The shape memory effect occurring in various alloys is due to a Martensitic phase transformation deforming the lattice. Because of elastic misfit of the product phase within the matrix of the parent phase inhomogeneous microstructures arise at two different length scales. As a consequence the deformation to be observed differs on different length scales and one thoroughly has to discriminate between different levels of description. For shape memory alloys the deformations on each level are discussed. Moreover, constitutive theories covering the whole range from microscopic dimensions up to macroscopic polycrystals are reviewed and their interrelations are presented.

Ferroelectric crystals are widely used for manufacturing smart actuators owing to their strong electromechanical coupling effect and the prompt response to the applied electric fields. Many ferroelectric actuators are operated under cyclic loading conditions. The cyclic-loading strengths of these materials are, however, substantially lower than their monotonic-loading strengths. It has been observed that the macroscopic properties of these materials deteriorate after a large number of cycles of the applied electric field. This is the so-called electric fatigue. Recent experimental investigations suggest that microcracking may be the major cause of electric fatigue. The authors investigated the interactions of ferroelectric twins with grain boundaries and pre-existing microcracks. They have demonstrated that the stress fields exhibit a power-law singularity at the intersecting points of twinning planes and grain boundaries. This concentration in stresses may initiate microcracks at the intersecting points. They have also shown that the formation of ferroelectric twins at a pre-existing crack tip results in stronger singularities of the stress and electric fields than the common (root)r-singularity. This indicates that the interaction between the ferroelectric twins and the microcracks may promote crack growth.

Matrix second order systems arise in a variety of structural dynamics and control problems. The analysis and design of such systems is traditionally done in frequency domain or in time domain (state space framework). The formulation of the control design problem in matrix second order form (i.e., configuration space framework) has many advantages over first order state space form. In this paper, a novel approach for designing a stabilizing controller in a second-order model of piezoelectrically controlled flexible beam is proposed.

This paper deals with the problems of converting a continuous-time uncertain system to an equivalent discrete-time interval model and constructing a robust hybrid control law for an uncertain sampled-data system. The system matrices characterizing the state-space representation of the original uncertain materials and structures are assumed to be interval matrices. The Pade approximation method together with interval arithmetic is employed to obtain the approximate discrete-time interval models. A technique is developed to estimate the less conservative modeling errors. These modeling errors are used to modify the obtained Pade interval approximants. The resulting modified interval models are able to tightly enclose the exact discrete-time uncertain model. Various digitally redesigned nominal controllers, which are developed for digital control of continuous-time nominal systems, are extended to the corresponding interval controllers for robust digital control of continuous-time uncertain systems. Using the digitally redesigned interval controllers, the dynamic states of the digitally controlled sampled-data uncertain systems are able to closely match with those of the original analogously controlled continuous-time uncertain systems for a relatively longer sampling period.

An adaptive control algorithm with on-line system identification capability has been developed. One of the great advantages of this scheme is that an additional system identification mechanism such as an additional uncorrelated random signal generator as the source of system identification [Eriksson and Allie, Acoust. Soc. Am. 85, 797 - 802 (1989)] is not required. A time varying plate-cavity system is used to demonstrate the control performance of this algorithm. The time varying plate-cavity system is used to demonstrate the control performance of this algorithm. The time varying system consists of a stainless steel plate which is simply supported on a rigid cavity where the cavity temperature can depend on time. For a given externally located harmonic sound excitation, the system identification and the control are simultaneously executed to minimize the transmitted sound in the cavity. The control performance of the algorithm is examined for two cases. Keeping the cavity temperature constant for the first case, the external disturbance frequency is swept with 2 Hz/second from below to above a resonance frequency of the plate-cavity system. The simulation shows an excellent frequency tracking capability with cavity internal sound suppression of 40 dB. For the second case, the cavity temperature is lowered to a half of its original value in 60 seconds while the external sound excitation is fixed with a frequency. Hence, the cavity resonant frequency decreased and passes the external sound excitation frequency. The algorithm shows 40 dB transmitted noise suppression without compromising the system identification tracking capability.

