The paper gives an outline of a recent research program on smart structures at the University of Stuttgart in which 16 research projects have been combined. The program is expected to last about 10 years. The covered fields range from smart materials and their integration into composites to shape adaptation of aircraft wings, active vibration suppression and noise control. The program is initiated by the university, supported by the German Research Foundation, and designed in coordination to related industrial projects.

This paper presents an integrated finite element based computational methodology for analyzing smart composite structures with piezoelectric sensors and actuators. The method accounts for the coupling of the mechanical, electrical and thermal fields, which these structural systems will be subjected to in practical applications. 3D thermopiezoelectric composite finite elements are used to model the host structure and the piezoelectric sensors and actuators. The finite element equations are integrated with control algorithms based on the linear quadratic regulator, independent modal space control and the modified independent modal space control, to provide active vibration control capabilities. The capabilities have been incorporated into a computer program called SMARTCOM. Numerical examples illustrating the computation and/or control of deformations due to thermal excitations are presented and comparisons are made to other methods where possible. The present method provides accurate modeling of the smart structures and is seen as a convenient methodology, in that it permits modeling of the complex behavior of the smart structure in one integrated package.

In this paper, a design methodology for enhancing the acoustic power radiated from fluid-loaded piezoelectric transducers at a particular operating frequency is developed. For many applications the operating frequency is fixed by the absorption of the material and the desired depth of penetration (e.g., therapeutic ultrasound). For therapeutic ultrasound and other industrial applications, the acoustic power is the critical figure of merit. The acoustic power radiated from the transducer system is computed from a finite element formulation of the coupled acoustic, elastic, piezoelectric equations of motion. The sensitivities of the acoustic power to two design variables: the length of the piezoelectric element and the thickness of the matching layer, are derived. Using these sensitivities, a novel design methodology in which remeshing is avoided is developed and the effectiveness of the method is studied. Results from the application of this framework for transducer design demonstrate the dramatic increase in radiated power possible from this two member design space.

In order to improve the predictions of dynamic behavior in laminated composite structures, several lower vibration modes from experimental results are used to update the mechanical properties followed by the updated frequencies. As an updating process of the natural frequencies, the optimization algorithm based on conjugate gradient method is adopted. The mechanical properties of lamina, E₁, E₂, (nu) ₁₂ and G₁₂, are design parameters for the identification process. The proposed method is applied to predict the dynamic behavior of laminated composite plates of [0]_8T and [+/- 45]_2S separately and interchangeably. Also, the mixed case for [0]_8T and [+/- 45]_2S is examined to check the possibility for the improved prediction generally. The good agreement is obtained between the measured frequencies and the numerical ones. Based on the results for all the cases studied, the proposed approach has a clear potential in characterizing the mechanical properties of composite lamina.

The problem of flutter suppression using self-straining actuators has been analyzed using the full continuum model of Goland-Ashley and the time-domain solution thereof developed. The theory yields a necessary condition for flutter to occur as well as a formula for the divergence speed. Aeroelastic modes are shown to be the roots of the determination of a 3 X 3 matrix, which involves the Theodorsen function which has the entire negative real axis including zero as an essential singularity line. Computer calculations are presented for the numerical values of the Goland model where the first pitching mode flutters. It is shown that the flutter speed increases as the twisting control gain alone increases (no bending control). There is a critical value of the gain beyond which the pitching mode is stable but the bending flutters but the flutter speed increases as the pitching control gain is increased. The situation is reversed for the bending control. Here the flutter speed actually decreases as the bending control gain increases (no pitch control). There is a critical value for the gain beyond which the pitching mode ceases to flutter but the bending mode--actually the `clamped/rolling' mode--flutters but the flutter speed decreases as the gain is increased. The effect is similar whatever the value of the pitching control gain. It is noted that increasing control gain may decrease flutter speed in highest-order modes.

In this paper, the aspects of modeling and control design methodology for improving roll maneuver performance in aircrafts (for achieving a desired roll rate) by deforming a flexible wing with piezoelectric actuation and sensing are studied. An integrated finite element model of a laminated composite plate embedded with smart piezo actuators and sensors subject to aerodynamic loading giving rise to a steady roll rate is developed. The resulting model in the generalized coordinates which has nonsymmetric aerodynamic damping matrix and a nonsymmetric stiffness matrix (due to aerodynamic stiffness) is then transformed to real but nonorthogonal modal coordinates and a reduced order model is developed. A new control design algorithm based on `Reciprocal State Space' framework is then developed to achieve the desired roll rate and to simultaneously suppress the flexible mode vibrations. The research carried out clearly delineates the relationship and interaction between the structural, aerodynamic and piezo actuation based control subsystems and underscores the importance, potential and the vast scope of the proposed integrated approach to improve aircraft maneuver performance.

A new aeroelastic modal formulation in terms of real modal matrices and modal-state variables is introduced. Real biorthonormality relationships for aeroelastic modes are given with respect to structural matrices. The solution for distributed-parameter-control of an aeroelastic system is developed by modal synthesis from modal-state-space control inputs. In particular, the globally power optimal Independent Modal-Space Control technique is used for maneuver (set-point) control of an aeroelastic system by a modal-performance-output synthesis approach. Control power functionals for an aeroelastic system are defined by any actuation profile and control design. The known solution for the synthesized distributed-parameter closed-loop aeroelastic system is optimally approximated via a gain distribution error minimization technique integrating the transient and power performance characteristics of the system for implementation by distributed, spatially-discrete actuation profiles. For the same purpose, a Galerkin approximation is also given. The method is illustrated for a lifting surface simulating a wing to twist the wing tip to a prescribed angle of attack by using different distributed actuation profiles. Various warped wing shapes can be affected by the approach by synthesizing through different selections of aeroelastic modes for control design resulting in different control power requirements.

Nonsymmetric deformation in tension and compression was measured for a PZT-ceramic. Besides direct measurements in tension and compression tests a method to obtain the nonsymmetric deformation from bending tests was developed. Large differences in strength between tensile and bending tests were found and related to the nonlinear stress distribution in the bending bars and to the statistical size effect. The deformation behavior of PZT-ceramics is mainly investigated under compressive load. Non-linear stress- strain curves were observed and interpreted by domain switching processes. Early results on electroceramics were reported by Subbarao et al. for polycrystalline barium titanate. From these results Subbarao et al. concluded that the Young's modulus would be different in tension and compression. A more detailed analysis of their data shows significant plastic strain contributions in tension and negligible compressive plastic strains, i.e. a non-symmetry in plastic strains. This behavior must have consequences on strength in bending bars due to non-linear stress distribution.

