The performance of smart structural systems is influenced by structural parameter variations, operating conditions and modeling errors. A mathematical model of the smart structural system must include not only the nominal plant, but also the uncertainties in the system. Often information related to these uncertainties is available during the system identification process, however, most system identification techniques do not address these issues. A system identification technique which incorporates structural uncertainties in the model of structural systems is developed in this paper. This comprehensive modeling technique is useful for the analysis and design of robust control systems for smart structures. The structured uncertainty modeling technique is useful for designing robust controllers such as H_(infinity ) and H₂/H_(infinity ). The H₂/H_(infinity ) control methodology is particularly useful since it increases the stability robustness of the closed loop system while achieving a specified performance. This methodology is used in this paper for designing robust controllers for smart structural systems. A 2D lattice structure is used as the experimental test bed in laboratory investigation to demonstrate the identification technique. Seven interlaced beams form the lattice structure. A model including the first two modes of the structure is generated incorporating structured uncertainty on the eigenvalues. A H₂/H_(infinity ) controller is designed and implemented on the lattice structure and closed loop experimental results are included.

Smart structures lend themselves naturally to a decentralized control design framework, especially with adaptation mechanisms. The main reason being that it is highly undesirable to connect all the sensors and actuators in a large structure to a central processor. It is rather desirable to have local decision-making at each smart patch. Furthermore, this local controllers should be easily `expandable' to `contractible.' This corresponds to the fact that addition/deletion of several smart patches should not require a total redesign of the control system. The decentralized control strategies advocated in this paper are of expandable/contractible type. On another front, we are considering utilization of micro-strip antennas for power transfer to and from smart structures. We have made preliminary contributions in this direction and further developments are underway. These approaches are being pursued for active vibration damping and noise cancellation via piezoelectric ceramics although the methodology is general enough to be applicable to other type of active structures.

In recent studies, neural network based controllers for vibration suppression of smart structures have been reported. Many of these controller have been successfully implemented in simulation as well as using PC based data acquisition hardware. These studies have shown that in addition to conventional controller design methodologies, neural networks offer an effective basis for design and implementation of controllers. With the introduction of the Electronically Trainable Analog Neural Network (ETANN) chip i80170NX by Intel and a digital neural network chip Ni1000 by Nestor Corp., hardware implementation of neural network based controllers has been made possible. These neural network chips have also found applications in other areas such as signal processing and character recognition. In this paper, the capabilities of the ETANN based robust controllers for smart structural systems have been investigated. Robust controllers like the Liner Quadratic Regulator (LQR) and Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) are implemented on a cantilevered plate system using the ETANN chip. Specially shaped PVDF film is used as sensors and PZTs as actuators. The LQG/LTR controller is implemented in two neural network configurations for dynamical systems suggested by Narendra and Parathasarathy. Analog hardware components used in the interface between the ETANN chip and the actuators/sensors on the smart structure test article have been developed. Practical considerations and limitations of the fully analog implementation of the controllers which are not considered in simulations have been discussed in the paper. Practical consideration in training the analog neural network chip for optimal performance has also been described. Experimental results of the closed loop performance of the smart structural system are presented.

Shape memory alloys (SMA) are applied as actuator materials in smart structures and in fastening and pre-stressing devices. Shape memory alloys can be divided into three groups: one-way alloys, two-way alloys and magnetically controlled SMAs. The magnetically controlled SMAs recently suggested by one of the present authors are potential actuator materials for smart structures because they may provide rapid strokes with large amplitudes under precise control. The most extensively applied conventional SMAs are Ni-Ti and Cu- based alloys. Iron-based shape memory alloys, especially Fe-Mn-Si steels, are becoming more and more important in engineering applications due to their low price. The properties of Fe- Mn-Si steels have been improved by alloying, for example, with Cr, Ni and Co. Nitrogen alloying was shown to significantly improve shape memory, mechanical and corrosion properties of Fe-Mn-Si-based steels. Tensile strengths over 1500 MPa, recovery stresses of 300 MPa and recoverable strains of 4% have been attained. In fasteners made from these steels, stresses of 700 MPa were reached. The beneficial effect of nitrogen alloying on shape memory and mechanical properties is based on the decrease of stacking fault energy and increase of the strength of austenite caused by nitrogen atoms. Nitrogen alloyed Fe-Mn-Si- based steels are expected to be employed as actuator materials in pre-stressing and fastening applications in many fields of engineering. Nitrogen alloyed shape memory steels possess good manufacturing properties and weldability, and they are economical to process using conventional industrial methods.

A novel structure for designing a large deflection bending muscle is first presented. The structure is composed of a flexible beam, a thin-wall elastic tube, and an embedded nickel- titanium shape memory alloy (SMA) wire as an large motion bending actuator. The advantage of this kind of structure is that a small actuating strain of the SMA wire can generate a large bending of the muscle. Mathematical modeling of the bending muscle system is then performed, which uses Brinson's model of SMAs for the embedded shape memory alloy wire. Hysteretic nonlinearity of the SMA wire's behavior, geometric nonlinearity of large deflection of the flexible beam, and follower loads on the flexible beam complicate the analysis of the muscle's behavior. This bending muscle system turns out to be a highly nonlinear system. A numerical approach is thus followed by the use of finite element method to predict the behavior of the bending muscle.

