We show on a sample application how to compute magnetization and magnetostriction curves for magnetostrictive materials by appraising the behavior of the underlying microstructures. We take into account the kinematical constraints on the accommodation of elastic effects, and we highlight the role of material symmetry in the selection of energetically optimal microstructures.

The variational study of material instabilities such as phase transitions, the formation of defects in crystalline materials, the onset of microstructure and the development of fractures, has needed new mathematical techniques since the problems involved generally escape the old theories. Some of the analytical progress that has been made recently towards the understanding of these phenomena is outlined.

We introduce a new numerical method, based on rigorous perturbative techniques, for the calculation of the patterns of electromagnetic scattering produced by bounded obstacles. As preliminary examples show, our method can lead to results of good accuracy in a wide variety of challenging problems involving large scatterers.

We present some numerical results for the solution of non-convex variational problems. In general, the problems of interest do not attain a minimum energy. Functions that generate a minimizing sequence of energies develop infinitely fine oscillations, and it is believed that these oscillations model the fine scale structures that are ubiquitously observed in metallurgy, ferromagnetism, etc. Direct simulation of these variational problems on discrete meshes is plagued with practical problems. We present a simple 1-D example that exhibits problems typical of those encountered with such an approach. Many of these problems can be traced to the fundamental problem that the variational problem doesn't have a solution. An alternative is to consider the generalized solutions of L. C. Young. We present some numerical experiments using this algorithm for variational problems that involve vector valued functions.

This paper provides general models of multilayered linear elastic plates containing piezoelectric inclusions. Several configurations are investigated. In particular, the plate with thin distributed inclusions is treated using homogenization techniques. Different sorts of electrical boundary conditions are imposed on the inclusions. A by product of this work is the possibility to choose the electrical boundary conditions in order to create an additional finite differences operator in the plate equation. Using the homogenization techniques, this operator becomes a partial differential operator.

In this paper we do computations that describe a rigid, uniaxial, ferromagnetic material in a varying applied magnetic field. Our computations are based on a relaxed model with a nonlocal exchange energy. The model is based on the theory of Young-measures, but we show that our calculations can be based on only the first and second moments. Thus, we can do rigorous and accurate calculations without examining the full oscillating sequences that induce the Young-measure. We show that by varying the strength of the exchange energy we can induce hysteresis and observe hysteresis subloops and domain rotation.

In this paper we present energy minimization problems for deformations of materials whose bulk energies have two potential wells. (Two-well models have often been used in simple models of shape memory alloys.) The higher-dimensional models feature relaxed bulk energies derived from double-well potentials with two compatible quadratic wells. The relaxation of the double quadratic well can be calculated explicitly. The relaxed minimization problems are regularized through the use of spatially nonlocal forces. These forces are related to Van der Waals capillary forces and interfacial or coherence forces used in phase fraction theories. We describe an algorithm for computing stationary points of the energy, and do a number of calculations on 1-D static deformations. Our calculations show a rich class of metastable states that form themselves into hysteresis loops and subloops.

Simulations of magnetic, magnetostrictive, and pseudoelastic behavior exhibit hysteresis. These systems have a highly nonlinear character involving both short range anisotropy and elastic fields and, when appropriate, dispersive demagnetization fields. In this report we discuss our experience with this type of computation and the applications which it may serve. We implemented continuation based on the conjugate gradient method, although the same results were obtained by other methods as well. Nonetheless, the propensity of optimization procedures to become marooned at local extrema when applied to nonconvex situations presents a fundamental challenge to analysis. We present some computational results and diagnostics, developed using methods of nonlinear analysis. In a simple case described in the paper, the width of the hysteresis loop may be determined analytically. For a magnetic system, this analysis rests on the introduction of a shadow energy for a simplified version of the system. This simplified version suggests possible dispersive interactions that may be attributed to shape-memory or pseudoelastic body. We provide a brief illustration of this. A principal objective of this investigation is to study the magnetostrictive behavior of Terfenol-D.

