In a previous paper, the authors investigated the lowersemicontinuity properties of two generalizations of the classical Preisach operator; the smoothed Preisach operator and the Krasnoselskii / Pokrovskii (KP) integral hysteresis operators. In particular, it was demonstrated that the output least squares identification problem for the KP operator is well-posed over compact subsets of the Preisach plane. The identification of the hysteretic control influence operator was shown to be equivalent to the identification of a measure in the space of probability measures taken with the weak- topology. In this paper, a consistent and convergent approximation scheme is introduced for this class of integral hysteresis operator. The Galerkin approximation scheme is shown to be function space parameter convergent. A numerical example is presented that illustrates aspects of the theory derived in this paper. 1 Introduction and Motivation While there has been unprecedented interest in utilizin...

We present a variational framework based on sesquilinear forms for Galerkin approximation techniques for state feedback control in problems governed by infinite dimensional dynamical systems. Both parabolic and second order in time, hyperbolic partial differential equations with unbounded input and unbounded observation operators are included as special cases of our treatment. 1 Introduction In this paper we discuss the linear quadratic regulator (LQR) problem for a class of (essentially parabolic) unbounded input or boundary control problems. A variational framework using sesquilinear forms is developed to treat Dirichlet and Neuman boundary control problems for parabolic equations and strongly damped elastic systems. Using such a framework, convergence of Galerkin approximations to solutions of Riccati equations is also established. The boundary control problem for parabolic systems has been studied extensively over the last two decades, inspired by the monograph of J.L. Lions [21] ...

In this paper, the modeling of boundary conditions for an imperfectly clamped circular plate is discussed. This model is derived under the assumption that there is some variation in both the boundary displacement and slope when the plate oscillates. To account for this oscillation, boundary moment terms, involving parameters to be estimated through fit-todata techniques, are included in the model. The well-posedness of the model is demonstrated and appropriate approximation techniques are outlined. Finally, under natural assumptions for this model and approximation scheme, results leading to parameter convergence are given. 1 Introduction An important consideration in the modeling of structural and structural acoustic systems involves the determination of appropriate boundary conditions for the vibrating structure. In many applications, the clamped nature of the structure leads to the use of clamped or fixed boundary conditions, in which case, it is assumed that zero displacements an...

We report on our efforts to model nonlinear dynamics in elastomers. Our efforts include the development of computational techniques for simulation studies and for use in inverse or system identification problems. As a first step towards the full dynamic case, we present the static inverse problem, with experimental results. We also present results from the simulation of dynamic experiments. 1 Introduction A problem of fundamental interest and great importance in modern material sciences is the development of new materials for use as both passive and active vibration suppression devices. Materials such as elastomers, rubber-like composites typically filled with inactive particles such as carbon black and silica, are frequently used in parts such as engine mounts and springs. One could imagine using active fillers, such as piezoelectric, magnetic, or conductive particles, to create a "smart" material which could be used as an active vibration suppression device. In the quest to develop...

A phenomenological characterization of hysteresis in magnetostrictive materials is presented. Such hysteresis is due to both the driving magnetic elds and stress relations within the material and is signi cant throughout most of the drive range of magnetostrictive transducers. An accurate characterization of the hysteresis and material nonlinearities is necessary to fully utilize the actuator/sensor capabilities of the magnetostrictive materials. Such a characterization is made here in the context of generalized Preisach operators. This yields a framework amenable to proving the well-posedness of structural models that incorporate the magnetostrictive transducers. It also provides a natural setting in which to develop practical approximation techniques. An example illustrating this framework in the context of a Timoshenko beam model is presented.

We report on our efforts to model nonlinear dynamics in elastomers. Our efforts include the development of computational techniques for simulation studies and for use in inverse or system identification problems. 1 Introduction A problem of fundamental interest and great importance in modern material sciences is the development of both passive and active ("smart") vibration devices constructed from polymer (long molecular chains of covalently bonded atoms often having cross-linking chains) composites such as elastomers filled with carbon black and/or silica or with active elements (i.e., piezoelectric, magnetic or conductive particles). These rubber based products (even without active elements) involve very complex viscoelastic materials that are not at all like metals (where large deformations lead to permanent material changes) and do not satisfy the usual, well-developed linear theory of (infinitesimal) elasticity for deformable bodies. They typically exhibit mechanical properties ...

Based on a distributed parameter model for vibrations, an approximate nite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the e ectiveness of this design. 1

In this paper we present an approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems. These systems include as a special case those modeling a large class of nonlinear elastomers.

We investigate time domain based electromagnetic inverse problems. This is done in the context of general polarization models (which include the familiar Debye and Lorentz models as special cases) for dielectric materials. A one-dimensional model based on time-windowed pulsed inputs is formulated and well-posedness results are given for the simulation problem. Numerical investigations of problems involving estimation of dielectric parameters in a slab geometry are carried out. We also present results for use of secondary reflections to estimate geometry of the slab. 1 Background A survey of the mathematical literature reveals considerable interest in the identification of material parameters describing electromagnetic phenomenon. For our purposes, we categorize the materials and the models employed to describe them as either dispersive or non-dispersive, where dispersive materials are those in which electromagnetic waves of different frequencies have different phase velocities. When...

We present a time domain approach for the investigation of dispersion mechanisms of a medium in electromagnetic field problems. Maxwell's equations coupled with a generalized electric polarization model are considered. The polarization is given in terms of a convolution of the electric field with an impulse response funtion. Existence, uniqueness and continuous dependence of solutions on data are presented for a one-dimensional dispersive medium case. Estimation of electromagnetic properties of media is demonstrated via numerical examples. Parameters representing the electromagnetic property of a medium may include the static permittivity, relaxation time, natural frequency, static conductivity, etc. depending on the polarization model chosen. 1. Model Formulation Microwave images of tissue structures and soils play very important roles in many areas, including clinical and environmental medicine. These microwave images are useful in detection=enhanced treatment of abnormality of hum...