An important application of smart materials and structures is the control of periodic disturbances or vibration in environments such as aircrafts and helicopters. In these cases, the source of the noise is a rotating machine, so that a large component of the disturbance is periodic. While it is often possible to take measurements on the machine that is the source of the periodic disturbance, concerns of reliability and maintainability sometimes make such measurements undesirable, if not impossible. Then, the problem is to attenuate a periodic disturbance whose frequency is unknown. An adaptive algorithm is presented in this paper for periodic disturbance attenuation, using the concept of a phase-locked loop. For simplicity, the disturbance is assumed to be sinusoidal. An approximate analysis is performed and the results are found useful to select the design parameters. Simulations are presented that demonstrate the ability of the algorithm to reject sinusoidal disturbances with unknown frequency, and to follow signals with slowly varying magnitude and frequency. The effect of measurement noise and of additional disturbances is also analyzed. The results provide numerical measures of the parameter variations and of the loss of performance in the presence of noise.

For the case of linear, time-invariant, finite-dimensional systems, the connection between the so-called standard problem of H_(infinity ) control and classical Nevanlinna-Pick interpolation is now well known. Indeed H_(infinity )-admissible closed loop transfer functions (i.e. those closed-loop transfer functions corresponding to compensators which guarantee internal stability of the closed loop system for a given open loop plant) can be characterized as all stable transfer functions which in addition satisfy a collection of interpolation conditions (explicitly computable from the original open loop plant). Not so well known is that this frequency domain-type approach, when interpreted operator theoretically in the time domain, extends mutatis mutandis to time-varying systems as well. In this short note we review the standard problem of H_(infinity )-control and its connection with robust stabilization, sketch how the standard solution can be recovered as the solution of a matrix Nevanlinna-Pick interpolation problem, and indicate how the ideas (including a notion of point evaluation and frequency response function) generalize to the time-varying case.

The simulation of a magnetoelastic system subjected to magnetic field loading gives rise to hysteresis. Examples related to Terfenol-D are presented and some methods of analysis discussed.

Structural optimization problems with non-affine boundary conditions must usually be solved numerically. Here we present an example of such a problem which can be solved analytically. Our method utilizes extremal composites as structural components, and makes use of the explicit form of an optimal energy bound.

This paper considers an optimal control problem constrained by coupled hyperbolic and parabolic-like dynamics arising in an acoustic structure interaction. A numerical algorithm, based on the FEM, is formulated for computations of solutions to associated Matrix Algebraic Riccati Equations. Results of a numerical simulation of the algorithm are presented.

In this paper, we address two issues: digital redesign of a continuous-time interval system using an interval chebyshev quadrature approximation method; and translation of the newly digitally redesigned pulse-amplitude modulated controller into an equivalent pulse-width modulated controller via a high-order Taylor-series approximation method. Using this new interval digital redesign technique, the dynamic states of the digitally controlled sampled-data interval system are able to closely match those of the original analogously controlled continuous-time uncertain system for a relatively longer sampling period.

This paper describes an approach for designing a structure-control system based on the linear quadratic regulator which suppresses vibrations in structures. Bounds are placed on the control forces to simulate real actuators. The structure and control system are optimized with an objective function of the total weight of the structure and the control devices. The design variables are the bounds (which are proportional to the weight of the control devices) on each control force and the cross-sectional areas of the structural elements. A constraints are placed on the time required to reduce the energy of the vibration to 5% of its initial value, structural frequencies and upper and lower bounds on the design variables. As an example to illustrate the application of an approach, a wing box idealized by rod elements is used. The actuators and sensors are collocated and assumed to be embedded in structural elements.

Smart material systems enable near collocation of sensors and actuators for controlled structures. Distributed sensors and actuators, placed in close proximity to one another, yield high bandwidth control systems that exhibit passivity characteristics that can be exploited in the design of robust structural control laws. Transfer function properties of Single-Input- Single-Output (SISO) systems with collocated sensors and actuators are well understood. In this paper, analogies between the SISO case and Multiple-Input-Multiple-Output systems with collocated sensors and actuators are developed. The analogies are based on the eigenproperties of complex symmetric matrices; namely, that the eigenvectors of complex symmetric matrices are orthogonal to their simple transpose, and that the eigenvalues of complex symmetric matrices are bounded by the definiteness of their real and imaginary components. These theorems are derived and applied to the analysis and control of nongyroscopic, noncirculatory mechanical systems. Transfer matrices of mechanical systems with collocated sensors and actuators are shown to be complex symmetric matrices whose eigenproperties are determined by the type of collocated feedback. These properties are derived for both the general damping case and for the case of modal damping. An optimal control technique based on the eigenproperties of complex symmetric systems is developed. The technique is a constrainted convex optimization program that can incorporate many different types of performance and constraint specifications. The technique is derived in the paper and a design example is included.

Thanks to the recent advances in control of structures by distributed piezoelectric elements, the concept of independent control and sensing of the structural modes has reemerged in the published literature. In particular, to this end, piezoelectric orthogonal actuators and sensors have been introduced. On the other hand, Independent Modal-Space Control (IMSC) of distributed-parameter-system (DPS) is a well-known approach advocated by the author and his associates throughout the past two decades. In the 1980's it has been shown by its proponents that the IMSC method ultimately represents a globally optimal distributed-control and distributed-sensing approach to structural control. Piezoelectric elements are not exception to the general theoretical concepts of distributed-control and sensing of DPS's via the IMSC method. By a constructive theoretical approach, it is shown in this paper that the recent results characterized by the phrases `independent modal control' and `orthogonal actuators and sensors' constitute precise piezoelectric realizations of the IMSC method of the author and his past associates, almost two decades after its introduction.