An important incentive not to neglect dynamic effects in the study of martensitic transformations is the failure of the usual energy minimization arguments to predict the observed coexistence of phases at nonminimal energy and the associated hysteresis phenomena. Here we suggest that a simple viscoelastic dynamic model is capable of capturing these phenomena.

Many mathematical models currently used for modeling shape memory alloy behavior in a control setting make use of an internal variable that has the interpretation of being the phase fraction of either austenite or martensite. Recently, more detailed models have been introduced that further discriminate phase species. These models seem to be pitched at the correct level for implementation in FEM based design protocols in that they are sufficiently detailed to accurately reflect much of the underlying physics, without having to track individual events at the microscale. In order for these models to enjoy reliable predictive status, it is necessary that conditions be built into them that ensure proper qualitative behavior for all processes to which the model will be applied. We discuss how the constitutive functions which enter into these models (such as the phase fraction envelope curves) can be validated to ensure proper behavior in general processes.

Smart structure has become an increasingly common term describing a structure embedded or bonded with a large number of lightweight active electro-mechanical sensors and actuators. In this paper, we consider the modeling and control issues related to smart structures bonded with piezoelectric sensors and actuators from the passivity viewpoint. We show that when a piezoelectric patch is used both as an actuator and a sensor, the mapping from the voltage input to current output is passive, which implies that any strictly passive feedback controllers are stabilizing. Issues related to the design of the passive feedback controller with performance optimization and controller order reduction are investigated.

A new structural vibration control concept, using piezoelectric materials shunted with real- time adaptable electrical networks, has been developed. The variable resistance and inductance in an external RL circuit are used as control inputs. Novel energy-based parametric control schemes are created to reduce the total system energy (the main structure mechanical energy plus the electrical-mechanical energy of the piezoelectric material and electrical circuit) while minimizing the energy flowing into the main structure. The performances of the controllers are examined through computer simulations on a beam example. It is shown that the structure energy level and vibration amplitude can be suppressed effectively.

This paper discusses 2-D distributed transducer shape and shading and their implications for the active control of plates. Two-dimensional transducer shaping is shown to be a useful design tool for the control problem. In addition, transducer shaping can be combined with gain-weighting to provide close approximation of continuously shaded transducer distributions. An optimization method is described which can be used to fit the approximation to a continuous distribution. The analysis is applied to two examples of transducers used to control a rectangular, simply supported plate. The first relies on shaping alone and is shown to spatially filter out the even-even modes. The second was developed using the optimization technique and is shown to provide `all-mode' controllability and observability.

An inductive learning method is used for online control of a structure. The controller has the benefit of being designed without the need for a system model and is able to adapt to varying system parameters. The learning method is empirical in nature where the trials and errors of the controller generate a stimulus-response function which is used to improve the performance of the system. Numerical experiments were performed with the quantized inductive learning (QIL) algorithm on simple linear systems and a simulation of a simply supported aluminum beam. In both cases, the algorithm controlled the dynamic response of the system from an arbitrary initial condition. The QIL algorithm learned the control function without access to the computer model. Other issues associated with the development of this algorithm were examined concurrently. The effects of various performance indices, varying the sampling periods, and changing the levels of quantizations were determined and evaluated. In addition, QIL was used to reject sinusoidal disturbances on these systems. Finally a comparison of the QIL algorithm with state feedback was made to compare the effectiveness of this method with a standard model-based approach.

The design and implementation of control strategies for large, flexible smart structures presents challenging problems. Uncertainties stem from control structure interaction, modeling errors, and parameter variations (such as fuel consumption). We developed a new algorithm called H_(infinity ) robust control for natural frequency variations (H_(infinity )/NF) that includes the knowledge of the natural frequency uncertainty bounds. In addition, we were successful in implementing this algorithm on a flexible smart structure in our laboratory. This smart structure was a cantilever beam that used NiTiNOL shape memory alloy (SMA) actuators. The performance of H_(infinity )/NF algorithm was compared with the modified LQG/LTR algorithm using a settling time specification. The H_(infinity )/NF controller exhibited dramatically reduced sensitivity to natural frequency uncertainty as compared to the modified LQG/LTR controller. The standard LQG/LTR control algorithm produced controllers that saturated the NiTiNOL actuators used on the test article. To overcome this saturation problem, we used a modified LQG/LTR design algorithm. We successfully implemented the proposed algorithm on a simple cantilever beam test article.