In recent years, polyvinylidene fluoride (PVDF) film has been extensively used in the development of distributed sensors. However, very few results are available for shaping distributed sensors for control of two dimensional structures. In this study, we have utilized simple geometric shapes for the implementation of feedback controllers on a cantilevered plate system. Multiple distributed sensors along with their time derivatives are used for system identification and the implementation of complex controllers. The resulting direct implementation minimizes the electronic hardware requirements of the controller. A system identification technique for deriving a state variable representation of the structural system using distributed sensors is studied. The state variables of the model are defined as the quantities being measured by the distributed sensors. This technique was originally developed for one-dimensional structures and is extended to the two-dimensional plate system in this paper. The availability of the states of the system simplifies the state space control system design and the implementation of full-state feedback controllers. Linear quadratic regulator (LQR) and H_(infinity ) controllers can be implemented with simple analog hardware. A full state feedback LQR controller is implemented on the experimental system which incorporates all of the necessary signal conditioning electronics. The results of simulation and experimental results are presented.

The goal of this paper is to examine the benefits of integrated control/structure design optimization using covariance control in the presence of saturation limits and performance robustness. A key element of this approach is the use of a covariance parameterization of the control law, allowing saturation and performance robustness to be easily included. The controller design variables are the elements of the Cholesky decomposition of the closed loop system covariance matrix. Applying the approach to an example from the literature it was found that the total structural mass and the control effort were reduced while output rms for the nominal model was decreased. In addition, the optimizer was also able to meet the performance robustness constraints while reducing the performance robustness control effort measure. In examining the results, it was found that the optimizer judiciously altered the closed-loop system by adding phase between the modal resonance frequencies to improve the overall broad-band performance and to help with improving the robustness of the system.

This paper describes an approach for designing a structure-control system based on the linear quadratic regulator (LQR) which suppresses vibrations in structures. Bounds are placed on the control forces to simulate real actuators. The control system is optimized with an objective function of the time to reduce the energy of the vibrations to 5% of its initial value. The design variables are the bounds on each control force with a constraint on the sum of the bounds. As an example to illustrate the application of an approach, a wing box idealized by rod elements is used. Control systems are designed for this structure using four and eight actuators for several locations.

In this paper, we discuss the use of new methods from robust control and especially H^(infinity ) theory for the explicit construction optimal feedback compensators for several practical distributed parameter systems. Indeed, based on operator and interpolation theoretic methods one can now solve the standard H^(infinity ) control problem for a broad class of systems modelled by PDEs. On our approach, the complexity of the computations involved is only a function of the weighting filters, and not the state space dimension which is why we can handle infinite dimensional systems with no approximations involved. These techniques are based on certain operator theoretic notions connected with a class of operators which we call skew Toeplitz. These are precisely the operators which appear in the H^(infinity ) optimization problem.

Actuators and/or sensors embedded into a host material will disrupt the physical properties of the host. Finite element analysis was used to determine and to minimize the stress concentrations which arise in a `smart' material system due to the embedded optical fiber sensor. A parametric study was undertaken to determine the theoretical mechanical properties of the interface coating that minimizes the disruption of the host material properties due to the optical fiber inclusion. The effects of transverse tensile and thermal loading were studied, and also the residual thermal stress concentrations due to the manufacturing process were taken into consideration. The stress concentrations in the composite host are affected by the dimensions and mechanical properties of the interface coating. The results show that with careful selection of the interface coating properties the stress concentrations in the host material caused by the optical fiber inclusion can be reduced and be similar to those of the pure host material.

The dynamic response of an adaptive beam containing embedded mini-devices (sensors and actuators) is investigated analytically and experimentally in this paper. The dynamic model is based on Hamilton's variational principle and the mechanical interactions between the beam and the devices are modeled using Eshelby's equivalent-inclusion method. The dynamic model is verified experimentally, using a cantilever beam made of ALPLEX plastic as host material and piezoelectric devices (PZT-5H) as active mini-devices for sensing and actuation. The experimental setup is outlined and the analytical results are compared with the experimental ones. The capability of mini-actuators to change the dynamic behavior of the adaptive beam is explored for the adaptive stiffening case.

Transverse piezoelectric mode ceramic-polymer composites provide several advantages over conventional longitudinal mode composites. It has been shown, from both analytical and experimental results, the hydrostatic performance of 1 - 3 tubular and 2 - 2 plate piezocomposites can be significantly improved by utilizing the transverse piezoelectric effect. By varying the geometry of the piezoelectric ceramics and the configuration of constituent phases, the undesirable components of piezoelectric response of the composites can be eliminated. Moreover, the effective uniaxial and hydrostatic responses can be greatly enhanced by optimizing the physical properties of the constituent phases and the structures of the composites.