In this paper a finite element model of polarization switching in piezoelectric ceramics is presented. A plane strain four-node element with nodal displacements and voltage degrees of freedom is used. The element incorporates two types of polarization switching: 90 degree(s) and 180 degree(s) switching with electric flux as a switching criterion and with piezoelectric coefficients dependent upon electric field values. The model is used to compute strains for a partially electroded rectangular plate and a hole in a square plate simulating a void in a material. In both of these simulations sufficiently large electric fields are applied to cause domains to rotate 180 degree(s) with calculation of strains along the boundary between dissimilarly poled regions being investigated. In addition to this study, 90 degree(s) domain wall motion is studied on a fully electroded rectangular plate with domains along the diagonal rotated 90 degree(s) and domains in the corners retaining their original polarization. For each of these three cases: partially electroded specimen, void in plate, and full 90 degree(s) switching, the analytical results are compared with experimental data obtained from a Moire interferometer. Comparison between experimental data and theoretical results indicates reasonable agreement between the two suggesting the correct physics is incorporated in the analytical model. In a separate analytical study, stress concentrations near both holes and cracks in the presence of an electric field are calculated. For the linear problem or low electric field values the crack geometry generates significantly larger stresses than a circular hole. For the nonlinear problem, where domain wall motion occurs, the hole and the crack have stress intensity factors of similar magnitude. Finally, reducing the peak stress with implication to extending fatigue life of the piezoceramics is suggested.

Experimental investigations suggest that crack growth in ferroelectric ceramics under alternating electric field appears to be governed by the magnitude of the applied electric field relative to the coercive field, defined as the theoretical strength of applied electric field that is required to induce macroscopic polarization switching. This paper presents the stress analysis for a ferroelectric bar under longitudinal vibration induced by laterally applied alternating electric field. These results indicate that the internal stresses oscillate at a frequency near the system resonance frequency, independent of the frequency of the applied electric field, and the oscillating stresses have substantially larger amplitudes when polarization switching takes place. These indications support the notion the polarization switching intensifies the internal stresses and hence promotes microcracking.

The reliable performance of piezoelectric ceramics in smart structures is hampered by the propagation of cracks from microflaws in the devices. Discrepancies between experimental and analytical results indicate that the established linear theory is insufficient to characterize the cracking behavior of these materials. In fact, the direct extension of linear elastic fracture mechanics to coupled electromechanical problems cannot even reproduce the overall trends observed in the laboratory. In the interest of developing a fundamental understanding of piezoelectric fracture, we present a physics-based analytical model which accounts for nonlinear material response to applied electric fields. By adopting a multiscale viewpoint, the mechanical and electrical singularities at the crack trip are separated. At the local length scale, nonlinear electrical behavior is explained in terms of the effects of discrete electric dipoles, and the crack driving force is altered by the resulting interaction forces. A closed-form expression is obtained for the local energy release rate, which is independent of the exact distribution of dipoles. The model is general enough to account for arbitrary material anisotropy and crystal orientation, for any mechanical or electrical mode of cracking. Analytical predictions of the dependence of fracture stress on applied electric field agree qualitatively with empirical observations in cases for which experimental data are available.

The adaptive H_(infinity ) filter was established by adding a forgetting factor to the H_(infinity ) filter in order to identify structural systems with time-varying dynamic characteristics. The Akaike-Bayes Information Criterion was used to determine the optimal forgetting factor. The behavior of the adaptive H_(infinity ) filter in identifying time-varying structural systems was studied in detail by checking digital simulation results obtained using both the adaptive H_(infinity ) and Kalman filters. These results show that the adaptive H_(infinity ) filter efficiently tracks variation in the structural parameters and is more robust than the adaptive Kalman filter for identifying structural systems with time-varying dynamic characteristics.

This paper presents new feedback actuators to achieve an accurate position control of a flexible gantry robot arm. The translational motion in the plane is generated by two d.c. motors and controlled by employing electro-rheological (ER) clutch actuators. The generated motion can be continuously controlled by controlling the intensity of electric fields imposed to the ER fluid domains of bi- directional rotating ER clutches. On the other hand, during control action of the translational motion, a flexible arm attached to the moving part produces undesirable oscillations due to its inherent flexibility. The oscillations are actively suppressed by employing feedback voltage to the piezoceramic actuator bonded on the surface of the flexible arm. Consequently, an accurate position control at the end-point of the flexible arm can be achieved. In order to accomplish this control target, the governing equations of the proposed system are derived and rewritten as transfer functions to design a robust H_(infinity ) controller. The control electric fields to be applied to the ER clutch and the control voltage for the piezoceramic actuator are determined via the loop shaping design procedures in the H_(infinity ) control technique. Control results are provided to evaluate the effectiveness of the proposed methodology.

To identify dynamic parameters of structural systems, we have to solve non-linear optimization problems because the system transfer equation of a structural system is usually a non-linear function of the system's parameters. The purpose of this paper is to develop a method to linearize an observation equation with respect to structural parameters, which is derived from the system transferequation, and used it to identify the dynamic parameters of linear and non- linear dynamic structural systems. The numerical examples were satisfactory for identifying the dynamic parameters of model structures with eight degrees of freedom.

Iterative redesign techniques are proposed to integrate the design of the structural parameters and the active control parameters for vector second-order lumped-parameter structural systems. The objective is to minimize the required active control effort to satisfy given output variance constraints and robust performance constraints. The problem is formulated as an iterative sequential control design followed by control/structure redesign. Each step of the iterative algorithm is formulated as a Linear Matrix Inequality (LMI) optimization problem that can be solved effectively using available LMI solvers. Convergence of the proposed algorithm to a solution that provides improved control effort and robust stability compared to the single- step structural design followed by control design is guaranteed. Both static state-feedback and dynamic output feedback problems are considered. Numerical examples demonstrate the use of the proposed iterative algorithms.