A piezoelectric strut exhibits hysteresis and creep due to the piezoelectric coefficient. These nonlinearities annoy a control engineer who uses the piezoelectric strut as a control actuator. Intensive experiments were performed by the authors to derive a linear model for the piezoelectric strut/power amplifier system. A servo-loop was designed to eliminate the nonlinearities. Experimental results of the open-loop and closed-loop systems are presented in this paper to validate the analytical model and control design.

When continuous-time systems are discretized in the digital controller design process, it is often the case that unstable discrete-time zeros (i.e., zeros outside the unit circle in the Z- plane) result regardless of whether or not there are unstable zeros in the original continuous- time plant. Such a system is recognized as being nonminimum phase. Unfortunately, many design techniques in adaptive control are dependent upon pole-zero cancellations and stable plant invertibility and, therefore, cannot be utilized when the plant is nonminimum phase. In this research, a matrix parameter recursive least squares adaptation law is developed for the zero annihilator periodic (ZAP) controller first introduced by Bayard and later extended by Jakubowski. This direct adaptive control scheme allows for the construction of an optimal set of matrix controller gains that place the transmission zeros of the system at the origin, alleviating the nonminimum phase condition, and force the system output to track a desired reference signal. Simulations are presented that demonstrate the performance of the adaptive ZAP controller on a 12-state, 2-input, 2-output partial model of one of the Astrex struts, where the model of the particular strut exhibits nonminimum phase characteristics.

This paper details the design and implementation of a fuzzy controller for the ASTREX flexible space structure model. the novel control strategy is the first attempt to apply fuzzy logic to the feedback control of a large-scale structure system. The ASTREX system at Edwards Air Force Base consists of three flexible trusses, joined to a flexible base system and culminating in as line-of-sight positioning instrument. Smart control of each truss is accomplished by three axial piezoelectric actuators on each truss, and six bending sensors. Two sensors are grouped with each actuator, in collocated and nearly collocated positions. control system design procedure is detailed. The open-loop system is simulated to determine the appropriate universes of discourse for the input fuzzy membership functions. Output magnitude of the controller is determined by the dynamic range of piezoelectric actuators. The architectural design of fuzzy logic controllers in currently an open issue. there exist many different forms of fuzzy logic controllers, and the performance characteristics of each type cannot generally be determined a prior. Results of preliminary investigations in to the type of fuzzy logic controller necessary for efficient control of flexible structures are shown using simulations involving partial models of one beam of the ASTREX flexible satellite.

This work considers the limits of modal analysis based identification of the coefficients on a partial differential equation model of a programmable structure. The programmable structure considered here consists of a cantilevered beam with embedded self sensing piezoceramic actuators and surface mounted control module. A Euler Bernoulli beam model is used as the basic equation of motion. This model is modified to include internal (strain rate) and external (linear viscous) damping mechanisms. In order to model the effects of the embedded piezoceramic as well as the control module, the modulus (EI), density, and damping coefficients are modeled as piecewise constant. An assumed mode approximation is used with off diagonal terms neglected. This numerical approach is then used along with measured frequencies and damping ratios to estimate the various damping and stiffness coefficients. The consistency of the estimates is compared with increasing mode number and the limitations of the procedure are discussed.