Interfacial bond strengths of shape memory alloy wires embedded in a polymer matrix and subject to various surface treatments were estimated using pullout tests. Bond strength data was compared to in-situ wire displacements obtained using heterodyne interferometry. Experimental data shows that sandblasting of wires increases the bond strength while handsanding and acid cleaning actually decrease the bond strength. Plasma coating the wires did not significantly alter the adhesion strength. Comparisons with displacement data show that an increase in bond strength results in a decrease in displacement of the wire.

The great many advantages to using composite materials in structural applications are often overshadowed by the fact that composites possess relatively low impact resistance and the fact that the damage from impacts is often at a location that makes detection difficult and costly. An inexpensive and reliable method of detecting location and severity of damage in composites would be of great benefit. Embedded optical fibers have previously been used to detect damage using an optical fiber fracture concept, where the optical fiber is intended to fracture at the load that causes damage to the composite host, which in turn prevents light from being transmitted through the fiber. Untreated optical fibers have been embedded in composites subject to loading for this purpose, and the strengths of the optical fibers were found to be such that only severe damage could be detected. To tailor the sensitivity of the fiber, an etching technique was developed to predispose optical fibers to break at a known load. Ductile metallic coated fibers have been suggested as a potential alternative to fiber breakage-type damage sensors, where permanent deformation in the coating is used as a metric of thermal or mechanical overloads. One possible advantage offered by this configuration over etched fibers is that the information includes more than just binary (go or no go) data. The actual magnitude of the event may be recoverable from the residual strain data. If the metal coated optical fiber sensor concept proves feasible for damage detection, then the mechanical and physical attributes that are desirable in a coating must be determined. Sirkis and Dasgupta used non- linear analytical techniques to investigate behavior of a metal coated fiber (not embedded) subjected to axial tension and uniform thermal loading, and found that the concept was feasible. Chang and Sirkis then tested this type of sensor in uniaxial tension and by embedding them in graphite/epoxy plates subjected to impact loading. However, the analysis provided by Sirkis and Dasgupta is of little use in designing the embedded sensors because it did not account for the host material system. This paper remedies this limitation by using non-linear analytical techniques to determine the strains and stresses in a metallic coated optical fiber embedded parallel to the reinforcing fibers in a unidirectional fiber reinforced composite material. While this analysis can be used to investigate the relationship between coating material properties and sensor performance, this paper focuses on the effect that structurally embedded, ductile metal coated optical fiber sensors have on the strength characteristics of the host composite system.

A critical step in the design and development of large strain ceramic actuators is the choice of material and composition. The number of available materials is rapidly growing. It now includes the range of soft to hard PZTs, relaxor ferroelectric PLZT and PMN.PT, and electric field induced phase transformation materials PLSnZT. The development of new materials is leading to ever larger strain, but there is a catch that device designers should be aware of. In some systems increased strain is achieved by developing compositions near thermodynamically metastable states, resulting in temperature, stress, and frequency dependence of the strain/electric-field coupling. This work examines the behavior of several compositions of PZT and 8/65/35 PLZT under combined stress and electric field. Additional data is available for a relaxor ferroelectric composition 8/65/35 PLZT (Lynch 1993, 1994). The results show that the addition of dopants to increase hardness reduces the piezoelectric coefficients, but it also increases both the electrical and mechanical yield points. This allows operation over a broader electric field and stress range with less internal heating due to dielectric loss. The materials that produce the largest strain and the least hysteresis in the presence of compressive stress are not necessarily those with the largest piezoelectric d₃₃₃ coefficients.

We use equations of linear elasticity to study vibrations of a simply supported rectangular elastic plate when time harmonic voltages are applied to piezoelectric actuators attached to its bottom and top surfaces. The actuators are modeled as thin surface films, and mixed edge conditions are employed to simulate simple supports.

Bulk waves can be created in a thin piezoelectric plate by applying an electrical signal to interdigital electrodes deposited on each side of the plate. These transducers can be used to generate ultrasonic bulk waves with a wide range of frequencies and amplitudes controlled by a number of electrodes and a delayed voltage independently applied to each electrode. The current work centers on feasibility study of damage detection via amplified ultrasonic signals generated by interdigital transducers. To this end, finite element simulation of the generation and detection of bulk waves in piezoelectric substrates by means of interdigital transducers is presented and their potential application as probes in smart structures is also discussed.

