Browsing by Subject "Elastomers"
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Item Global attractors for damped abstract nonlinear hyperbolic systems(Texas Tech University, 1997-05) Pinter, Gabriella A.This dissertation is concerned with the long time dynamics of a class of damped abstract hyperbolic systems that arise in the study of certain smart material structures, namely elastomers. The term smart material refers to a material capable of both sensing and responding actively to outside excitation. These properties make smart materials a prime canditate for actuation and sensing in next generation control systems. However, modeling and numerically simulating their behavior poses several difficulties. In this work we consider a model for elastomers developed by H.T. Banks, N.J. Lybeck, B.C. Munoz, L.C. Yanyo, formulate this model as an abstract evolution system, and study the long time behavior of its solutions. We remark that the question of existence and uniqueness of solutions for this class of systems is a challenging problem and was only recently solved by H.T. Banks, D.S. Gilliam and V.I. Shubov. Concerning the long time dynamics of the problem, we first prove that the system generates a weak dynamical system, and possesses a weak global attractor. Our main result is the existence of a "strong" dynamical system which has a compact global attractor. With the help of a Lyapunov function we are able to characterize the structure of this attractor. We also give a theorem that guarantees the stability of the global attractor with respect to varying parameters in the system. Our last result concerns the uniform differentiability of the dynamical system.Item The theoretical treatment of visco-elastic properties of silicone elastomers as a function of temperature and strain rate(Texas Tech University, 1988-08) Dinivahi, Murty V. R. N.Silicone elastomers have been used as structural sealant components since the early 1970s. Physical properties such as elastic modulus, cross-link density, viscosity, shear modulus, and the effect of orientation arising from processing are considered in this study. There are few published mathematical models which adequately describe elastomer behavior nor is there much in the published literature to verify experimental results. A new model was therefore developed. Stress-strain data were obtained from an Instron machine which was utilized to conduct experimental studies. It was observed that the elastic modulus of the two silicone elastomers used in this study decreased with an increase in temperature. This interesting phenomenon has not been reported in the literature hitherto.