume fraction but remain relatively small. However, thermal stresses in the matrix may reach rather high values reducing the strength of the matrix by a significant factor.

A one-dimensional model for shape memory alloys is presented that permits the simulation of actuatoric behavior. It is an improved version of the Muller-Achenbach single crystal model and calculates the length change as a response to electric heating. Based on this model, a polycrystalline version is developed, which is shown to be in excellent agreement with experimental results. Finally, as an illustrative application, a real-time control is calculated for an adaptive beam using SMA actuators.

Shape memory alloys (SMA) are well known materials. There is a lot of technical applications making use of their unique properties. Most of the significant applications are based on use of the thermomechancial properties. Growing number of those applications causes a need for an universal mathematical model with ability to describe all thermomechancial properties of SMA by relatively simple final set of constitutive equations that could be helpful for development of further sophisticated shape memory applications. Unfortunately, a lot of attention has been paid to metallurgical research of shape memory alloys in a few last decades and less attention was dedicated to shape memory modeling. Our model does not claim to be a universal model, but only one contribution to modeling of shape memory effect for binary SMA. The model is adapted for the most applied SMA -- nitinol and is based on the hypothesis that in the course of shape memory effect the distances of first atomic neighbors (Ni-Ti) remain nearly unchanged, whereas the distances of second neighbors (Ti-Ti and Ni-Ni) change substantially. Consequently, we consider some mechanical properties of Ni-substructure and Ti- substructure separately. The mechanical behavior of Ti- substructure is modeled as elastic whereas that of Ni- substructure as elasto-plastic. The resulting relatively simple differential constitutive equations express relationship among internal stress tensors, macroscopic stress tensors, macroscopic strain tensors and temperature.

Several decades ago, the principles of dynamic systems and controls were directed towards large engineering structures. In more recent years, the use of feedback control systems technology has been introduced to cause a structure to be 'smart,' or to be semi-actively controlled. As structural control matures, and such things as 'intelligent' structures and 'smart' systems methodology become understood and accepted in the broader scientific and technical circles, the uttering of some thoughts in reflection becomes appropriate. The paper recounts the author's personal role and experiences, examines trends and underlying issues in structural control, and concludes with admonitions, recommendations and visions concerning future directions in structural control.

This paper presents the study of controlling steady-state vibrations of a cantilevered skew isotropic plate using higher-order saturation phenomena. PZT (lead zirconate titanate) patches are used as control actuators, and a laser vibrometer (measuring velocities) or PZT patches (measuring displacements) are used as sensors. Modal testing, finite element analysis, and a scanning laser vibrometer are used to reveal the plate's bending-torsional dynamic characteristics due to non-rectangular geometry. Results show that a mode shape can be significantly different from the corresponding operational deflection shape under the excitation of a PZT patch at the modal frequency. The control method uses linear second-order controllers coupled to the plate via different low-order nonlinear terms to establish energy bridges between the plate and controllers. Each linear second-order controller is designed to have a 1:2 or 1:3 or 1:4 internal resonance with one of the plate vibration modes and hence is able to exchange energy with the plate at or around the specific modal frequency. Because of nonlinearities and internal resonances, different orders of saturation phenomena exist and are used to suppress modal vibrations. Several nonlinear saturation controllers are designed and analyzed to show their feasibility and efficiency. Both perturbation analysis and direct numerical integration are used, and some experiments are performed to validate these saturation controllers.

Nonlinear oscillations of a thin, isotropic panel bearing piezoceramic patches are studied in this work. The thin panel, which is clamped along all four edges, forms one of the boundaries of an enclosure. Rigid walls form the other boundaries of the enclosure. The piezoceramic patches are located symmetrically on the top and bottom surfaces of the flexible panel. Nonlinear relationship between the free strain experienced by a piezoceramic patch and the applied electric field is considered along with panel nonlinear elasticity to derive the equations of motion of the plate-enclosure system. It is shown that a voltage input into a piezoceramic actuator pair results in both parametric and external excitations to the panel. For harmonic excitations, the features of the nonlinear responses obtained in the simulations show good agreement with related experimental results. It is seen that for the cases considered, the actuator nonlinearities have a stronger influence on the response than the panel nonlinear elasticity.