Infinite or semi-infinite domain problems occur frequently in the modeling of smart structures. Interaction of fields with complex geometries in conjunction with infinite or semi-infinite domains is modeled by introducing a mathematical boundary within which the finite element representation is employed. On the mathematical boundary, the finite element representation is matched with analytical representations in the infinite/semi-infinite domain. The matching has been done with and without slope constraints on the boundary. Drilling degrees of freedom at each of the nodes of the finite element model are introduced to reduce artificial reflection at the mathematical boundary. Of the different methods studied, it was found that a combination of slope constraint and drilling d.o.f. can reduce spurious reflections from the mathematical boundary. Examples involving elastic and acoustic wave scattering by a simple structure in a semi-infinite half space are considered. The method can also be easily applied to electromagnetic field problems.

The approach to modeling and control of smart flexible structures presented in this paper is based on the claim that an intelligent structure requires an internal knowledge of self which may be acquired from local models of substructure dynamics. This approach employs analog models of the flexible structures in model-based controller designs. These analog models are created using VLSI circuitry and are embedded into the physical structure. The model of a composite structure is formed by interconnecting the analog models of single finite elements. The goal of this research is to devise such analog VLSI circuit models of single elements that can be easily connected together to model flexible structures. The circuit models are highly repetitive and, thus, are amenable to integration on a VLSI chip. A simple finite element circuit model has been integrated on an analog VLSI chip. Results clearly show that the poles of the circuits correspond very closely with the theoretical poles of the beam.

In this paper, we study a mathematical model which describes a particular fluid/structure interaction system of current interest at the NASA Langley Research Center.

This paper discusses the Adaptive Neural Control (ANC) Architecture for on-line system identification and adaptive control. After reviewing results to-date involving control of structural vibration, we describe extensions of the ANC architecture to handle adaptive control of smart structures involving large numbers of distributed actuators and sensors.

We investigate the prospects for intelligent control of smart composites (containing sensors, actuators, power supply, and signal conditioning) that are envisioned for applications in rotorcraft systems (rotor blades, power shafts, fuselage shell). This paper is concerned with multi-dimensional wavelets and relevant heuristic procedures for fast and parsimonious identification. We also discuss some control techniques based on the idea of a homogeneous system model.

Presented below is a summary of the results obtained to date on the verification of a novel state space model identification technique called PLID (pseudo linear identification), given in Hopkins et al. This technique has several unique features that include: (1) optimal joint parameter and state estimation (that gives rise to its nonlinearities); (2) provisions for sensor, actuator, and state noise; (3) and it converges almost surely to the true plant parameters provided that the plant is linear, completely controllable/observable, strictly proper, time invariant, and all noise sources are zero mean white Gaussian (ZMWG). Experiments carried out on a flexible, modally dense 3-D truss structure standing 4 feet tall have shown PLID to be a robust technique capable of managing significant deviations from the assumptions made to prove strict optimality. Using the 3 actuators and 3 sensors attached to the structure, models varying in size from 24 to 64 states have been used to approximate this infinite dimensional testbed in the frequency range between 50 to 500 Hz. Sensor signals with rms levels of approximately 2 volts have been predicted by PLID to within 0.01 volts rms.

Comparisons are made between viscoelastic damping and certain types of feedback control. In situations where the sensors and actuators of a feedback control system are collocated, a designer can choose the parameters of the control law to mimic viscoelastic damping. This equivalence is illustrated for a simple mass-spring system and a more complicated finite element. Unfortunately, though, a feedback control law that mimics viscoelastic damping is not very practical because the constant high frequency gain makes it sensitive to unmodeled dynamics. A more practical control law, such as positive position feedback, rolls off at high frequencies, making it less sensitive to dynamics beyond its bandwidth. A finite element for a structure with active-passive members is derived by combining positive position feedback with the Golla-Hughes-McTavish model of viscoelastic damping. A technique based on H_(infinity ) power flow optimal control is introduced as a guideline for designing structural elements that contain both active and passive energy dissipation mechanisms.

A methodology is proposed for designing a structure and robust control for optimum performance. The problem is formulated as a nonlinear mathematical optimization problem with structural weight as the objective function and constraints within the realm of structural and control design requirements. The control approach selected for this investigation is based on multi-input multi-output H₂ - H_(infinity ) theory which can tolerate structured and unstructured uncertainties. The constraints were imposed on the structural frequencies and gain separation between open-loop and closed-loop systems. The application of the design methodology is illustrated on a wing box idealized with bar elements and composite box-beam.