Active noise control of a plate structure with multiple disk shaped piezoelectric actuators is studied. The plate is excited by an acoustic pressure field produced by a noise source located below the plate. Finite element modeling is used for the plate structure which is modeled by a combination of 3D solid, flat shell and transition elements. In the optimization procedure, the sound energy radiated onto a hemispherical surface of given radius, defined as the objective function, is minimized. The design parameters are the locations and sizes of the piezoelectric actuators are well as the amplitudes of the voltages applied to them. Automatic mesh generation is addressed as part of the modeling procedure. Numerical results for both resonance and off resonance frequencies show remarkable noise reduction and the optimal locations of the actuators are found to be close to the edges of the plate structure. The optimized result is robust such that when the acoustic pressure pattern is changed, reduction of radiated sound is still maintained. The robustness of an optimally designed structure is also tested by changing the frequency of the noise source using only the actuator voltages as design parameters.

The sound radiation from vibrating NITINOL-reinforced plates coupled with acoustic cavities are controlled by heating sets of shape memory alloy (NITINOL) fibers embedded along the neutral planes of these plates. Thermal, dynamic and acoustic finite element models are developed to study the fundamental phenomena governing the coupling between the dynamics of the NITINOL plates and the acoustic cavities. The models are used to compute the frequencies, mode shapes and sound radiation for different initial tensions and activation strategies of the NITINOL fibers. The predictions of the models are validated experimentally using a square glassfiber/polyester resin plate, whose sides are 19 cm and thickness is 0.254 cm, mounted on a 19 cm X 19 cm X 38 cm cavity. The plate is reinforced with 58 NITINOL fibers that are 0.55 mm in diameter which are embedded inside vulcanized rubber sleeves placed at the plate mid-plane. The results obtained indicate close agreement between the theory and experiments. Also, it is shown that activating all the NITINOL fibers results in increasing the first mode of vibration from 240 Hz to 277.5 Hz and increasing the corresponding loss factor from 0.014 to 0.039. Such significant shift of the modal characteristics of the plates results in suppressing the amplitude of vibration of the plate by 76% and attenuating the sound pressure level radiated inside the cavity by 62%. Therefore, the experimentally validated theoretical models presented in this paper provide invaluable means for predicting sound radiation from NITINOL-reinforced plates in coupled acoustic cavity.

A finite element (FE) formulation is presented for modeling the dynamical response of smart structures with embedded piezoelectric ceramic devices subjected to transient loading. The FEM formulation presented is based on a variational principle using the concept of virtual work. An unconditionally stable method ((alpha) -method) is utilized for the direct integration of the equations of motion and can be put in the form of a 3-step linear multistep method of second order equations. A thin cantilever plate with piezoelectric devices is investigated to show the feasibility of the analysis and numerical simulation. The code employs 20 node isoparametric 3D piezoelectric elements, flat-shell elements and transition elements at the interface of the piezoelectric devices and the plate. Under a given external loading, the structure and the embedded sensors deform and the voltage response of the sensor can be calculated as a function of time. Such calculations can be useful as a design tool for smart structures.

Active constrained layer damping consists of either replacing or augmenting the constraining layer for a viscoelastic material with piezoceramic actuators in an attempt to improve vibration suppression properties by synergism between passive and active damping techniques. An important question in such configurations is whether the reduction in actuation ability of the piezoceramic on the beam due to a relatively soft viscoelastic layer is compensated for by enhanced passive damping due to increased shear in the viscoelastic material. Some tradeoffs between pure passive, pure active control, and active constrained layer damping are discussed here. Velocity feedback and LQR are investigated. Several authors have researched and developed formulations for active constrained layer damping techniques. The approach presented here differs from most in that it employs an energy principle for the equations of a beam with partial active/passive constrained layer damping transients. An offshoot of this is the thickness of the viscoelastic layer can be arbitrarily small (even zero), thus opening up the possibility of simulating the realistic design problem where the optimal sizing, length, and thickness of a treatment is subject to a total thickness restriction. The results show that the active constrained layer damping treatment provides better vibration suppression than passive damping treatments, and it even out performs pure active control for low-gain applications.

The shear strains in the visco-elastic cores of beams controlled by Active Constrained Layer Damping (ACLD) treatments are determined and compared with those of beams controlled by Active Control (AC) and conventional Passive Constrained Layer Damping (PCLD) treatments. Such comparison is essential in quantifying the individual contribution of the active and passive damping components, to the overall damping characteristics, when each operates separately and when both are combined to interact in unison as in the ACLD treatments. The comparisons are based on distributed-parameter and finite element models which describe the behavior of beams controlled by ACLD as well as beams treated by AC and PCLD treatments. The distributed-parameter models give closed-form expressions for the energy dissipation characteristics of the ACLD treatments in comparison with those of the AC/PCLD treatments. Also, the finite element models are validated experimentally using visco-elastic cores which are photo-elastic in order to study the distribution of the shear strains inside these cores. The results obtained indicate that the ACLD treatments are capable of developing shear deformations, in the visco-elastic cores, higher than those generated by the AC/PCLD treatments when the ratio of the longitudinal rigidity of the constraining layer to that of the base beam is less than 1. With such enhanced shear deformation capabilities, the ACLD treatments can develop high damping and effective attenuation of the vibration of critical systems as the blades of rotorcrafts.