In high-precision motion systems, like wafer stages and electron microscopes, mechanical vibrations are a major point of concern. Often, these vibrations have small amplitudes (micrometers) and relatively high frequency (greater than 50 Hz). The so-called Smart Disc (a combined piezoelectric actuator and sensor) is a device that might be used to suppress these vibrations actively. The feasibility of the Smart Disc concept is investigated, using an experimental set- up, consisting of a double mass-spring system, with two Smart Discs. This system has two badly damped resonance modes, to be damped by the Smart Disc(s), by means of feedback of the measured local interaction forces to the actuated displacements. The corresponding control problem, is to minimize the vibrations of the two masses, as a result of a disturbing force. With the experimental set-up, some aspects have been investigated. In the modeling phase, the system revealed high-frequent (3 kHz) resonance peaks, which appeared to originate from the Smart Disc housings. These dynamics have been identified and taken into account in the control design. Because of these high-frequent dynamics near the Nyquist frequency, and the high gain at that frequency (which is inherent to the Smart Disc concept) discrete time effects have been taken into account explicitly. Besides conventional active vibration control strategies, more sophisticated (MIMO H_(infinity ), discrete time) control design strategies have been applied successfully.

Distributed vibration control of an elastic beam is analyzed. The elastic beam is sandwiched between two thin layers of mono-axially oriented piezoelectric material. One layer acts as a distributed sensor while the other behaves as an actuator. A displacement feedback control with a time delay is implemented. In this feedback, the distributed sensor signal which is proportional to strains is amplified and applied to the actuator after a time delay. Because of the nature of the problem the control action enters as a boundary control. An evaluation of the control effectiveness, natural frequency and damping is made for the case of a cantilever beam. Comparisons are given with the uncontrolled cases and zero-delay systems.

A dynamic control model of suppressing external disturbance to beam-plates with piezoelectric sensors and actuators is developed by means of the scaling function transform of the Daubechies wavelet theory. By virtue of this new mathematical tool, an explicit formulation of identification of deflection configuration is expressed in terms of electric charge/current signals measured from piezoelectric sensors. After a control law of negative feedback of the identified deflection and velocity signals is employed, the wavelet Galerkin method or wavelet weighted residual method is used to determine a distribution of control voltage applied on the piezoelectric actuators. Due to that the scaling function transform is like a low-pass filter which can automatically filter out high- order signals of vibration or disturbance from the measurement and the controller employed here, this model does not lead to those undesired phenomena of control instability which is often appeared in a control system and caused by the spilling over of high-order signals from measurement and controller if no special technique is taken in the control system. Finally, a numerical simulation is carried out to show the efficiency and ability of the control program proposed in this paper. It is found that this control model is more efficient than a control program of convection to the example.

This paper is concerned with the real-time automatic tuning of the positive position feedback controller for smart structures by the genetic algorithms. The genetic algorithms have proven its effectiveness in searching optimal design parameters without falling into local minimums thus rendering globally optimal solutions. The advantage of the positive position feedback controller is that if it is tuned properly it can enhance the damping value of a target mode without affecting other modes. In this paper, we develop a real-time algorithm for determining a tuning frequency of the PPF controller based on the genetic algorithm. Hence, the traditional positive position feedback controller can be used in adaptive fashion in real time. To this end, the digital PPF control law is downloaded to the DSP chip and a main program, which runs genetic algorithms in real time, updates the parameter of the controller in real time. The real-time tuning of the PPF controller is applied to cases of initial disturbance and persistent harmonic disturbance. In both cases, the real-time tuning is achieved successfully. Hence, vibrations are suppressed satisfactorily. The experimental results also show that the PPF controller tuned by GA gives better performance than the manually tuned PPF controller for accommodating harmonic disturbances did.

This paper presents a neural network controller for a piezoelectric controlled structure by emulating the control performance of a Linear Quadratic Gaussian (LQG) controller. The configuration of the Artificial Neural Network (ANN) is simple, yet it is efficient in terms of its high learning speed and good generalization ability. A case study is presented to demonstrate the performance of the ANN controller versus the LQG controller. The test results for different disturbances on the structure show excellent agreement between the ANN and LQG controllers.

The heat conduction equation and the dynamic boundary value problem for simple piezothermoelastic materials with time- dependent properties are derived directly from the first and second laws of thermodynamics. It is also shown that the conventional form of the heat conduction equation for geometrically nonlinear anisotropic thermoelastic media does not satisfy the principle of material frame indifference. A consistent form of the heat conduction equation is suggested.