Flexural vibrations of smart beams are considered where distributed actuators and sensors are realized by means of piezoelastic layers. Utilizing a variational formulation, the direct piezoelectric and the pyroelectric effect are incorporated into beam theory via suitable approximations for the axial components of electric field or electric displacement, respectively. Influence of shear and rotary inertia is taken into account in the manner suggested by Timoshenko. It is shown that the effects of the direct piezoelectric and the pyroelectric effect lead to effective stiffness parameters. The present coupled Timoshenko-type theory thus is equal to computational complexity when compared to the commonly used decoupled theory. This advantageous behavior is utilized for studying thermally induced deflections and calculating natural frequencies.

A general Selective Modal Control (SMC) design methodology is presented for piezolaminated anisotropic shell systems which utilizes Selective Modal Transducers (SMT's) recently developed by the authors for piezo-shells in order to realize any number of possible modal control strategies. An SMC design procedure is specified which defines a step-by- step framework through which structural and control sub- design processes are effectively integrated. Several conditions which sufficiently ensure asymptotic stability are derived and then discussed in the context of deriving SMC methods which are stability robust to modeling and implementation errors. Several SMC examples are then given in which SMT's are designed and control laws chosen so as to allow for (1) the contributions of any given mode to the active energy extraction rate to be directly specified, (2) pole locations to be selectively and dynamically varied, or else (3) both pole locations and SMT design constants to be optimally determined. A numerical example is presented in which a stability-robust optimal SMC method is developed for a cantilevered anisotropic cylindrical shell panel. Maintaining a linear feedback law, a single self-sensing SMT is employed whose design parameters were chosen so as to optimize the system response to a given initial excitation. Frequency and transient response analyses show a dramatic enhancement in system performance and accurately concur with theoretical predictions. The example serves both to illustrate the design process and to independently validate SMT and SMC theoretical results as applied to shell systems characterized by zero-Gaussian curvatures.

The problem of controlling the dynamic response of cantilevers exposed to blast loading is addressed. The structure to be controlled consists of a thin-walled beam of a closed cross-section contour which encompasses a number of non-classical features such as transverse shear, primary and secondary warping and anisotropy of the constituent materials. The control is achieved via the use of the directionality property featured by advanced composite materials and of the actuating capabilities provided by piezoelectric devices which are bonded or embedded into the host structure. The cases of the 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 the patch location upon the control efficiency are discussed. Other issues related with the minimization of the input power required, and implications of the limitation of control input voltage are also addressed.

Currently developments of piezocomposite materials and piezoelectric actuators have been based on the use of simple analytical models, test of prototypes, and analysis using the finite element method (FEM), usually limiting the problem to a parametric optimization. By changing the topology of these devices or their components, we may obtain an improvement in their performance characteristics. Based on this idea, this work discusses the application of topology optimization combined with the homogenization method and FEM for designing piezocomposite materials and piezoelectric actuators. The homogenization method allows us to calculate the effective properties of a composite material knowing its unit cell topology. In the design of piezocomposites, new effective properties that improves the electromechanical efficiency of the piezocomposite material are obtained by designing the piezocomposite unit cell. Prototypes of the optimized piezocomposites were manufactured and experimental results confirmed the improvement. In the design of piezoelectric actuators, we focus on the low frequency flextensional actuators which consist of a piezoceramic connected to a coupling structure that converts and amplifies the piezoceramic output displacement. By designing new kinds of coupling structure flextensional actuators for different tasks can be obtained.

Optical design of piezoelectric smart structures is studied for cabin noise problem and an experimental verification is investigated. A rectangular enclosure of which one side of the enclosure is made with a plate while the rest sides are assumed to be rigid is considered as a cabin. Disk shaped piezoelectric sensors and actuators are mounted on the plate structure and the sensor signal is returned to the actuator with a negative gain. An optimal design of the piezoelectric structures for active cabin noise control is performed. The design variables are locations and sizes of disk shaped piezoelectric actuators and sensors, and actuator gain. The excitation frequency is chosen for a resonance as well as off resonance of the coupled system. To model the enclosure structure, the finite element method which is based on a combination of 3D piezoelectric, flat shell and transition elements, is used. For the interior acoustic medium, the theoretical solution of a rectangular cavity in the absence of elastic structure is used and the coupling effect is included in the finite element equation. The optimal design is performed at several frequencies and the results show a remarkable noise reduction in the cavity. An experimental verification of the optimally designed configuration is performed and it confirms the feasibility of piezoelectric smart structures in cabin noise problems.

Compliant mechanisms are currently used in conjunction with induced-strain actuators to provide stroke amplification. These compliant or flexure mechanisms are preferred over conventional rigid-link amplifiers because they avoid problems with clearances in mechanical joints. Many of the current compliant amplifiers are designed using ad-hoc or intuitive methods, however. In this paper, a topology optimization algorithm developed for systematic design of compliant mechanisms is applied to the design of compliant stroke amplifiers for induced-strain actuators. The underlying formulation for the optimization method is presented, and is then illustrated by two design examples. The functionality of the optimal solutions are verified by finite element analyses.

The design of adaptive mechanical structures is divided into three parts: the structural design, the controller design and the placement of actuators and sensors. The objective of the design is to create a mechanical structure, which corresponds with the physical and technical requirements. The controller design includes the definition of the optimal controller law and the parameters required to create an actuator adjustment from the perceptible signals of the structural answer. The placement of the actuators and of the sensors give an answer to the question about the optimal distribution of the actuators and sensors in the structure. The sensor placement determines which signals are available to the automatic controller. The position of the actuators in the mechanical structure determines at which points control forces may act to influence the structural behavior in a suitable manner. The determination of the optimal position of the actuators require information about the controller design, the sensor position and the layout and the behavior of the structure. Based on the ideas of the shape optimization and topology optimization, a procedure will be presented, to handle simultaneously the discrete positions of the actuators and the continuous parameters of the controller. The method is based on an augmented Lagrangian function to include additional conditions and the discontinuity of the discrete variables into the objective function. The method will be demonstrated by an test example.