In this paper, a new active constrained layer (ACL) configuration is proposed to improve the active action transmissibility of the current ACL treatment. Introducing edge elements, the active action from the piezoelectric cover sheet can be transmitted to the host structure more directly. On the other hand, such a configuration still has the passive damping ability from the viscoelastic layer. In other words, it has the benefits of both the current ACL and a purely- active system. Analysis results indicate that the proposed new approach can suppress vibration effectively, and it can achieve better performance with less control efforts as compared to systems with purely-active or current ACL treatments.

In this paper a set of controllability and observability conditions are proposed for vibration control systems with viscoelastic damping. Both conditions are stated in terms of the eigenstructures (eigenvalues and eigenvectors) of the control systems under consideration. They are similar to the well known eigenvector tests, except that to determine controllability, the knowledge of the stress-strain relations of the viscoelastic damping material is needed in addition to the modal information.

A structural control concept, using multiple active-passive hybrid actuators (piezoelectric materials with active voltage sources and external passive RL circuits) on a ring structure, is investigated. A method is developed to simultaneously optimize the active control gains and the values of the shunt resistors and inductors. Kalman filter is employed to estimate the states of this multi-input-multi-output systems. Analysis results indicate that the proposed approach can suppress vibration and noise radiation effectively, and it can achieve better performance with less control effort as compared to a purely active system.

The paper discusses the objectives, issues and research directions of the ONR program on active materials and adaptive structures. It addresses the mechanics tools necessary for the design of this new class of structures. The paper reviews the research in the mechanics of materials of high strain active materials and engineering active materials, hybrid active materials, constitutive modeling, failure of ferroelectric ceramics, and active material interaction with host material. Understanding failure mechanisms in active materials was recognized early in the program to be of great importance to reliable design of high performance actuators and their acceptance by the design community. New concept of engineering active materials, and developments of hybrid active materials are introduced, as means to achieve high performance actuation. The paper covers different design approaches for high strain/high frequency actuators and new actuator concepts and the mechanics of embedding of actuators in composite structures.

A non-linear constitutive model for relaxor ferroelectrics developed by Hom and Shankar is examined and verified with electromechanical experiments. This model links polarization and strain to the electric field and stress in an electrostrictive material. A set of tests were performed to study the quasi-static electrical behavior of PMN-PT-BT materials under prestress. Another set of tests investigate the effect of DC electric field on the elastic modulus of the material. The results show excellent correlation between the predicted behavior of the model and the experiments. Failure models for electrostrictive ceramic materials are presented which address the issues of actuator reliability. The constitutive model of Hom and Shankar is incorporated into a nonlinear finite element code. A new finite element technique for computing the J-Integral for cracks in electromechanical materials is developed. This technique is based on the domain integral method and computes both the mechanical and electrical contributions to the energy release rate. The finite element code and the J-Integral computation are used to study crack growth in multilayered electrostrictive ceramic actuators.

Experimental observations indicate that electric fatigue of polycrystalline ferroelectric ceramics is partially recoverable through thermal treatments at temperatures that are too low to heal microcracking which is considered to be the primary cause of electric fatigue. It has been conjectured that this thermally-recoverable fatigue is due to domain pinning. This paper presents a theoretical model for the domain pinning effect on macroscopic properties of polycrystalline ferroelectric ceramics. The numerical results suggest that domain pinning can indeed lead to the type of fatigue behavior as observed.

Exact line-integral representations for transient dynamic stresses induced in anisotropic elastic and piezoelectric bodies due to electro-mechanical sources of arbitrary shape are derived according to a methodology already established by the authors. A numerical example involving piezoelectric ceramics is provided to show the behavior of stresses due to applied forces.

The isothermal full Gibbs function which is negative definite and the adiabatic internal energy which is positive definite are used to develop a linear fracture theory for isothermal and adiabatic cracking in a piezoelectric material, respectively. Both the full Gibbs function release rate and the internal energy release rate for crack propagation are evaluated and revealed to be positive functions of crack lengths and remote loads, even under pure electric loads only. When the electric permittivity inside the crack is treated as zero, each of the full Gibbs function release rate and the internal energy release rate has a compact form in terms of the mode II, I, III stress and electric displacement intensity factors.

The problem of controlling the bending vibration of cantilevers modeled as thin-walled beams of closed cross-section incorporating a number of nonclassical effects, such as transverse shear, secondary warping and heterogeneity, is investigated. The control is carried out by means of piezoelectric materials bonded or embedded into the host structure. The control law represents a combination of displacement, velocity and acceleration feedback. The capabilities and efficiency of this control methodology are illustrated and a number of relevant conclusions are outlined.

A 1D model for multilayered planar beams is defined by joining 1D beam models a la Cosserat together. An interlaminar stress arises naturally from the expression of the inner working, and its singular part at the boundary as well. Local and boundary balance equations are derived from an assumed expression for the working.