Nondestructive damage detection is an important issue in aging civil engineering, aerospace structures, and several other areas. This study presents an attempt to use parameterized partial differential equations and Galerkin approximation techniques to detect and locate damage. Dynamical analysis is carried out using structure bonded piezoceramic patches as both sensors and actuators. Our presentation demonstrates the flexibility and accuracy of this approach. It is mode independent and can sense the presence of damage and locate certain damages to a satisfactory precision. As an example, a beam with a pair of piezoceramic patches bonded to it is used as the test structure; several computational examples with holes of different size, shape, and location in the beam are investigated.

A method of non-contact interrogation of electronic and opto-electronic systems embedded within composite materials has been recently demonstrated. The method is based upon inductive coupling between external and embedded coils etched on thin electronic circuit cards. Measurement at two frequencies allow the coil separation and the value of an electrical parameter of interest to be determined. An investigation into the practicability of utilizing neural processing to calculate these parameters was carried out. The final system utilized a hierarchical architecture of three neural networks combined with an adaptive measurement of voltage at a frequency determined by the coil separation calculated by one of the neural networks. The system was implemented using custom electronics and a PC laptop computer. A description of the design process is given together with system performance parameters.

Various dynamic response data manipulations are presented as part of the ongoing process of developing a complete, model-independent, inductive learning, damage identification method. Dynamic response data, that consist of spatial and temporal information, are verified to be dependent on changes in physical properties of a structure (i.e., mass, stiffness, damping, damage). Simulated experiments were performed on a 500 mm X 600 mm X 3 mm steel plate with simply supported boundary conditions. As a method to test the procedure, a point mass was added to the model in various locations of the structure. Using an array of sensors and a piezo-electric actuator, impulse-response functions and frequency-response functions were determined for the entire domain of sensor-actuator pairs. These impulse- response functions and frequency response functions of different sensor-actuator pairs were input into an inductive algorithm. Inductive learning methods require definitions of a dependent variable, independent variables, and specific examples. Using piecewise manipulations of the aforementioned functions and repeated data acquisition (to take into random transduction errors), these definitions were specified. An automated damage identification method incorporating the use of inductive learning is presented and shown to be successful..

An active material system may be generalized as an electro-mechanical network because of the incorporation of the actuators (electrically driven) and sensors (that convert mechanical energy into electrical energy). This paper summarizes most of our research in the area of the electro- mechanical impedance (EMI) modeling of active material systems. In this paper, a generic electro-mechanical impedance model to describe the electro-mechanical network behavior (time domain and frequency domain) of active material systems is discussed. The focus of the discussion is on the methodology and basic components of the EMI modeling technique and its application to assist in the design of efficient active control structures. This paper first introduces the basic concept of the electro-mechanical impedance modeling and its general utilities in the area of active material systems. The methodology of the EMI modeling technique is illustrated using an example of PZT actuator-driven mechanical systems. The basic components in the EMI modeling are discussed. Finally, some applications of the EMI modeling approach are presented.

Piezoelectric actuators are being used in increasingly complex structures. An actuator that can be removed and used again would be beneficial in testing actuator placement before the permanent actuator would be attached. Furthermore, an actuator that has similar response characteristics to the permanent actuator would be beneficial in estimating the response characteristics of the actuator before it is attached. A concept for such a removable, reusable actuator has been developed, constructed, and used. This paper describes the differences in authority among three removable, reusable actuators as compared to a permanent actuator. The permanent actuator is bonded to the host structure with only strain gauge cement. This paper also quantifies the changes in authority of the three removable, reusable actuators as they are removed several times from the host structure. When comparing removable and permanent actuators, the stiffer bonding technique typically had greater actuation authority. When comparing authority reduction of removable actuators over ten applications of the actuator, greater reduction occurred with actuators that incorporated a stiffener.