Homogenization techniques for determining effective properties of composite materials may provide advantages for control of stiffness and strain in systems using hysteretic smart actuators embedded in a soft matrix. In this paper, a homogenized model of a 1D composite structure comprised of shape memory alloys and a rubber-like matrix is presented. With proportional and proportional/integral feedback, using current as the input state and global strain as an error state, implementation scenarios include the use of tractions on the boundaries and a nonlinear constitutive law for the matrix. The result is a simple model which captures the nonlinear behavior of the smart composite material system and is amenable to experiments with various control paradigms. The success of this approach in the context of the 1D model suggests that the homogenization method may prove useful in investigating control of more general smart structures. Applications of such materials could include active rehabilitation aids, e.g. wrist braces, as well as swimming/undulating robots, or adaptive molds for manufacturing processes.

We propose to understand the microstructural features of magnetoelastic interactions as a decomposition of a macroscopic and a microscopic vector fields. The source of such a decomposition is to be found in a reinterpretation of the main nonlocal, differential constraint on magnetization as a local condition if we introduce an auxiliary stream function.

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 an accurate model P of the hysteresis and then use the inverse P^-1 as a compensator (inverse compensation). This paper focuses on the problem of determining P and P^-1 for a piezoelectric stack actuator. The KP operator is used to formulate the hysteresis operator P and from this an approximation P_m is derived. Compensation is then defined in terms of the inverse of the approximation, P_m^-1. Experimental data collected on an unloaded piezoelectric stack actuator is used to demonstrate the concept of inverse compensation. The parameters of P_m are identified using only major hysteresis loop data and results are given that show P_m provides an accurate model for both major and minor hysteresis loops. Results are then presented that demonstrate the capability of the inverse P_m^-1 to compensate for the actuator hysteresis.

We obtain a model for the non-linear electromechanical motion of piezoelectric rod with domain switching. We assume the piezoelectric body as a continuum with a microstructure given by the effective number of switchable aligned dipoles. As in previous related works, by using suitable mechanical internal constraints and electrical semi-inverse hypotheses, we arrive at a 1D functional. With standard variational techniques then we get 1D equations of motion for the non- linear extension and bending of a piezoelectric rod with domain switching.

A time-dependent, constitutive model is proposed for electrostrictive, relaxor ferroelectric materials. The model is based on Ising spin theory, and simulates stress, electric field and temperature dependent phase transformations in a ceramic material. The resulting model is consistent with Devonshire's theory for temperature induced phase transformations, however it captures the non- linear saturation response characteristic of ferroelectrics driven by high fields. Electric hysteresis occurs when bifurcations cause the solution state to jump between stable branches. The model shows that these bifurcations depend on electric field, stress and temperature. This bifurcation approach differs significantly from phenomenological models based on phase switching. A 1D version of the constitutive model is used to predict the induced strain and polarization as a non-linear function of applied field for a Lead Magnesium Niobate-Lead Titanate-Barium Titanate ceramic. The results are compared with experiments at various temperatures.

In the frame of the continuum theory of lattice defects the 90 degree(s) twin boundary in ferroelectrics is treated as a source of inhomogeneity and internal distortion in both elastic and electric field. The respective elastic and dielectric components of thermodynamic forces acting on the boundary are determined from the balance of total electro- elastic energy of the body and its loading system. Finite element model of the basic side-wise movement of a single twin boundary in barium titanate crystal under electrical and/or mechanical loading has been used in evaluating the thermodynamic forces and predicting the trends in the twin boundary movement. The effect of the 180 degree(s) substructure has been incorporated in the model by means of `softening' the dielectric distortion. The results are compared with known experimental observations. It is shown that the magnitude of the dielectric force on distortion strongly depends on 180 degree(s) substructure in the crystal. The movement of the 90 degree(s) twin boundary, therefore, cannot be predicted unambiguously because it depends on the degree of unequilibrium in substructure and on its rigidity. Several loading cases by aiding and opposing electric voltage or mechanical surface tractions are considered and the case of combined loading is investigated.

The thermo-mechanical behavior of polycrystalline shape memory alloy (SMA) under complex loading (uni-axial loading, multiaxial loading and varying temperature) has been studied by experiments in our laboratory for several years. Recently, the research has been extended theoretically, and a mechanical model of polycrystalline SMA and the corresponding mesoscopic constitutive equations have been developed. The model presented in this paper is constructed on the basis of the crystal plasticity and the deformation mechanism of SMA. The variants in the crystal grains and the orientations of crystal grains in the polycrystal are considered in the proposed model and the derived constitutive equations. The volume fraction of the martensite variants in the transformation process and the influence of the stress state on the transformation process are considered, as well. Besides, the deformation behavior of SMA in the heating and cooling process under different stress states is highlighted in this paper. Some calculation results obtained by the constitutive equations, which are derived from the model, are presented and compared with the experimental results. The deformation behavior of SMA under complex loading conditions can be well reproduced or predicted by the calculation based on the constitutive equations derived from the model.

The use of smart materials (piezoceramic elements) in structure vibration damping has risen in popularity. The ability to use these materials as both sensors, capturing a voltage upon straining of the material, and actuators, acquiring a displacement due to an electric voltage, has increased. The work presented in this paper develops the use of robust intelligent control as applied to smart materials. A steel cantilever beam was constructed as the experimental (physical) plant. Piezoceramic material, lead zirconate titanate, was surface mounted as both sensors and actuators. The controller was formed using algorithms produced from adaptive fuzzy controls. Fuzzy model reference learning control (FMRLC) is a learning system with the capability to improve its performance over a period of time when various plant uncertainties are introduced. The expected goal of this paper is to dampen the fundamental vibration mode of the beam utilizing the intelligent control algorithm developed. Other controllers, such as positive position feedback (PPF) and direct fuzzy (DF), were developed and compared to the adaptive fuzzy controller. The robustness of the system was also examined when the cantilever beam system properties changed. Extra masses were added to account for the variations of the system parameters. The FMRLC controller showed a dramatic improvement over the PPF and DF. It is the adaptive nature of the FMRLC that makes the system robust to parameter changes.