In studying the behavior of piezoelectric material one has to handle with the two aspect related to their mechanical and electric properties. In this paper we give a complete and thorough analysis of the Saint Venant problem for linear elastic piezoelectric cylinders. It is well known that, from a mechanical point of view, the problem of determining the deformation of a cylinder once fixed the resultant forces acting on its bases can be solved in analytical form only under restrictive assumptions. In particular general solutions are available within the so called `Clebsh-Saint-Venant' hypothesis (T equals 0). This hypothesis we will use in our paper. In this way we are able to give the general solution for the problem of linear piezoelectricity in the case of a cylinder in contact with a medium with low permittivity, and the case in which the cylinder is in contact with conductors at an assigned potential. We find that it is possible to control in the first case Poisson effect, and in the second flexural deformation.

We use the 3D linear theory of elasticity to analyze the steady state vibrations of a simply supported rectangular linear elastic laminated plate with PZT sensors and actuators. It is assumed that there is perfect bonding between different layers. Numerical results for a plate containing one embedded actuator layer and one embedded sensor layer are presented.

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

A design approach for a rotatory joint actuator using a contractile shape memory alloy (SMA) wire is presented and an example design is followed. In this example, the output torque of the actuator is 18 Newton-meters, and its angular range is 30 degrees. Compared with a SMA spring type actuating component, a SMA wire type actuating component uses less SMA material and uses less electrical energy when it is electrically powered. On the other hand, a SMA wire type actuating component must have a large SMA wire length to produce a required amount of angular rotation of the joint. When pulleys are used to arrange a lengthy SMA wire in a small space, the friction between pulleys and pins is introduced and the performance of the joint actuator is degenerated to some degree. The investigated joint actuator provides a good chance for developing powered orthoses with SMA actuators for disabled individuals. It can relieve the weight concern with hydraulic and motor-powered orthoses and the safety concern with motor-powered orthoses. When electrically powered, a SMA actuator has the disadvantage of low energy efficiency.

A mixture model is proposed to model domain switching in polycrystalline ferroelectric ceramics. Each grain is modeled as a body of mixture consisting of distinct types of domains which are characterized by their mass fractions as internal variables. In this model, domain switching corresponds to changes of mass fractions of the corresponding domains. A thermodynamics-based criterion is proposed to govern domain switching in quasi-static processes. With the present model, one can make grain-level calculations of internal stress and electric fields to which microcracking, the primary cause of the electric fatigue, is attributed. The explicit solution to an idealized 1D polycrystalline ferroelectric system is presented in order to explore the implications of this model.

A micromechanics-based modeling and simulation of the reorientation process of single crystal shape memory alloys under externally applied mechanical loading are performed in this paper. The work is based on the recently developed micromechanics constitutive theory of single crystal under thermoelastic martensitic transformations. In the modeling, the crystallographic theory of martensitic transformation is used to obtain the kinematic relations of the deformation process, and the elastic strain energy and total free energy of the constitutive element are derived by using thermodynamics and micromechanics self-consistent approaches. The effect of microstructural state variables of the material such as the volume fraction of each kind of variants, their spatial distribution, shape parameter of martensite variants, etc. on the macroscopic behavior of the material is quantitatively taken into consideration. In this paper three kinds of microstructure rearrangement during reorientation process are simulated: (1) reorientation between two kinds of variants; (2) reorientation among 4 kinds of variants; (3) reorientation among 24 kinds of variants; all under both monotonic and cyclic loading. Modeling predictions of the reorientation process reasonably simulate the microstructure processes happening in real materials.

Piezoelectric sensor of a vibration control system is studied in this paper. The control system was based on the concept of active attenuation, the response of a structural elements can be cancelled by a control motion of opposite signature. The effectiveness of the control system was determined by the phases of the excited traveling wave and the control wave. It is found that the amplitude and phase of the sensed vibrational signal depends on the length of the piezoelectric sensor. The dependence of the phase and amplitude of the sensed vibrational signals on the length of piezoelectric sensors on a cantilevered beam were measured and compared with numerical results.

A thermally induced phase transformation in a Shape Memory Alloy (SMA) polycrystal occurs gradually over a range of temperatures unlike the first-order transition (at a single temperature) of a SMA monocrystal. This spread in transformation temperatures is believed to be caused by such factors as material inhomogeneities and internal stresses in the polycrystal. Taking a recently proposed thermodynamic model by Bo and Lagoudas for the Two-Way Memory Effect of SMA materials as a starting point, we extend it to account for the presence of initial heterogeneities, by introducing a statistical distribution in the Gibbs free energy function. The extended theory is then used as a basis to correlate strain recovery vs. temperature measurements from thermally induced cyclic phase transformation in untrained polycrystalline wires.

Shape memory alloy has been considered as an actuator for applications that require low bandwidth, high force, and large displacement. Two factors have limited the usefulness of such actuators: hysteresis and bandwidth limitation. This paper considers the hysteresis phenomenon from a control point of view. We first consider the application of the Preisach hysteresis model to describe the SMA hysteresis, and demonstrated experimentally that the two key assumptions: minor loop congruence and wiping-out property hold approximately. We then consider the feedback control of the force exerted by the SMA wire. By using a simple lumped temperature model, we argue that proportional feedback with a suitable range of gains would render the closed loop stable. This is verified experimentally in a simple experimental setup consisting of a flexible aluminum beam and to a Nitinol shape memory alloy wire that applies a bending force to the end of the beam. When the gain is chosen too high, clear instability has been observed despite the low bandwidth of this system (about 1 Hz).