To actively and intelligently control the elastic motions of structures, smart devices (sensors and actuators) need to be attached to or embedded in structural components. In this article an effective semi-numerical approach for mathematical modeling of interfaces between the host structure and smart devices is proposed. The model is based on the component-mode syntheses via receptance method which is most suitable for vibration analysis and control. By utilizing the receptance method, large mass and stiffness matrices of the conventional finite element models are replaced by natural frequencies and mode shapes of the host structure and those of the attached or embedded elements. Three types of interfaces are investigated: point, line, and surface interfaces. Contrary to conventional methods, the line and surfaces are modeled as actual lines and surfaces rather than a finite number of points. The latter, drastically reduces the degrees of freedom and significantly improves the accuracy of the numerical values. Finally, such formulation results in a huge reduction in the size of the model and tremendous gain in computational speed.

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 and it is found that the sensor at that location is not only non-intrusive but also sensitive to the characteristic of the structure.

A special design theory for distributed piezoelectric actuators is introduced, for reducing noise and vibration in structures. A uniform cylindrical shell is taken as an example of a host structure to illustrate the effectiveness of the design theory. The actuators are designed to reduce the shell structural vibration and interior noise in a wide range of frequencies, for cases where the input disturbance is tonal. Extensive computer simulations were completed to study various aspects of the design theory. In addition, experiments were conducted and the test results strongly supported the theoretical development.

The payload compartment of space launch vehicles is an acoustically severe environment with sound pressure levels that often exceed 130 dB. Many of the design constraints for satellites are driven by the launch loads and any reduction in these loads would allow lighter spacecraft and significant cost savings because of reduced launch weight and testing requirements. In order to determine the levels of sound attenuation possible in such an application, a simple experimental apparatus consisting of a flexible plate backed by a rigid rectangular cavity has been built to mimic the behavior of a launch vehicle payload compartment. An external speaker is used to simulate the pressure loading caused by vehicle exhaust and turbulent flow around the launch vehicle. This paper provides a comparison of the harmonic disturbance attenuation capability and transient/convergence performance of a fixed analog feedforward and a filtered-x LMS adaptive feedforward controller for the cavity backed plate problem using piezoelectric ceramic actuators on the flexible plate and polyvinylidene fluoride pressure and plate vibration sensors. Controllers are developed for the first plate controlled mode and the first cavity controlled mode.

Several features of the analytical curved piezo-actuator model (in-phase and out-of-phase) are presented including the influence of actuator size, location, thickness, and shell aspect ratio on the excitation of shell modes. It is shown that in-phase driven piezo-actuators are better than out-of-phase driven actuators for exciting low circumferential order cylindrical shell modes. The angular wrap, angular location, and the shell aspect ratio are important factors which influence the shell response. Also, the coexistence of in-plane (theta) line force and pressure load in the in-phase model naturally cancel at certain high circumferential (n) modes so that no extra efforts need to be expended in suppressing them. The simplicity of the problem depends on the shell aspect ratio. It is more complicated for shells with aspect ratios between 3 and 7. The reason being that several medium axial (m) order modes coexist close to the excitation frequency and also several circumferential orders are resonant.

A problem of continued interest concerns the control of vibrations in a flexible structure and the related problem of reducing structure-borne noise in structural acoustic systems. In both cases, piezoceramic patches bonded to the structures have been successfully used as control actuators. Through the application of a controlling voltage, the patches can be used to reduce structural vibrations which in turn leads to methods for reducing structure-borne noise. A PDE-based methodology for modeling, estimating physical parameters, and implementing a feedback control scheme for problems of this type is discussed. While the illustrating example is a circular plate, the methodology is sufficiently general so as to be applicable in a variety of structural and structural acoustic systems.

A time domain model for simulating the noise transmission through an elastic plate into a rigid cavity has been developed. This model is used to study the noise attenuation capability and transient-convergence of the filtered-x LMS feedforward control algorithm. Piezoelectric transducers (PZTs) are considered to be bonded on the elastic plate and are used as actuators in the control scheme. In this study, the fully coupled acoustic-plate interaction equations are solved using time dependent Green's function techniques, where a time varying air mean density is considered. The effects that the time varying mean density has on the transmission of sound and on the stability of the filtered-x LMS adaptive controller are discussed.