We are researching a new paradigm for CAD which aims to support the early stages of mechanical design well enough that designers are motivated to actually use the workstation as a conceptual design tool. At the heart of our approach is shape synthesis, the computer generation of part designs. The need for such automation arises from the fact that any mechanical part is defined by two kinds of geometry: features that are critical to its function (application features), and the material that merely fleshes out the rest of the part (bulk shape). Application features are most often associated with contact surfaces of the part, for example, a bore for a bearing or a mounting surface for a motor. They are the high-level entities in terms of which the designer reasons about the design. Bulk shape must obey certain constraints, such as noninterference with other parts, minimum allowable thickness of the part, etc., but is somewhat arbitrary. We are developing a system wherein the designer inputs the application features, along with topological constraints, degrees of freedom, and boundary volumes, then the bulk shapes of the parts are synthesized automatically. Overall economy is enhanced by reducing the amount of input necessary from the designer, by providing for more complete exploration of the design space, and by enhancing manufacturability and assemblability of the component parts. This paper presents the functional requirements of such a system, and discusses preliminary results.

This paper advances the state of the art in the selection of minimal configurations of sensors and actuators for active vibration control with smart structures. The method extends previous transducer selection work by (1) presenting a unified treatment of the selection and placement of large numbers of sensors and actuators in a smart structure, (2) developing computationally efficient techniques to select the best sensor-actuator pairs for multiple unknown force disturbances exciting the structure, (3) selecting the best sensors and actuators over multiple frequencies, and (4) providing bounds on the performance of the transducer selection algorithms. The approach is based on a novel, multidimensional householder QR factorization algorithm applied to the frequency response matrices that define the vibration control problem. This paper presents the theoretical development of the method, as well as experimental results from active vibration control demonstrations for the ARPA SPICES (synthesis and processing of intelligent cost-effective structures) project.

In this work, the problem of optimal placement of piezoelectric actuators along a flexible structure is considered. The design goal is to optimize the actuators' performance in vibration suppression of a beam cantilevered on one end to a rotating hub. First the control problem is presented as an infinite-dimensional linear quadratic regulator problem. Then an approximation framework based on a Legendre polynomials based Galerkin method for approximating the control system is developed. Two different approximate performance measures that are based on the LQR cost function are considered and numerical examples are presented to illustrate efficacy of each measure.

Presented is a characterization of a novel phenomenon in shape-memory alloys experimentally observed in our laboratory. The observed phenomenon is a relatively fast cyclic solid phase transformation of elastically restrained SMA Nitinol wires subjected to cyclic pulses of voltage showing a maximum vibration frequency of about 13 Hz at which the amplitudes of oscillations become vanishingly small. However, our conclusion is that wider bandwidth for such vibrational solid phase transformations is possible under different types of restraining forces and heat transfer conditions. In our case free convection in air was the case. The observed meso-phases may very well be different combinations of Martensite and Austenite solid phases of shape memory alloys such as Nitinol. Our system was in the form of a parallel assembly of 0.8 mm diameter, 238 mm long Nitinol wires acquired from Dynaloy, Inc., circumscribed inside a helical compression spring with flat heads, end-capped by two parallel circular plates with embedded electrodes to which the ends of the SMA wires are secured. Thus, the wires can be electrically heated and subsequently contracted to compress the restraining helical spring back and forth. The question answered is; how fast a cyclic voltage can be applied to the system to induce cyclic Martensite-Austenite solid phase transformations. The answer appears to depend on the voltage pulse amplitude, its frequency, stress level in the wire bundle, ambient temperature, aerodynamic environment, and initial wire temperature. Regardless of the initial wire temperature, the equilibrium temperature set in the wires appears to have a value midway between the Martensitic transition temperature M_s and Austenitic transition temperature A_s. These vibrations appear to have potential for micro-electro- mechanical actuations and micro-robotic applications for biotechnological and medical uses. A mathematical model is also presented to simulate the electro-thermo-mechanics of such vibrational solid phase transformations. The proposed model takes into account all pertinent variables such as the strain (epsilon) , the temperature of the fibers T(t) as a function of time t, the abient temperature T₀, the Martensite fraction (xi) , the helical compression spring constant k, the frictional effect and the coefficient of friction (mu) and the overall heat transfer coefficient h. Numerical simulations are then carried out and the results are compared with experimental observations.

Many of the smart materials being investigated (e.g., piezoceramics, shape memory alloys (SMAs), and magnetostrictives) exhibit significant hysteresis effects, especially when driven with large control signals. Furthermore a single input single output hysteresis model may not adequately capture the corresponding nonlinear effects due to the influence of an unmodeled parameter, and two input hysteresis models may therefore be more appropriate. In this paper the Preisach model and inverse compensator for a piezoceramic sheet actuator is described and experimental data presented. The effect of a large independent applied stress on the observed applied electric field to measured strain hysteresis for a piezoceramic sheet actuator is demonstrated.