The paper concerns the development of a time dependent constitutive model of polyvinylidene fluoride (PVDF), a thin film piezoelectric polymer. Experimental evidence indicates that PVDF thin films can be characterized as orthotropic materials with different material properties in regard to the orientation of the aligned molecular chains of the polymer. Based on the experimental results, the constitutive equations of linear hereditary viscoelasticity are used to characterize the mechanical properties of PVDF.

This paper summarizes techniques for modeling geometric properties of THUNDER actuators which arise in the fabrication process. These actuators are high performance composites comprised of layers of piezoceramics in combination with aluminum, stainless steel, brass or titanium bonded with hot- melt adhesive. During the construction process, the assembly is heated under pressure to high temperatures, cooled and repoled to restore the actuator capabilities. This process provides the actuators with the robustness necessary to withstand the high voltages required for large displacement and force outputs. The process also provides the actuators with their characteristic curved shape. In this paper, relations between the thermal and electrostatic properties of the material and the final geometric configuration are quantified. This provides an initial model that can be employed in control applications which employ THUNDER actuators.

The systems theory approach to the feedback stabilization of finite-amplitude disturbances in plane Poiseuille flow results in high-order system models to accurately represent the disturbance dynamics. From a practical standpoint, a controller developed for a specific flow control task will often have to be implemented in real-time. The need for the synthesis of rigorous control theory and experimental methods has been noted by several researchers over the years. A key step to this synthesis is the development of low dimensional descriptions of flow dynamics for control synthesis. This paper examines the use of the optimal projection method for reduced-order controller synthesis for flow disturbance model systems with relatively high order (greater than 40).

Microtechnologies and microsystems engineering use new active materials. These materials are interesting to realize microactuators and microsensors. In this category of materials, Shape Memory Alloys (SMA) are good candidates for microactuation. SMA wires, or thin plates, can be used as active material in microfingers. These microstructures are able to provide very important forces, but have low dynamic response, especially for cooling, in confined environment. The control of the SMA phase transformations, and then the mechanical power generation, is made by the temperature. The Joule effect is an easy and efficiency way to heat the SMA wires, but cooling is not so easy. The dynamic response of the actuator depends on cooling capabilities. The thermal convection and conduction are the traditional ways to cool the SMA, but have limitations for microsystems. We are looking for a reversible way of heating and cooling SMA microactuators, based on the thermoelectric effects. Using Peltier effect, a positive or a negative electrical courant is able to pump or produce heat, in the SMA actuator. A physical model based on thermal exchanges between a Nickel/Titanium (NiTi) SMA, and Bismuth/Telluride (Te₃Bi₂) thermoelectric material has been developed. For simulation, we use a numerical resolution of our model, with finite elements, which takes into account the Peltier effect, the Joule effect, the convection, the conduction and the phase transformation of the SMA. We have also developed the corresponding experimental system, with two thermoelectric junctions, where the SMA actuator is one of the element of each junction. In this paper, the physical model and its numerical resolution are given, the experimental system used to validate the model is described, and experimental results are shown.

Among the numerous studies published in the field of shape memory alloys (SMA), an important part is devoted to the thermomechanical properties of these materials. Few studies have been done in order to develop control laws of SMA actuators for temperature, position and force control with guaranteed stability and performances. The reason is that these materials have a highly nonlinear dynamic behavior (including hysteresis) because of the physical principle of motions which is a solid-solid phase transition (between an austenitic and a martensitic phase). It is then difficult to guaranty stable control and to predict the dynamic behavior in closed-loop (trajectory and effort). For this purpose, this paper is focused on control of such actuators. To obtain a control law for the closed-loop motion or force control, we use a nonlinear dynamic model performed in a previous work. With this dynamic model, we use nonlinear control techniques based on the Lie algebra to obtain the control laws for the position or the force closed-loop. Experimentation show that the proposed method is very useful for the control of SMA actuators.

The incorporation of an active control system into an aerospace structure as part of a smart structure has raised the issue of: How does the controller respond when the structure is damaged? The answer is usually dependent on the answer to numerous other questions regarding the type of controller, the type of damage, the application of the smart structure, etc. However, previous research has indicated that the Direct Model Reference Adaptive Control (DMRAC) algorithm has potential in preventing the damaged smart structure from becoming unstable. Maintaining stability following an impact damage is of minimal usefulness if the controller can not also provide satisfactory performance before the damage event. This paper presents the simulation results of research comparing a velocity and position feedback controller with a DMRAC controller. The primary areas of concern were the undamaged performance (damping augmentation) and the damaged performance (stability and steady state response). The traditional controller design performed better before the damage occurred, but the DMRAC controller was significantly better after the damage occurred.