Three models for two-layered beams in which slip can occur at the interface are described. In the first, beam layers are modelled under the assumptions of Timoshenko beam theory. Along the interface a `glue layer' of negligible thickness bonds the surfaces so that a small amount of slip is possible. Dissipation is assumed to be proportional to the rate of slip. The second is obtained from the first by letting the shear stiffness of each beam tend to infinity. The third is obtained from the second by assuming that the moment of inertia parameter is negligible. In this case an analog of the Euler-Bernoulli beam is obtained which exhibits frequency- proportional damping characteristics.

It is shown that the concept of localiton, introduced in the frame of localization of light by randomly rough surfaces, can be extended to other kinds of structures like impedance sheets or a set of random dielectric rods. Rigorous numerical calculations show the structure of these new localiton. Finally, the possibility of observing such a localized field from experimental measurements is suggested.

A number of related but somewhat conflicting theories have been proposed to explain the pseudoelastic hysteresis exhibited by shape memory alloys (SMA). Some recent experimental results motivated us to introduce yet another model of thermoelasticity. Attempts to justify this model from a micro-thermomechanical perspective have led to the theoretical considerations in this paper. These discussions provide support for the model and they given new perspectives on previous approaches. Based on these ideas, a proposal is made that a realistic microscopic model of polycrystalline SMAs should be based on homogenization of a system of non-linear crystallites and dislocations. A route of attack for this new problem in homogenization theory is indicated.

Recently the authors published a new micromechanical model to describe the kinetic behavior of shape memory alloys. Here the stress-strain-temperature-transformation behavior is investigated. The model describes a differential equation for the volume fraction of the new (martensitic) phase (which grows during a thermomechanical process) in dependence on the temperature and/or stress history of the process. In the newly extended version it contains, as a second basic equation, the differential relationship between strain, volume fraction of the new phase, temperature, and loadstress. The strain is an effective property of the considered system. Integrating the differential stress-strain-temperature-volume fraction relation under consideration of the initial conditions leads to a useful integral relation of the mentioned quantities. Of special interest is the hysteresis behavior during phase transformation. A friction-like term in the model changes sign when the process changes the direction. Thus the model also allows us to explain subloop behavior. Exact bounds for the dissipation energies for loops can be given. The agreement of the results of the model with experimental results is fairly good.

The inclusion of piezoceramic rods in a passive polymer can greatly enhance the piezoelectric effect. We analyze this phenomenon from the point of view of the theory of composite materials, focusing on the evaluation of d_h, the hydrostatic piezo-electric coefficient, d_hg_h, the hydrophone figure of merit, and k_h, the hydrostatic coupling factor measuring the efficiency of energy conversion. We show how these quantities can be expressed as algebraic functions of a single microstructural parameter, p. In the limit of large elastic contrast (soft matrix, hard ceramic), this theory gives a first-principles explanation of the decoupling effect of the composite on the hydrostatic piezo-electric coefficient, as well as the role played by the porosity and Poisson's ratio of the matrix phase. Using a differential effective medium type scheme, we compute the aforementioned properties for two commercial polymer-piezoceramic composites. It is thus shown that this effective medium approach provides a simple yet self-consistent framework for the design of effective 1-3 piezocomposites.

A piezocomposite with coated cylindrical fibers of a circular cross section are considered. The fibers are parallel to each other and randomly located in the transverse plane. The composite cylinder assemblage model is adopted and simple formulae are derived for all the effective constants, except for the transverse shear modulus. This last parameter is estimated by a mean field theory approximation.

This paper describes some recent developments that treat the simultaneous optimization of material and structure for minimum compliance. The basic idea is to represent the material properties for a linear elastic continuum in the most general form possible, namely as the unrestricted set of elements of positive semi-definite constitutive tensors. The cost of resource is measured through certain invariants of the tensors, here the 2-norm or the trace of the tensors. The advantage of this general formulation is that analytical forms for the optimized material properties can be derived and that effective methods for computational solution can be devised for the resulting reduced structural optimization problem.