A new class of materials called smart tagged composites has great potential for use in structural health monitoring. This paper introduces concepts and interrogation schemes for piezoelectric tagged composite materials. Experiments were undertaken to demonstrate the feasibility of piezoelectric tagging by incorporating PZT-5A particles into a polyester matrix. Several types of diametral compression specimens were fabricated and tested to failure while monitoring the induced charge across electrodes placed on the front and back faces of the specimens. The effect of volume fraction of piezo particles and glass reinforcement was investigated along with connectivity of the piezo phase. Small amounts of graphite were added to some specimens to aid in the poling process, however this proved to be of little benefit. The greatest sensitivity and highest induced fields were obtained for a pseudo 1 - 3 piezocomposite system with 6% volume fraction loading of the piezo phase.

A micromechanical model of the authors is formulated in such a way that it can be used to investigate the damping behavior of a rod consisting of shape memory alloys. The model delivers kinetic equations and stress-strain-temperature-volume fraction relations of the transformed (Martensitic) phase. These are coupled with the equations which describe the heat conduction and the (free) vibrations of a rod. Phase change leads to energy dissipation and thus to damping. From the kinetic equation and the constitutive law the dissipated energy and the dissipation rate can be derived at a given temperature. They attain a maximum at a certain fixed temperature between Martensite start and Martensite finish temperature. In order to maximize damping it would be optimal to have this certain temperature everywhere in the considered specimen. Let the rod be heated (or cooled) from its fixed end, then one gets a temperature distribution T(x,t) depending on the distance x from the fixed end at any time t. The total mechanical energy of the rod which is the sum of its kinetic energy and strain energy is calculated as function of time and of the heating (cooling) temperature. One finds that also the optimal damping takes place if this temperature lies between Martensite start and Martensite finish temperature.

A transient analysis, using the finite element method, is presented to study the behavior of piezoelectric materials, including non-linear plasticity effects. The analysis involves the development of an elastic-plastic constitutive law for piezoelasticity. A mixed implicit-explicit integration scheme is constructed to solve the finite element equations so as to exploit the highlights of both transient integration methods. The developed program is used to study the transient behavior of a piezoelectric actuator. Linear solutions show an edge effect resulting in changes in the curvature of the surface during the initial step transient response. The effects of plastic deformation on the behavior of a piezoelectric actuator are presented. Such calculations can be used to predict behavior of a sensor or actuator after an extreme loading event.

Nonlinear, quasi-static finite element calculations are performed for multilayered, electrostrictive, ceramic actuators. Both a stand-alone device and an array of devices embedded in a 1 - 3 composite are studied. The numerical model is based on a fully coupled constitutive law for electrostriction which uses strain and polarization as independent state variables. This law accounts for the stress dependency of ceramic's dielectric behavior and simulates polarization saturation at high electric fields. Two-dimensional plane strain computations are done for a single actuator constructed from Pb(Mg_1/3Nb_2/3)O₃- PbTiO₃-BaTiO₃ (PMN-PT-BT). The stress state near an internal electrode tip is computed and a fracture mechanics analysis is performed to assess the device's reliability. The effect of compressive prestress on the actuator's induced strain response is also predicted. In a second problem, a 1 - 3 composite embedded with an array of PMN-PT-BT multilayered actuators is studied with a plane stress version of the finite element technique. A unit cell model is used to compute the surface displacements of the composite.

In this paper, we start by giving an existence result for a general piezoelectric material the representation of which uses three curvilinear coordinates. Next, we particularize such a result to a three-dimensional piezoelectric shell, and then we show how this existence result can be extended to two-dimensional theories including, or not, the effect of transverse shear strains. Finally, we indicate how to approximate general piezoelectric thin shells by conforming finite element methods.

The so-called smart structures frequently have more sensors than actuators, due to the lower cost and simpler instrumentation. The passivity based controller, which is frequently used in structural control due to its inherent robustness properties, requires sensor/actuator collocation; therefore, it can at best utilize only a subset of the sensors. This paper considers the design of a `squaring down' matrix which would render a system passive subject to some additional performance considerations. This problem is cast as a set of linear matrix inequalities (LMIs) which can be efficiently solved due to the recent advance in interior point methods in convex programming. We applied this procedure with the assumption that the sensors provide displacement as well as velocity information which is generally not true. We show that the proposed scheme can be implemented without the use of such velocity information. Simulation results involving a single flexible beam with torque input and hub position and strain gauge output are presented.