Shape memory alloys (SMAs) are an important material in the fabrication of many smart devices. In response to the need to understand and predict the behavior of SMAs there have been much work performed in developing constitutive models to describe and predict the complex behavior of these materials. This work examines differences in computational simulations of a SMA device due to the choice of SMA constitutive model. The device considered is a hollow SMA tube subjected to torsion loading. The device is designed for use in the DARPA sponsored Smart Wing program lead by Northrop-Grumman. The device is designed to warp the wing frame in order to produce wing twist. Applied moment vs. angle of twist per cm are the parameters of interest for the device. Calculated results are compared with each other. The basis of the computational study are experiments previously completed by Keefe et al. Constitutive modeling approaches considered include pure austenite, pure martensite and constitutive models proposed by Tanaka, Liang-Roger and Lagoudas et al.

THUNDER^TM (thin-layer composite unimorph ferroelectric driver and sensor) represents a new class of piezoceramic- based actuators capable of generating significant displacements and forces in response to input voltages. The performance capabilities of THUNDER^TM actuators are due to the component materials and process used in their construction. A typical THUNDER^TM actuator is composed of metallic backing materials (e.g., aluminum or stainless steel), a piezoceramic wafer, and adhesive in spray or film form. The materials are bonded under high pressures and temperatures and then cooled to room temperature after the adhesive has solidified. Due to the prestresses which result from the differing thermal properties of the component materials under cooling, the actuator is highly durable with respect to mechanical impacts and voltage levels. As a result of this construction voltages in excess of 800 V can be applied to new actuator models without causing damage. This provides the actuators with significant displacement and force capabilities. In this paper, we discuss the development of evaluation criteria which are suitable for characterizing the actuator capabilities and provide a legitimate methodology for comparing THUNDER^TM properties with those of other smart material actuators. For example, the concept of blocked force is often used to quantify the force capabilities of an actuator. However due to the inherent curvature and mode of operation, standard techniques for measuring blocked forces are inappropriate for THUNDER^TM actuators. Furthermore, changing operating conditions, frequency, etc., often make blocked force measurements ambiguous. We will discuss techniques for evaluating THUNDER^TM properties in a manner which limits such ambiguities when comparing with other smart materials. We note that the evaluation issues discussed here are germane to a variety of high performance smart material transducers.

Wavelets provide a new tool in vibration, identification and control. By their properties wavelets transform are stronger than FEM and FFT. We dispose to several wavelets family as Haar, Daubechies, Morlet, Mallat, etc. and use the filter banks for vibration analysis. This paper deals with the problem of controlling the bending oscillations of a thin walled cantilever beam with arbitrary cross section. The control is achieved via the action of a bending moment applied at a tip of structure. A possibility to generate the control bending moment at the wing tip is via the implementation into the structure of piezoactuators. The velocity feedback control allows the possibility to generate damping through the feedback gain coefficient. Feedback law where the bending moment at a tip is proportional to the velocity is included into matrix wavelet implementation. Numerical examples for PDE are computed and compared with other examples for particular cases included in earlier paper of Librescu, Na. The paper uses the Haar wavelet transform to algebrize PDE leading to a powerful and general method to study the nonlinear problems with more flexibility and localization of peak resonance in comparison with other procedures.

This paper presents the design and experiment results of active position control of a shape memory alloy (SMA) wires actuated composite beam. The composite beam is honeycomb structured with shape memory alloy wires embedded in one of its phase sheet for active actuation. The potential applications of this experiment include thermo-distortion compensation for precession space structure, stern shape control for submarines, and flap shape control for aeronautical applications. Shape memory alloy wires are chosen as actuating elements due to their high recovery stress (maybe greater than 700 MPa) and tolerance to high strain (up to 8%). However, shape memory alloy wires are inherently nonlinear and pose a challenge for control design. A robust controller is designed and implemented to active control the tip position of the composite beam. The experiment setup consists of the composite beam with embedded SMA wires, programmable current/voltage amplifier to actuate the SMA wires, an infrared laser range sensor to detect the beam tip displacement, and a real-time data acquisition and control system. Experiments demonstrated the effectiveness of the robust control.