This paper deals with the propagation of electromagnetic waves in random dielectric media. It presents a field theoretical approach to address this problem and focuses its application to the case of high dielectric constant contrast.

The non-local constitutive relations describing a chiral medium which lacks reflection symmetry are different from an ordinary dielectric medium. When `chiral' inclusions (either because of their handed geometry or because they are made of a chiral material) are dispersed in a dielectric host medium, the effective properties of the resulting composite can be described by constitutive relations that make the effective medium effectively chiral or achiral. In most effective medium theories, there is preference to model the fields in terms of the fields in the host medium so that the effective medium resembles the host medium rather than the inclusion material. Four different effective medium models are examined for chiral inclusions in the long wavelength limit for the purpose of predicting effective properties of microwave chiral composites.

A dynamic system with satisfactory performance generally consists of a mechanical system (the plant) and a controller that drives the mechanical system to meet certain performance requirements. Traditionally the control engineer designs the controller only after the plant design is completed. This two-step approach to plant and controller design does not provide the best system design because the dynamics of the plant and the dynamics of the controller often oppose each other. This paper presents an application of the iterative system equivalent optimal mix algorithm to perform a smart design of a nine-member truss substructure and its accompanying controller. The objective of the design algorithm is to reduce the amount of energy used by the controller to maintain control performance, subject to the structure design constraints. Two unique features of the algorithm are that each iteration of the design problem is stated as a convex quadratic programming problem, and the control effort monotonically converges to its final value.

Solution of nonlinear optimal control problems on analog parallel networks is proposed. Recurrent neural networks whose dynamic equations have a Lyapunov function are developed. Such circuits relax to an equilibrium which is the minimum of the Lyapunov function. Nonlinear optimal control problems are formulated in terms of a Lyapunov function and thus are solved using the recurrent networks. Convergence for linear and nonlinear classes of problems is considered. The method is demonstrated by developing and simulating a network to solve a nonlinear vibration problem. Simulation results demonstrate solution times are accurate and extremely fast. Solution times are shown to be independent of the size of the problem.

Much of the research done in recent years towards the development of the smart or adaptive structure focuses on the application of active control to alleviate undesirable structural responses. Classical optimal control algorithms are not directly applicable to most civil engineering applications because the control gains neglect the effects of the external forcing function and assume a time invariant system (which allows the differential Riccati equation (DRE) to be reduced to an algebraic Riccati equation). The reason for these assumptions is that the time dependent DRE can only be stably integrated backwards in time. This study presents a more effective LQR control algorithm for civil structure applications, based on a proposed methodology for forward integrating the DRE. A set of dual equations are presented together with an optimization technique for obtaining the DRE solution from a forward integrable dual form. In addition, a matrix-valued integration procedure is formulated for and applied to the differential Riccati equation with time variant plant and weighting matrices.

This paper models a two-arm flexible manipulating system by a set of generic partial differential equations, from which the transfer matrices for the flexible arms and revolute joints have been constructed. Based upon the compatibility conditions at the connecting points, the global system dynamic equation has been derived. Joint moments are used as the control actions. A typical control problem for end-effector vibration suppression has been investigated. Control law computation proceeds in the frequency domain based on the pole- placement method. The effectiveness of the vibration suppression by using distributed parameter modeling technique along with the application of transfer matrix method is indicated by means of the decay of the end-effector response time history computed based upon the modal expansion method.

The two-scale asymptotic homogenization method is used for the evaluation of the behavior of composite materials with periodic structures, which includes not only the capability to compute effective macroscopic properties of the material but also approximations to the behavior of the material in terms of its microscopic geometry. A software, using finite element methods, has been developed to implement the homogenization methodology. Thermal, elastic, visco-elastic, and piezoelectric properties are treated for continuous parallel fibers, short fibers, ellipsoidal inclusions, foams and woven fabric composites. Results obtained from the proposed model are compared with those obtained from fully 3-D finite element simulation of the elasticity problem.