Smart materials such as piezoceramics, magnetostrictive materials, and shape memory alloys exhibit significant hysteresis, especially when driven with large input signals. Hysteresis can lead to unwanted harmonics, inaccuracy in open loop control, and instability in closed loop control. The Preisach independent domain hysteresis model has been shown to capture the major features of hysteresis arising in ferromagnetic materials. Noting the similarity between the microscopic domain kinematics that generate static hysteresis effects in ferromagnetics, piezoceramics, and shape memory alloys, we apply the Preisach model for the hysteresis in piezoceramic and shape memory alloy materials. This paper reviews the basic properties of the Preisach model, discusses control-theoretic issues such as identification, simulation, and inversion, and presents experimental results for piezoceramic sheet actuators bonded to a flexible aluminum beam, and a Nitinol SMA wire muscle that applies a bending force to the end of a beam.

A general and systematic approach to control the longitudinal load transmissibility in a rod by coupling generalized substructures is presented. This approach illustrates a general concept of `substructure' by formulating the active controllers as virtual substructures coupled to the main structure. The dynamics and load transmissibility of a rod is modeled in modal state space form. The three control algorithms such as IMSC, ELVC and GSLQ are formulated as three different substructures also in state space form so that an explicit substructure dynamics can be realized. The performance of the different algorithms is based on the reaction force at the fixed end due to a disturbance force at the other (free) end. A performance measure is defined as the reaction force ratio of the closed-loop (coupled with the substructure) to the open-loop (without the substructure). The performance as a function of frequency of all three virtual substructures is presented. This general approach has provided a way to appreciate the effect of any substructure (either a controller or an attached structure) on the main structure. And it has important implication for designing substructures for the desired response of the total structure.

In this paper we are concerned with Smart Materials that contain many actuators and sensors along with digital signal processing electronics that allow for the implementation of a control algorithm. Smart Materials have been proposed for the active control of sound from a vibrating structure. Here we investigate the design of structural control systems for these Smart Structures for noise suppression. First we model the radiated acoustic waves in terms of the velocity of the surface of the structure. Then we formulate an optimal control problem as a linear system that has a transmission zero in the path between the disturbance force and the shape that radiates best. A geometric description of the problem relates control problem to the acoustics. This optimal control problem is solved using a genetic algorithm.

This paper presents a simple, effective and economical system capable of suppressing periodic vibration (external or self induced) affecting a structure or payload. The approach used integrates piezoelectric materials/actuators, sensors, and low-cost electronics in a novel way. The key innovation is the use of phase-lock-loops (PLL) and switch capacitor filters (SCF) for the on-line identification, tracking and control of periodic vibration. This method concentrates its control action at those frequencies where periodic vibration is detected. Among the advantages of this approach are: it is conceptually simple, easily expandable and modular; the controller does not rely on a model of the structure, and it only needs some approximate notion of the frequency range where the periodic disturbances are expected to occur; it is robust and can be operated at high gain without loss of stability; it is not significantly affected by the presence of random vibration or sensor noise; and it can be implemented with inexpensive electronics. The effectiveness of this new approach was experimentally evaluated using a test unit consisting of a simple structure, accelerometers and Terfenol-D actuators. The structure was excited by driving one of the actuator with sinusoidal and random signals. The resulting periodic disturbances were measured using the accelerometers. The acceleration signals were passed though a bank of PLLs and associated SCFs to detect the fundamental frequency and harmonics. This information was used to drive another actuator that rejected the original disturbances, and attenuation levels as high as 30 dB were achieved.

Neural network based predictive control for random vibration suppression has been demonstrated on a cantilevered beam with bonded piezoelectric actuators and sensors. This real time system is run on a 60 MHz Pentium processor and is considered a stepping stone to both adaptive flutter suppression and buffet load alleviation in advanced aerospace vehicle. An extended neural control system using Intel/Nestor's ETANN analog neural network chip is discussed. Generalized neural predictive control uses a neural network based model of a system to make predictions about the effect of future control signals on the response of the system. These predictions can be used with a tailored performance index to determine the optimal control signal for the modeled system. A comparison of this approach with both PID and pole placement control methods shows ease of implementation comparable to that of the PID controller with the approximate performance of the pole placement method. The advantages of neural control over conventional control techniques include a simpler and more cost effective design methodology as well as the capability to learn on-line the time varying nature of a system due to wear, loss of actuators, or other causes.

Terfenol-D is a `giant' magnetostrictive material offering mechanical strains on the order of 1000 X 10^-6 m/m. Dynamic transducers constructed using Terfenol-D as the motion source offer displacements based on approximately +/- 500 (mu) strain. These transducers are known to be nonlinear; however, in some applications they can be treated as linear systems and their behavior approximated by the classic pair of linear transduction equations. This approximation is made in this study to facilitate analysis. Several simple analog and digital controllers are used with acceleration feedback to improve transducer linearity. A nonlinearity of particular importance when using Terfenol-D transducers is wave form distortion. The distortion is a result of nonlinear strains vs. magnetization relationships and the magnetic hysteresis occurring within the Terfenol-D. The net result is the presence of integer harmonics in the transducer voltage, current, and output velocity. Assuming the harmonics to be disturbances, an expression is developed for predicting the change in harmonic amplitudes of acceleration as a function of frequency and parameters for the controller, load, and transducer. Experimental measurements comparing controlled and uncontrolled output accelerations are presented to validate the approach. A significant extension of the linear range of transducer behavior, due to feedback control, is also demonstrated.