Shape memory alloys (SMAs) are identified with two main characteristics; shape memory effect, and pseudoelasticity; temperature and stress induced phase transformations respectively. By pseudoelasticity, SMAs sustain large amount of strain, without permanent plastic deformation, and recover it upon heating. Constitutive models have been proposed for single/polycrystalline SMAs. The first practical model, was proposed by Tanaka (1985, 1986). That consisted of one equation for stress vs strain, temperature, and martensitic phase fraction (MPF), and a set of kinetic relations, for MPF during phase transformations. Liang and Rogers (1990) proposed a model utilizing a simpler kinetic relation. Brinson (1993) developed a more versatile and realistic model, by incorporating the temperature and stress induced MPF into the kinetic relations. That predicts the material behavior throughout the entire temperature range. This paper presents a comprehensive understanding of temperature and stress induced phase transformation. A thorough interpretation of MPF and critical stresses of phase transformation versus temperature are discussed and capabilities of Brinson's model in reproducing the SMA characteristics under quasi-static thermomechanical loading are demonstrated. Such in-depth elaboration of these relationships has not been reported in the literature; yet is it is essential for capturing the nature of superelasticity. Exploring the capabilities of Brinson's model facilitates applications of autoadaptive materials in structural or mechanical systems.

Preisach model has enjoyed extensive applications in describing the hysteresis phenomena. However an important open question in the analysis of hysteresis using Preisach models is the determination of the model parameters. This is to determine the parameter of Preisach function and is referred as the identification problem. However, no general mathematical methods appear to be available for the identification of nonlinear hysteresis system. As a result customized identification algorithms must be developed for each specific area of applications. In order to more closely describe physical systems, it becomes increasingly difficult to compute the Preisach function and its associated parameters from experimental results as the complexity of hysteresis models increases. This paper presents a new approach -- a Wavelet identification of Preisach model. A wavelet can generate a special basis for all functions with finite energy and has some important properties such as orthogonality, symmetry, short support and accuracy. In this application the output of system and the Preisach functions are represented by a series of wavelets. The experiment data is used to determine the coefficients of the base functions. Then the Preisach function and the output of the hysteresis system can be directly calculated by using wavelet methods.

Model and experimental investigations of electrodynamic properties of tunable structures from liquid-impregnated porous magnetic media are presented. Microwave spectra of complex permittivity and permeability of dry and liquid- impregnated media with ethyl alcohol or water-alcohol mixtures were measured. Real and imaginary parts of permittivity were found to exceed the upper Wiener boundary. Dielectric and magnetic properties of liquid-impregnated porous ferrite media were modeled using non-local volume averaging theory (VAT). This approach accounts for several hierarchical levels and morphology of the system.

One important component in the development of many smart structures and microdevices is the growth of thin films. The control of the growth processes, therefore, is of interest. In the design of a control system for molecular beam epitaxy (MBE), it is important to have simple mathematical models that describe the different growth morphologies that a growing film may exhibit and incorporate atomic-scale information. Of the three types of models currently being considered (atomistic, continuum, and bulk), bulk models have the most interest to control. Still, due to the complexity of such models, however, a model reduction must be carried out to make real-time control possible. A model reduction routine based on a new version of the nonlinear Galerkin methods is proposed and explained for three different bulk models. A total reduction of one-third the number differential equations is obtained.

Shape Memory Alloys (SMAs) have been a major element of Smart Materials and Structures. Many applications, however, call for the embedding of SMA materials within structure components to sense and/or control the thermo-mechanical response of the structures. Therefore, the works on developing constitutive relationship of SMA composite are needed. In this paper, a one-dimensional constitutive law of Shape Memory Alloy composite is developed based on Brinson's one-dimensional SMA constitutive relationship. The thermo-mechanical behaviors of SMA composite are simulated implementing this constitutive relationship. In addition, the bending of a bias SMA composite is also investigated.

For the given input electric current profile, this paper proposes a method which is able to determine the transient temperature of the beam cross section and the embedded shape memory alloy (SMA) wires. Both the heat resistance at the interface between the SMA and the glass/epoxy beam matrix, and the heat convection between the beam surface and the surrounding air are considered. Based on Brinson's constitutive relation of SMA, an iteration procedure is then used to calculate the strain of SMA wires, and the mid-point deflection of the beam.