The paper is concerned with the stabilization of an elastic beam subjected to an time-dependent axial forcing. The direct Liapunov method is proposed to establish criteria for the almost sure stochastic stability of the unperturbed (trivial) solution of the structure with closed-loop control. We construct the Liapunov functional as a sum of the modified kinetic energy and the elastic energy of the structure. The dissipation of energy described by a viscous model of internal damping in the structure material is not sufficient to extract the energy coming from the parametric excitation. An influence of the damping of the finite bonding layer is described by the effective retardation time of the Voigt-Kelvin model. The distributed control is realized by the piezoelectric sensor and actuator, with the changing widths, glued to the upper and lower beam surface. The paper is devoted to the stability analysis of the closed-loop system described by the stochastic partial differential equation without a finite-dimensional approach. The effective stabilization conditions implying the almost sure stability are the main results. The fluctuating axial force is modelled by the physical realizable ergodic process. The rate velocity feedback is applied to stabilize the panel parametric vibrations. Calculations are performed for the Gaussian process with given mean value and variance as well as for the harmonic process with an amplitude A.

Tensegrity structures represent a special class of tendon space structures, whose members may simultaneously perform the functions of strength, sensing, actuating and feedback control. The paper exploits this advantage, proposing a smart tensegrity sensor for simultaneous measurement of six quantities: three orthogonal forces and three orthogonal moments. The paper shows how the static and dynamic characteristics of the device can be calibrated through pretension and damping adjustment. The external forces and torques of interest are estimated using the measurements provided by selected tendons. A state estimator, based on the linearized model, finalizes the design.

Smart Structural systems have gained lot of importance now- a-days and have found to have applications in several areas especially in the areas of aerospace, automotive and space applications. One of the essential aspects involved in the integration of smart structures is that of the control system design. Actuator limitation poses as a major obstacle in the real-time implementation of controllers for smart structural systems. This paper gives an account of the application of a controller design procedure to handle control input limitation problem in the design of controllers for smart structures. This procedure, called the limit protection design approach, uses a two-step design procedure to design a control system to achieve graceful degradation of performance in the presence of control input limitation. The solution of the limit protection compensator involves solving a set of bilinear matrix inequalities (BLMIs). An iterative procedure is given for the solution of the BLMIs. Finally, we give the simulation results got from applying the above said procedure on an experimental smart structure.

Control of vibration of a base excited cantilever 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 caused by external excitation can be annihilated by a control wave of opposite signature. Collocated sensor and actuator are used to sensing the traveling wave and generating the control wave. Experimental and numerical results showed that the vibration of a cantilevered beam is substantially suppressed.

The electromechanical coupling factor (EMCF) defined as the ratio of convertible electric energy to the total energy stored in a electroelastic structure is a good measure to evaluate the performance of PZT transducers. The concept of the EMCF can be utilized to optimize the design of actuators. Piezoelectric material properties are temperature dependent and the actuators must not reach the Curie temperature. The need for optimization of these devices results from nonideal behavior i.e. losses, saturation effects and other nonlinearities. In high power applications, where material losses can lead to excessive heat production, different loss mechanisms should be carefully considered to find the optimal design. A total loss factor, analogous to the concept of the EMCF, can be determined, which relates the dissipated energy to the energy stored in an electromechanical system for a given steady-state cycle of deformation. A periodic laminated beam model is considered to investigate the loss factor dependence on the thickness of the piezoceramic layer. Using the Bernoulli-Euler assumption for the electromechanical variables, the state equations of a planar laminated beam are derived. Different losses are determined by employing the complex material constants. The influence of different loss mechanisms on the total dissipated energy is investigated.

The objective of this paper is to describe the development of an analytical closed form solution to model a composite adaptive plate with embedded or bonded piezoelectric actuators and sensors. The mathematical model which describes the electromechanical coupling, the equations of motion and the boundary conditions is based on the Mindlin displacement field and on the Hamilton principle. The electromechanical coupling is a consequence of the piezoelectric characteristics of the actuator and sensor materials. This mathematical modelling technique for distributed actuators and sensors embedded in a composite adaptive plate is based on the Heaviside function.

An innovative actuation principle was introduced in a previous study to drive a rotary actuator by piezoelectric composite laminate. The driving element is a three layer laminated beam with piezoceramics sandwiched between two antisymmetric composite laminae. By taking advantage of the structural coupling, a rotary actuator similar to ultrasonic motors can be implemented. A prototype of the mentioned actuator has been fabricated. The objective of this study is to model this device by finite element method. A commercial finite element code, ANSYS, was employed to simulate the rotary actuator. The piezoelectric laminate and the rotor were modeled by solid brick elements and special constraint element was used to account for the contact between two separate bodies. Static and transient dynamic analyses were conducted to simulate the deformation and the angular motion of the rotary actuator, respectively. Parametric study was performed by modal and harmonic analyses to investigate the dynamic response of the driving laminate. The results of this study confirmed the proposed actuation principle and the developed computational model may be used for the optimization of future design.

An integrated dual approach aiming at controlling the dynamic behavior of anisotropic pretwisted beams rotating with constant angular speed about their longitudinal body axis fixed in the inertial space is presented. The approach is based upon the simultaneous implementation and use of the directionality property featured by the composite materials and of adaptive material systems technology. While the former control technique uses the anisotropy properties of the advanced composite material structures, the latter one exploits the actuating capabilities provided by the piezoelectric materials which are bonded or embedded into the host structure. A dynamic control law relating the piezoelectrically induced boundary bending moments with conveniently selected dynamic response characteristics of the structure is implemented, and its results upon the closed-loop eigenfrequencies of spinning beams are highlighted.

A major aim of smart structures is to reduce the amount of materials used to build them while achieving the same amount of dynamic control. This reduction can however lead to a loss of stiffness and a consequent instability of the structure in the presence of stresses. We have turned this problem around by examining how the use of dynamical instabilities can lead to improved control of given patterns in smart structures. In particular, we studied the possibility of dynamically switching between two configurations of a mechanical system, one in which the desired patterns are stable and one in which they are unstable. By comparing the performance of a distributed control in terms of time to switch and power consumption we established that unstable patterns often switch faster among themselves than stable ones without consuming more power.

Photo-resist dispensers traditionally apply a generous amount of resist on the wafer and then spin the wafer to reach a uniform desired thickness. With this technique, over 95% of expensive and hazardous liquid is wasted. The goal of this project is to reduce the waste by using a drop-on- demand ejection technology to apply the photo-resist. In practice, a controller turns out to be necessary to compensate for the variability of the performance of the ejectors, to insure the stability of the ejection, and to speed up the transient regime for drop-on-demand operation. The paper reports on the design and simulation of this controller.