A promising use of terfenol-D is as the actuating element in mechanical actuators. Actuators made from terfenol-D take advantage of the material's large displacement capabilities, high energy and relatively wide bandwidth. Terfenol-D actuators would be more useful if their distortion levels were lower. When operation of these actuators is restricted to strains where the material's behavior is linear, their performance is only comparable to standard actuators. Our objective was to design a control system to reduce distortion of a terfenol-D actuator. A terfenol-D actuator was tested to obtain operational data. Nonlinear system identification was performed with a fourth order Volterra expansion. The left inverse was estimated using piecewise linear functions. Feedforward compensation for a feedback controller was designed by representing the inverse/actuator model pair as a linear transfer function and using standard linear control design techniques. Because the inverse was found for operation at a single frequency, the out-of-band frequency response of the linear representation of the inverse/actuator was very severe. This made it impractical to close a feedback loop around the actuator. Instead, the inverse was used as a predistortion filter in open-loop control, which resulted in an 18 dB reduction in total harmonic distortion at the frequency of interest.

Lead, Zirconate, Titanate ceramics undergo polarization switching under electric fields, resulting in polarization hysteresis and strain butterfly loops. In addition, compressive stress inputs lead to ferroelastic 90 degree(s) polarization switching which interacts with the ferroelectric switching under the combined electric fields and stress inputs. In this paper, the phenomenological scalar Preisach model is modified consistent with the above physical phenomena to simulate the polarization and strain loops under the combined electric field and stress inputs. The hysterons that are used in the classical Preisach model are modified to take into account the effect of stress inputs and the effect of polarization switching. Simulations are carried out and the model is suggested as a simulation tool for nonlinear transformations occurring in materials.

Piezoceramic actuators are used in tandem with conventional actuator to design control laws for a Timoshenko slewing beam. The equations are presented in an abstract first order form. Feedback laws are obtained in the context of LQR theory. Convergent functional gains are obtained and time responses of the closed loop system are presented. It is shown that the piezoceramic actuators can significantly enhance the closed-loop response of the system.

This paper is concerned with the basic mathematical aspects of a newly suggested theory of smart composite structures. The governing equations describing the behavior of a smart composite structure incorporating sensors and actuators are derived. The basic optimization problems in the theory of smart structures are formulated. The discussion on some relevant aspects of the optimal control theory, and on similarities and discrepancies between the theory of smart structures and theory of optimal control is provided. The basic optimization problems for the smart structures are illustrated by the applied examples of practical interest. In these examples, two major sources of control are emphasized, namely, residual strains and material properties.

An active vibration control of a smart flexible structure featuring a piezofilm actuator is presented in this study. A governing equation of motion for the smart beam structure is derived and a state space model is obtained in order to formulate a controller. A new discrete- time sliding mode controller is proposed for a single-input linear system with mismatched uncertainties. The main difference between the discrete-time sliding mode control and the continuous-time sliding mode control is the determination of the existence condition of the sliding mode. In the discrete-time case, both the sliding condition and the convergence condition must be satisfied. In the design of the discontinuous controller, a time-varying gain that is a function of the relation between predetermined sliding surface and representative points in the state space is adopted to minimize a sliding region. In addition, for faster reaching to the sliding surface, an equivalent controller separation method is employed. The proposed controller is applied to the smart structure, and control responses of transient and forced vibrations are evaluated by undertaking both simulation and experiment.

The acoustic signature, i.e., the tonal peaks of the radiated noise spectrum, is important to the detectability and survivability of a ground combat vehicle. In the low frequency range below 200 Hz, the structure-borne noise radiation of the vehicle caused by excitation from its track and suspension, can be simulated by numerical models. The numerical simulation provides useful guidance to minimize the detectability through design modifications and countermeasures. A full vehicle finite-element structural model of the M1 Abrams tank was built with approximately 7,000 elements. The dynamic modal frequency response was computed using MSC/NASTRAN^TM with simulated force/moment input from the track and suspension. The output surface vibration velocities were then mapped on to an acoustic boundary-element model with coarser mesh of approximately 2,000 elements. The radiated far-field acoustic pressure was then computed on a 30 meter radius hemisphere using COMET/Acoustics^TM. The numerical results were able to predict the unique fundamental tonal frequencies and some of their amplitudes for different vehicle speeds with reasonable correlation to the test data.

Piezoelectric actuated smart systems are becoming increasingly popular. The proper selection and application of the adhesive bonds between the piezoceramic and the substrate play an important role in maximizing the strain transfer from the piezoceramic to the substrate. Detailed finite element models are developed in this study to model the strain transfer from the piezo actuator to the substrate through a finite thickness adhesive layer. A 2D nine model Lagrangian finite element has been used for this purpose. The finite element results are compared with the existing 1D analytical models and the limitations of the analytical models are brought out. A comprehensive set of results for various values of the shear lag parameter are presented for both extension and bending type actuation.