In this paper a robust controller has been implemented on a smart structure test article using the Intel's Electronically Trainable Analog Neural Network (ETANN) chip i80170NX. The smart structure test article used in this study was a cantilever plate with a pair of PZTs as actuators and PVDF film sensors. A two step connectionist approach was used to design and implement the neural network based controller. To meet the desired closed loop performance requirements, a simple linear quadratic regulator (LQR) controller is designed. The spatially distributed sensors allow the direct measurement and feedback of the states of the system. A copy of this controller is transferred into the ETANN chip and the trained chip is used to control the test system. A custom board and electronic circuits were developed for interfacing the neural network chip and the smart structure test article. The steps involved in training and implementing robust controllers on a smart structure have been outlined. Some of the practical considerations of implementing a robust controller using the ETANN chip have been pointed out and dealt with. Experimental verification of the closed loop performance of the conventional LQR controller as well as the neural network controller are also shown.

Various control methods of rotor blade vibration reduction based on individual blade control are presented and compared. The benchmark model used is based on a four-bladed helicopter at hover conditions. In this paper, three control strategies are investigated: LQR method of feedback control, feedforward control, and hybrid control (a combination of feedback and feedforward control). It was found that the LQR method provided substantial improvements in the system and very low gains. Feedforward control was found to be somewhat less effective and the hybrid control method, which combines both feedforward and LQR feedback methods, was proven to be the most effective method.

A one dimensional theory is developed for modeling the analysis of beams containing piezoelectric sensors and actuators. The equation of motion and associated boundary conditions are derived for the vibrations of piezoelectrically sensored/actuated beams. The effect of coupling between longitudinal deflection and bending deflection is investigated in the present study. For the practical applications, in accordance with the proposed beam theory, a one-dimensional finite element formulation is presented. Based on the above one dimensional theory, an entire treatment of designing a state feedback control system for the piezoelectrically sensored/actuated beams is also presented. The results show the proposed approach has several advantages.

A refined theory of laminated composite plates with piezoelectric laminae is presented. The formulation is based on linear piezoelectricity, and includes the coupling between mechanical deformations and the charge equations of electrostatics. The theory developed herein is hybrid in the sense that an equivalent single layer theory is used for the mechanical displacement field whereas the potential function for piezoelectric laminae is modeled using layerwise discretization in the thickness direction. For the equivalent single layer, the third-order shear deformation theory of Reddy is used. This hybrid feature is good in that it demonstrates a way in which multilayered smart skin piezoelectric structures may be analyzed to accommodate multiple voltage inputs and/or sensor outputs.

Optimization of the geometry and excitation voltage of a piezoelectric actuator embedded on a plate structure is studied to reduce the radiation of sound into the space above the plate when the plate is excited by the acoustic pressure field produced by a noise source located below the plate. In the more realistic case, one could consider the plate to comprise one wall of an enclosure containing a noise source. Finite element modeling is used for the plate structure that includes a full description of coupled fields in the piezoelectric actuator and elastic plate. Clamped boundary conditions are assumed in the calculations. The cost function for optimization is the sound energy radiated onto a hemispherical surface of given radius and the optimization parameters are the size of the rectangular PZT actuator (other shapes can also be considered) as well as the amplitude and the phase of the voltage applied to the PZT. Good results are obtained for both resonance and off resonance conditions. The optimization is robust enough that even if the pattern of the acoustic pressure field changes, the radiated sound is still minimized.

The sensor response of a piezoelectric transducer embedded in a fluid loaded structure is modeled using a hybrid numerical approach. The structure is excited by an obliquely incident acoustic wave. Finite element modeling in the structure and fluid surrounding the transducer region is used and a plane wave representation is exploited to match the displacement field at the mathematical boundary. On this boundary, continuity of field derivatives is enforced by using a penalty factor. Numerical results are presented for the sensor response in different host materials piezoelectric sensor materials. It is found that the sensor at that location is not only non-intrusive but also sensitive to the characteristic of the structure.