In this paper we consider the problem of deployment of tensegrity structures. Our idea is to make use of a certain set of equilibria to which the undeployed and deployed configurations belong. In the state space this set is represented by a connected equilibrium manifold and can be completely characterized analytically. The deployment is conducted such that the deployment trajectory is close to the equilibrium manifold and the deployment time is minimized.

We consider optimal H₂ and H_(infinity ) control design problems for distributed parameter systems with large arrays of sensors and actuators. We assume that the actuator and sensor array forms a regular lattice, and that the underlying dynamics have a property of spatial invariance with respect to shifts in the lattice. We show how Fourier transforms over the spatial domain reduces the optimization to a family of standard, finite-dimensional problems over spatial frequency. The solutions are then obtained by parameterized families of matrix algebraic Riccati equations. Such optimal controllers have a natural decentralized and separation structure which we analyze.

We investigate the control of steady-state vibrations of a cantilevered skew isotropic plate by using nonlinear saturation phenomena and PZT (lead zirconate titanate) patches as sensors and actuators. Modal testing and finite- element analysis are performed to study the bending- torsional dynamic characteristics due to the non-rectangular plate geometry. The control method uses linear second-order controllers coupled to the plate via quadratic terms to establish energy bridges between the plate and controllers. Each linear second-order controller is designed to have a 1:2 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 quadratic nonlinearities and 1:2 internal resonances, saturation phenomena exist and are used to suppress modal vibrations. To test this control technique in an efficient and systematic way, we built a digital control system that consists of SIMULINK modeling software and a dSPACE DS1102 controller in a pentium computer. Both numerical and experimental results show that this nonlinear control method is robust in suppression steady-state resonant vibrations without significant spill-over effects.

The forced vibrations of a piezo-laminated elastic beam, being driven by time harmonic voltages applied to the actuators on top and bottom surfaces, is analyzed using an exact elasticity solution. The analysis is carried out by using the method of Fourier series and the solution is exact within the assumption of linear elasticity and plane strain deformation. Numerical results are computed for various configurations of laminated beams, including an aluminum beam with actuators affixed on top and bottom surfaces. To show the capability of the elasticity solution, the static shape of laminated beams due to the piezoelectric induced strains are calculated and compared with approximate existing results.

This paper presents an analysis of the stress concentration in a shape-memory alloy sheet containing a circular hole and subject to arbitrary in-plane loading at great distances from the hole. The generalized Tanaka model is used to describe the constitutive behavior of the material and an approximate approach due to Stowell is used for the stress analysis.

In this paper, we report some results obtained in computational micromagnetism, particularly the numerical approximation of hysteresis phenomenon and the numerical approximation of closure domains. We successively consider a brief recall about micromagnetism, a mathematical modelization of a ferromagnetic material by using the total energy functional of the system, a choice of an appropriate functional space and an associated existence theorem, a convenient minimization algorithm based on an augmented Lagrangian method used in combination with an appropriated finite element method. These developments are illustrated upon the study of a piece of a very thin rectangular plate of a ferromagnetic material located in a coplanar unidirectional exterior magnetic field H_est. Under the action of H_est, we compute the internal magnetization of the plate and then, by decreasing step by step the external field from H_maxe_x to -H_maxe_x, we find back numerically two physical phenomena, the hysterisis and the motion of walls of the closure domains.

A generalized eigenvalue technique is developed for analyzing the structural-acoustic power efficiency of point force actuators. The eigenvalue technique is used to investigate the effect of actuator location and supporting boundary conditions on the power efficiency. Finite element analysis is used to compute the mode shapes of plates with boundary conditions that range from simply- supported to clamped. Power efficiency calculations are then performed for the case of a single point force actuator and an array of point force actuators. The analyses demonstrate that the power efficiency is strongly dependent on actuator location and frequency, but less dependent on the supporting boundary conditions.

Blade vortex interaction (BVI) noise has been recognized as the primary determinant of the helicopter's far field acoustic signature. Given the limitations of design in eliminating this dynamic phenomenon, there exists a need for control. In this paper, we present the application, first of feedback control strategies, and then of adaptive cancellation of Leishman and Hariharan's linear aerodynamic model of a trailing edge flap. Lift fluctuations caused by vortices are taken as output disturbance. The contribution of the vortices to lift is obtained from Leishman's indicial model for gusts. The use of an active structure for actuation is assumed, and the actuator is approximated as a lag element. To design an adaptive cancellation scheme that is applicable not only to BVI but also to general problems with periodic disturbances, we start with the sensitivity method but arrive at the same scheme derived by Sacks, Bodson, and Khosla who introduced a phase advance into a pseudo-gradient scheme. We discuss stability of the scheme via averaging.

Interior noise control in a cabin enclosure using active vibration control of the walls of the enclosure with discrete piezoelectric actuators and sensors is addressed. A hybrid approach using finite element formulation for the radiating walls of the enclosure. We use an exact 3D formulation without making the usual approximations for the electric field in the piezoelectric devices. The electrical boundary conditions and the charge on the electrodes are treated correctly. Computational time is optimized by using plate elements for the structure and 3D element for the devices with transition elements to connect them. A PD-controlled is used to relate the voltage output of the sensor in an open circuit conditions to the charge input to the actuator via appropriate gains to control vibrations. The acoustic part of the problem is modeled via a modal approach. The modal representation of the pressure is used as a mechanical force term on the structure which can be written in terms of a virtual mass. The driving team for the acoustic field is in turn the displacements on the surface of the radiating walls which is computed from the structural equations. This accounts for the acoustic field-structure interaction and the equations are solved simultaneously. By adjusting the feedback gain, significant noise reduction is achieved globally within the cavity for the dominant vibrational modes of the radiating panel.

A 1D continuum model is proposed for phase transformations in ferroelectrics. The complex constitutive model is composed of three parts: Helmholtz free-energy functions to characterize each phase of the material, kinetics to control the velocity of phase boundary, and nucleation criterion to determine the conditions under which a new phase is nucleated.