New class of automobiles has structural skins that are quite different from their current designs. Particularly, new families of composite skins are developed with new injection molding processes. These skins while support the concept of lighter vehicles of the future, are also susceptible to damage upon impact. It is important that their design should be based on a better understanding on the type of impact loads and the resulting strains and damage. It is possible that these skins can be integrally designed with active materials to counter damages. This paper presents a preliminary analysis of a new class of automotive skins, using piezoceramic as a smart material. The main objective is to consider the complex system with, the skin to be modeled as a layered plate structure involving a lightweight material with foam and active materials imbedded on them. To begin with a cantilever beam structure is subjected to a load through piezoceramic and the resulting strain at the active material site is predicted accounting for the material properties, piezoceramic thickness, adhesive thickness including the effect of adhesives. A finite element analysis is carried out to compare experimental work. Further work in this direction would provide an analytical tool that will provide the basis for algorithms to predict and counter impacts on the future class of automobiles.

The functional properties of composites with embedded shape memory wires are directly related to the generation of recovery stresses by prestrained shape memory wires. These wires operate during heating against the elastic stiffness of the matrix material. However, quantitative experimental data on the generation of recovery stresses by shape memory wires, matching these complex constraining conditions, are absent in literature. Therefore, the stresses generated by neat shape memory wires have been studied in detail. The thermomechanical conditions applied in these experiments were similations of the biasing and temperature conditions in polymer composites with embedded shape memory wires. Parameters of the experiment were prestrain of the shape memory wires and two additional parameters to simulate the effect of thermal expansion and stiffness of matrix materials. The influence of these parameters on the generated recovery stresses and on the hysteresis obtained in cyclic experiments has been examined. The results are helpful to understand the functional behavior of composites with embedded shape memory wires. The data can also be used for the experimental verification of modeling procedures for such composites. Some interesting results on stabilization of the shape memory behavior during thermomechanical cycling are also described in the paper.

Smart materials and structural systems are increasingly attracting attention from the engineering community because of their importance in current and future high performance structural applications. As these new structural systems emerge, there is an important need to have capabilities that can be employed for assessing their performance with reference to the primary functional requirement of structural integrity and control robustness as well as reliability. Furthermore, it is desirable to establish adequate performance metrics (which account for inherent or environmental uncertainties) that can be used as a quantitative basis for the comparative evaluation of various design options or for assessing the state of such systems that are already in service. In this study, two measures that can be used for probabilistic characterization and assessment of the performance of actively controlled smart structures are developed. The framework is based on the use of the probabilistic finite element strategy for modeling the parent (host) structure as well as the piezoelectric materials that are employed for sensing and actuation in the assembled system. The uncertainties inherent in the parent structure and the piezoelectric materials are propagated through the probabilistic finite element model. This enables rational and realistic characterization of the performance measures. The probabilistic models are based on the use of advanced reliability analysis algorithms which utilize fast probability integration algorithms that are robust and computationally more efficient than Monte Carlo simulation schemes. To facilitate efficient computation, an adaptive response surface methodology is employed for the approximation of the probabilistic finite element response quantities. Example problems are used to illustrate the robustness and usefulness of the proposed methodology.

In this paper, the integrated finite element methodology developed in our earlier work for designing active vibration control strategies in smart structures, is extended to compute the stresses and strains in the structure, due to combined thermal, mechanical and electrical excitations. A layered composite brick elements with linear strain-displacement and linear thermopiezoelectric constitutive relations is used to model the structure. The method, which has been encoded into a software called SMARTCOM provides a design and analysis capability that simultaneously accounts for the coupled thermopiezoelectric and control capabilities of the smart structural systems. Numerical examples are provided for structures with surface bonded piezoelectric sensors and actuators, under various types of mechanical, thermal and electrical load. Comparisons are made to other available solutions to verify the accuracy of the SMARTCOM simulations. The method provides accurate results and is seen as a valuable tool for the design and analysis of these smart structures.

The strain-temperature hysteresis for shape memory alloy (SMA) actuators has been shown to undergo large changes according to the applied load. This paper provides an adaptive hysteresis model capable of accounting for a time-varying hysteresis, specifically SMA hysteresis under a varying applied stress. Previous research has established excellent performance, in both numerical and laboratory experiments, of the adaptive hysteresis model for actuators with fixed hysteresis. In this paper, the performance of the adaptive model when there are significant changes in the hysteresis characteristics is examined in laboratory tracking experiments.