Based on the theory of invariants, polynomial constitutive relations for transversely isotropic piezoelectric porous materials are derived from the polynomial integrity bases for an energy density function depending on the strain tensor, porosity gradient and the electric field. They are assumed to be smooth functions of their arguments, are expanded about the values their arguments take in the reference configuration and all terms up to the quadratic terms in the gradients of the mechanical displacement, the electric potential and the change in volume fraction are kept. The second order constitutive relations so obtained are then specialized to the case of infinitesimal deformations and weak electric fields, and also to the case of infinitesimal deformations and strong electric fields.

We discuss the stability of steady state solutions for a hydrodynamic model of semiconductors. We study the case where the doping profile is close to a positive constant and depends on the spacial variable x. We shall show that the steady state solution is asymptotically stable with respect to small perturbations in H²(R).

`Electromechanical bending effect' of thin homogeneous piezoceramic plate in consequence of an uneven thickness polarization is investigated. The distribution of electrical field strength and polarization is determined taking into account the injection of electrons from the cathode. Theoretical and experimental data are compared. Formulas for calculation of the mechanical stresses, strains and electrical field strength in piezoceramic plates and shells are obtained. Engineering method and results of numerical calculation of deflection of a cantilever homogeneous piezoelectric plate are given. The comparison of the calculated and experimental determined deflection of the free end of a cantilever piezoceramic plate can be used for the estimation of the real polarization, which arises in the making of thin piezoelectric samples.

The paper deals with determination of specific material properties of a complex material architecture consisting of the elastic layer of finite thickness, the thin viscoelastic layer and the porous halfspace. Those properties should sustain specific external thermomechanical loadings.

Basic equations and boundary conditions describing the behavior of two layered magnetostrictive, ferromagnetic plates in a non-stationary magnetic field are obtained. On the basis of the formulated heterogeneous boundary problems it is shown that in the general case due to the heterogeneous structure of the plate and the magnetostrictive properties of its materials it is possible to excite bending resonance vibrations with the help of magnetic field periodic in time. The peculiarities of the account of magnetostrictive effect in the problems of static stability of ferromagnetic one-layer plate are revealed. The problem of forced lateral vibrations of two-layered magnetostrictive plate is considered.

In this paper the main equations and correlations, describing behavior of coupled magnetoelastic waves of small amplitude in ferromagnetic micropolar media are obtained. As an example plane waves propagation along the anisotropy axis in elastic-isotropic medium is considered. The possibility of magnetoacoustic resonance, caused by the micropolar medium properties account, is shown.

A method for modeling reflectionless conductive dispersive media is presented. The media are either half-spaces or finite dispersive slabs with a spatially varying impedance. The problem of finding reflectionless media for plane waves at normal incidence is formulated as an inverse problem where the constitutive relation is to be determined as a function of depth given a reflection kernel which is zero. The inverse problem is solved by a time domain Green functions technique. It is seen that non-reflecting half-spaces can be constructed in a number of different ways, whereas non-reflecting slabs only can be found if the backwall is non- conducting.

A thermo-electrical and thermo-mechanical model is developed to predict a shape memory alloy (SMA) tendon-actuated compliant beam structure. A geometrically non-linear static analysis is first carried out to investigate the deformed shape of a flexible beam with a SMA tendon actuated electrically. It is found that, when the beam tip deflection is less than 10% of its length, an approximate linear beam model is appropriate, allowing the use of linear beam theory in modeling the dynamic structural response. While the model with nonlinear beam theory is still preferred in model prediction, identification and for full understanding of structure behaviors. The actuation force applied by the SMA actuator to the beam is evaluated by using a thermodynamically based thermomechanical constitutive model for SMA. To calculate the temperature history in the SMA actuator for given electrical current input, the heat conduction equation in the SMA actuator is solved with the electrical resistive heating being modeled as a distributed heat source. Finally, the three steps in the formulation are connected through an iterative scheme that takes into account the static equilibrium of the beam, thus translating an input electrical current history into a beam strain output. The predictions of the proposed model are correlated with experimental results.

In this paper, we propose a method to actively control interlaminar stresses near the free edges of laminated composites by through-thickness thermal gradients. Theoretical solutions are given for optimal steady-state through-thickness temperature distributions under uniaxial loading that are required to eliminate or reduce the interlaminar stresses below a prescribed level. The optimal solutions are obtained by minimizing appropriate performance indices that are functions of the far-field properties, with respect to the through-thickness temperature differences. In the second part, an experimental investigation is conducted on a glass/epoxy cross-ply laminate with embedded piezoelectric sensors and a thermal heater. Through the experiment, a feasibility of the thermal control of interlaminar stresses is demonstrated.