A solution scheme based on the boundary integral equation method is employed to analyze plane electroelastic fields in piezoelectric solids with arbitrary shaped defects (cavities, cracks, etc). Constitutive equations for solids with hexagonal symmetry are used. The accuracy of the computational scheme is verified by comparing with analytical solutions reported in the literature for a circular cavity and a horizontal center crack in an infinite plane. Numerical results show a significant dependence of mechanical and electric fields on the geometry and orientation of cavities. Complex coupling between electric and mechanical fields is observed. Crack closure calculation of strain energy release rate of piezoelectric solids suggests that strain energy release rate is an accurate fracture criterion for piezoelectric solids, and electric loading may impede or enhance crack propagation. The present boundary element scheme can be used to analyze many interesting fracture problems involving smart structures element with embedded or surface mounted piezoelectric actuators.

This paper presents a simple mathematical model for surface deformation due to ionic interaction in connection with ion- exchange polymer-noble metal composites (IPMC) as biomimetic sensors and actuators. These smart composites exhibit characteristics of both actuators and sensors. Strips of these composites can undergo large bending and flapping displacement if an electric field is imposed across their thickness. Thus, in this sense they are large motion actuators. Conversely by bending the composite strip, either quasi-statically or dynamically, a voltage is produced across the thickness of the strip between the two conducting electrodes attached. Thus they are also large motion sensors. In this paper a simple mathematical model is presented for the role of ionic interactions, and in particular the sulfonic group actions and the metallic electrode anions, in surface deformation observed under an electric field in ionic polymeric-metal composite artificial muscles. It is shown that the columbic attraction/repulsion force distribution has its maximum at the edges of the surface and sharply decreases towards the center of the surface. Furthermore, the maximum force is not macroscopically scale dependent. This means that is attains its maximum over a short finite length. This fact can be used to design large force arrays with collective action for a number of industrial and medical applications. According to our findings an optimal muscle in force/motion capability should consist of series of miniaturized IPMC muscle strips similar to the structure of actual biological muscles' myofibrils consisting of sarcomeres. This paper further identifies key parameters involving the contraction/expansion force characteristics of sensors and actuators made of IPMC's.

Smart material actuator systems are being increasingly used in active vibration control, micro-motion as well as macro-motion applications. Viability of such macro-motion system depends upon how the induced strain in the smart material is transferred to the metal sub-structure. This paper presents results of experimental and theoretical investigations of the induced strain transfer from a piezoceramic material to the metal sub-structure through a bonding layer. The factors selected for the analysis in obtaining optimum strain transfer include the type of the sub- structure material, type of bonding material, thickness of bonding layer, and the thickness of the piezoceramic material. Taguchi method is used to experimentally investigate the individual effects of all these factors. A finite difference based numerical scheme has been developed to study such configurations. Results indicate that the finite difference and analytical methods agree well in determining the effect of parameters on induced strain transfer. Both experimental and theoretical results agree well within the scope of the Taguchi study in determining the effect of parameters. Results show that the type of substructure material and the thickness of piezoceramic play important roles in determining the effectiveness of strain transfer.

An impedance model is formulated for the prediction of the response of structures to induced-strain actuation. The approach utilizes finite element analysis (FEA) to determine the host- structure mechanical impedance. The method couples the numerically obtained impedance to an analytical vibration solution of the induced-strain actuator to determine the dynamic response of the active structure. The methodology is demonstrated in the computation of the dynamic response of a beam structure to induced-strain actuation. This system has been extensively explored by the active structures community. Comparisons of the predicted dynamic response of this structure are made to the predictions of models previously documented in the literature. Experiments are conducted for the purpose of model validation, and an excellent agreement is demonstrated between the predictions of the FEA-based impedance model and measurements made on physical systems. It is anticipated that the formulation extends the FEA-based impedance modeling approach to a broader class of active structures, those for which closed-form expressions of host-structure mechanical impedance are non- existent. Use of the FEA-based impedance approach is suggested when modeling generic distributed structures possessing material anisotropy, mass loading, and non-uniform boundary conditions.

This paper presents a novel integrated formulation and robust computational tool that can be efficiently employed for the design and analysis of actively controlled smart composite structural systems. The modeling simulation capabilities account for the coupling between thermal, mechanical and electric fields within the framework of an integrated structure/control strategy. The paper also reports the formulation and implementation of an optimization capability for the design and tailoring of smart structural systems. Finally, probabilistic and fuzzy models for rationally and systematically accounting for the uncertainties in structural, control, material, and load parameters are presented. The capabilities are packaged in a comprehensive and user- friendly software system (SMARTCOM) that can be readily applied for cost-effective design or response characterization of actively controlled smart structures.

This paper is concerned with the determination of multiple positive position feedback controller gains using genetic algorithms. The genetic algorithms have proven its effectiveness in searching optical design parameters without falling into local minima thus rendering globally optimal solutions. The use of genetic algorithms to the controller design have been investigated by many researchers but limited to the PID control, and optimal controls. In this paper, the genetic algorithm is applied to the positive position feedback control which has been successfully used for the active vibration suppression of smart structures. The advantage of the positive position feedback controller is that it can be easily implemented in analog circuits and each mode can be tackled independently. However, the disadvantage is that the natural vibration characteristics should be accurately determined a priori either theoretically or experimentally. In this paper, we develop a new algorithm for the determination of controller gains based on the genetic algorithm. Hence, the traditional positive position feedback controller can be used in adaptive fashion. Experimental results will prove its effectiveness.

We demonstrate the use of a wavelet-based system for detection and characterization of transients. Traditional matched filtering is implemented in the wavelet transform domain, providing us with efficient algorithms with potential for reduced noise and improved signal separation. These O(N) algorithms have been applied to experimental data from a sea trial, demonstrating their potential for online analysis of sensor data in health monitoring systems.

From the advantage and defect of current distributed optical- fiber sensors (DOFS) schemes, it could be seen that most of schemes except distributed anti-Stokes Ratio Thermometry (DART) are only possible in experiment, but unpractical. But DART is not able to be used on small and fine things especially for smart structures, because of its poor spatial resolution. As we all know that the relaxation time of Raman scattering is in the femtosecond range, and a optical pulse with width > 1 ps will not receive gain reducing, so the potential spatial resolution of DART can be smaller than 0.1 m, even 1 mm (for a pulse with width < 10 ps). Considering these, we firstly propose a novel scheme of DOFS based on spontaneous Raman back-scattering and the effect of high-order soliton, which uses time-correlated single photon counting as detector. The first-order and high-order solitons' effect in the system are theoretically investigated, and it is found that it is able to improve the spatial resolution observably by using high-order soliton in relatively short sensing distance (< 1 km). In the end, the possibility and difficulties of realizing the system based on present-day level of devices are considered.