A beam-type model has been developed for antisymmetric cross-ply laminated split cylindrical shells bonded to their concave sides with actuators, such as relatively thick lead zirconium titanate drivers. The model properly accounts for the bending-extension (b-e) coupling properties of the antisymmetric cross-ply laminates and the effects of stiffness and density of the actuators. Using this model, solutions have been obtained for simply-supported actuator- shells under direct-voltage actuation, free vibration, and sinusoidal-voltage actuation. From the solutions, analytical formulas have been derived to evaluate the bending deformation increase and fundamental frequency reduction of such actuator-shells due to the b-e coupling properties. The purpose of this study is to improve the performance of low-frequency wall- driven acoustic projectors, including split cylindrical transducers with the actuator-radiator configurations under the study. As is well known, the basic acoustic radiation mechanism of all these projectors is the conversion of the extensional deformation of the actuator into the bending motion of the radiator. Hence, it seems beneficial to use a radiator material with inherent b-e coupling properties. Indeed, application of the above-mentioned formulas to the existing laminates demonstrates that substantial bending deformation increase and fundamental frequency reduction of the split cylinders can be achieved.

The electrostatic field in a fiber-reinforced composite cylinder with a piezoceramic core is investigated by using analytical methods. General solutions for composite and piezoceramic cylinders are derived by using Fourier integral transforms. These general solutions are used to analyze the response of a cylinder to a band of radial pressure. Numerical solutions for displacements, electric field and interfacial stresses of a glass-epoxy cylinder with a core made out of piezoceramics PZT-4 or PZT-6B are presented. The numerical solutions confirms the complex nature of the coupled elastic and electric fields in the cylinder and its dependence on the material properties and the geometry of the composite system. The analytical solutions presented in this paper can be used to analyze a variety of stress analysis and micromechanics problems related to fiber-reinforced composite cylinders with embedded piezoceramic layers.

Electro-rheological fluids are capable of providing continuously variable damping forces in response to an electrical stimulus. Many prototype ER dampers have been described in the literature, most of these based upon exploiting the variable shear properties of the fluid. It is only recently that an alternative mode of operation--squeeze flow--has been identified and investigated. Squeeze-flow offers the prospect of simple forms of construction coupled with the ability to provide force levels consistent with industrial specifications. In this paper the authors summarize the principles of squeeze-flow operation and introduce a quasi-steady model to account for the vibrational behavior of a squeeze-flow cell. An experimental facility is described in detail and test results are compared with theoretical predictions. The paper concludes with some thoughts on future work into squeeze-flow behavior.

Procedures are presented for the accurate calculation of the band energy of a solid within the framework of the Hartree-Fock approximation. The starting point is a self-consistent calculation using a Gaussian basis. The method is applied to study the band energy of metallic lithium as a function of temperature. Calculated density of states, optical conductivity, K X- ray emission edge, and some other electronic properties agree with the experiment. We have found small energy-band changes for lithium, most notably a widening of electronic core states, and transfer of external electrons from s-symmetry states to p-symmetry states.

Experiments based on the Vicker's indentation technique are applied to a ferroelectric and a relaxor composition of lead lanthanum zirconate titanate. When polarized, the ferroelectric composition displays anisotropic crack growth. The anisotropy in crack growth is affected by electric field. Increasing the electric field increases the crack growth perpendicular to the field direction. The relaxor composition displays nearly isotropic crack growth even under electric field. Application of electric field slightly hinders crack growth perpendicular to the field. As the field level is increased, this effect diminishes. The effect appears to be related to intergranular residual stress.

A finite element approach has been used to model phase transitions in electro-mechanically coupled material. The approach is applicable to modeling a broad range of material behavior, including repolarizations in ferroelectrics as well as ferroelectric-antiferroelectric phase transitions in electroceramics such as lead lanthanum zirconate stannate titanate. A 3D 8 node element with nodal displacement and voltage degrees of freedom has been formulated using standard isoparametric shape functions. The elements utilize nonlinear constitutive relations for more accurate representation of material response at high electric fields. The phase/polarization state of the material is represented by internal variables in each element, which are updated at each simulation step based on phenomenological model. The model reproduces strain and electric displacement hysteresis loops observed in the material. The approach allows modeling of complex actuator geometries subject to non-uniform electric fields. An a sample application, the response of a piezoelectric wafer with interdigitated electrodes is analyzed. Such a geometry leads to stresses arising from non-uniform poling in the sample which can be computed using the finite element model.

In this study an analytic and experimental effort is presented to understand and improve the fracture toughness and the associated fatigue behavior of piezoceramic materials. Analytical models are presented on the premise that defects in the form of voids cause material degradation during electric excitation. A unit cell approach employing an exact linear electroelastic analysis is used to study the stress and electric field concentrations as a function of material properties. Our study indicates that for certain ratios of piezoelectric coefficients electric field induced stress concentrations are eliminated in the material. These results suggest that the electric fatigue life of a piezoelectric ceramic can be extended if the piezoelectric properties are appropriately tailored during the manufacturing processes. However, this analytical work is done within the frame work of linear piezoelectricity. To better understand internal stress concentrations arising due to nonlinear phenomena associated with polarization switching, we present experimental results using moire interferometer. This first application of moire interferometer to piezoceramics demonstrates the promise this experimental technique offers to better understand internal stress/strain distributions. In this initial presentation we present two fundamental results, that is the strain concentrations between domains oriented 180 and 90 degrees apart.