Regular 2D array of bianisotropic particles lying on a certain plane in free space is considered. The array (grid) is assumed to be infinite and the particles are small compared with the wavelength so that the dipole approximation is available. Here we use our recently developed theory of excitation of planar arrays of bianisotropic particles by plane waves. Both electric and magnetic moments of each particle are related between them and depend on the local field. Therefore the standard approach used in the theory of scanning antenna arrays cannot be applied. The analytical model allows to express the electric and magnetic moments induced in each particle through incident wave fields amplitudes. After calculating the electric and magnetic dipole moments induced in such an array by an incident plane wave we can evaluate the scattered fields. We calculate the reflection and transmission coefficients (which are dyadics) and analyze them.

A problem of electromagnetic interaction for 2D regular arrays of bianisotropic particles with rectangular cells is considered. They are excited by an incident plane electromagnetic wave. The local field in the point of location of an arbitrary chosen particle which can be named as reference-particle is formed by the incident wave and by field of all the particles besides reference-particle. Using dipole model we can express the local fields through only two vector complex values--electric and magnetic dipole moments of reference-particle. The relations between fields of other particles in the point of reference- particle location and dipole moments of the reference-particle are presented by several dyadics which are named as key dyadics. These dyadics play a very important role in solving of the problem of 2D and 3D regular grids excitation by an incident plane electromagnetic wave, because the equations relating electric and magnetic dipole moments of reference-particle with an incident wave field are presented through these dyadics and the polarizability ones. In this paper all components of key dyadics are exactly analytically calculated and their expressions are given in convenient for numerical calculations form.

The problem of electromagnetic mutual coupling of bianisotropic scatterers in the 3D regular arrays is considered. The arrays excited by a plane electromagnetic wave is assumed to be infinite in XY-coordinate plane and finite along OZ-axis, it is the lattice with rectangular cells. Each scatterer can be described as a couple of dipoles (electric and magnetic) having the arbitrary angle between them. The field interaction of these scatterers can be an important factor in the theory of bianisotropic composite media and also concerns the antenna array theory. A simple and rigorous model os such arrays is developed.

PLIF (Piezo Light Intelligent Flea) are a family of walking three legs microrobots, two legs are moved by means of piezo ceramic bimorph actuators, while the third is only passive. These robots are very small (2 cm X 2 cm) and very light (few grams) but at the same time relatively fast (20 cm/s) with the capability to move with very small steps (few microns). In the paper three different type of PLIF are described and some measurement performed with a camera are reported in order to identify the dynamical behavior of the robots. The dynamic measures pointed out that is very difficult to control these systems because of the high uncertainties in the interactions between the legs and the surface. Then a soft-computing approach for the control of such systems has been proposed by using infrared detector as sensors on the robots.

This paper introduces a technique for non-destructive, real-time health monitoring using a model-based observer to determine the onset and location of unintended changes in a structure. These changes could be caused by slipping in joints or latches in deployed structures, or by damage to structural components. An algorithm for calculating the observer feedback gains which allow localization of these changes is described. The algorithm is based on ideas from noninteracting control theory. The validity of the technique is demonstrated by applying it to a computer model of a structure.

This paper is devoted to the dynamic modeling and control of multilayered smart beams of solid cross-section with surface- bonded piezoactuator layers. In contrast to the classical assumption of the perfect bonding of constituent layers, herein the existence of interfacial bonding imperfections among the layers of the host structure is stipulated. The requirements of shear traction continuity and displacement jump across each interface are used to model structures featuring imperfect bonding. Their implications on free and forced vibration control is analyzed via a combined dynamic feedback control law relating their piezoelectrically induced bending moment at the beam tip with the various kinematic response quantities. Numerical results for cantilever adaptive beam experiencing flexural motion under transient distributed loading are presented. For the case of an out-of-phase electrical actuation of the smart structure, implications of the interface bonding imperfections on the structural quantities are investigated. The obtained results reveal the powerful role played by the proposed control methodology towards enhancing the dynamic response of cantilevered multilayered anisotropic beams to transient loadings. Also, the results are likely to contribute to a better understanding and reliable design of smart structures featuring interfacial bonding imperfections.

A wavelength scanning fiber-optic interferometer for distance measurement is introduced in this paper. The system includes two fiber-optic Fabry-Perot interferometers, one as a reference interferometer, the other as a sensing interferometer. These two interferometer models are analyzed and the optimal design is done. The theoretical estimation corresponds the experiments well.

The Recurve architecture is an actuation building block which combines the energy density and strain amplification of a bender with the design flexibility available through actuator arrays. While polymeric piezoelectric materials have been used in prior work to demonstrate this technology, the focus of this work was to demonstrate the use of piezoceramic materials with the Recurve architecture. To accommodate this, three basic connections were developed to allow for assembling Recurve actuation building blocks into array elements: a serial connection in which the Recurve elements are connected so that the displacement accumulates, a parallel connection in which the force from the Recurve elements sum, and a combination connection in which four Recurve elements are connected to increase both force and displacement simultaneously. These connections were demonstrated using a 2 X 2 and 4 X 2 PZT/Steel Recurve array prototype. Quasi-static experiments including free deflection, blocking force, and force-deflection, were conducted and compared to response predicted by analytical models.

The application of SMA actuators in smart structures usually involve thermally induced phase transformation with a variable applied stress in SMA actuators, resulting in thermomechanical non-proportional loading of SMAs in stress-temperature space. To investigate the constitutive response of SMAs under thermomechanical non-proportional loading, experiments for thermally induced phase transformation of binary NiTi SMA wires loaded by an elastic linear spring are performed in the Active Materials Laboratory at Texas A&M University. A constitutive model developed by Bo and Lagoudas and Lagoudas and Bo is used as the basis for the theoretical prediction of the response of SMA line actuators loaded by springs with different elastic constants. Model predictions are compared with experimental results.