Control of transient thermoelastic displacement of a two-layered composite plate constructed of isotropic elastic and piezoelectric layers due to nonuniform heating

Abstract

In this study, the theoretical analysis of the control of transient thermoelastic displacement is developed for a two-layered composite rectangular plate constructed of an isotropic elastic and a piezoelectric layer due to nonuniform heat supply. The transient three-dimensional temperature in a two-layered composite rectangular plate is analyzed by the methods of Laplace and ®nite cosine transformations. Exact solutions for isotropic elastic and piezoelectric plates of crystal class mm2 are used in the theoretical analysis. A three-dimensional transient piezothermoelastic solution is developed for a simple-supported combined plate. The analysis yields an appropriate electric potential which when applied to the piezoelectric plate, suppresses the induced thermoelastic displacement in the thickness direction at the midpoint on the free surface of the isotropic plate. As an example, numerical calculations are carried out for an isotropic rectangular plate made of steel, bonded to a piezoelectric plate of cadmium selenide. Some numerical results are shown for temperature change, displacement and stress in transient state, when the transient thermoelastic displacement are controlled. IntroductionPiezoelectric materials exhibit coupled effects between the elastic and electric ®eld, and have become of major interest lately as functional materials used in actuators or sensors [1]. It is possible to make a system of intelligent composite materials by combining piezoelectric materials with structural materials. Several analytical studies concerning piezothermoelasticity of intelligent composite materials have been reported. In particular, the control of thermoelastic displacements was treated in [2±7]. The piezothermoelastic problem concerning control of thermally induced elastic displacements of an isotropic plate with a piezoelectric plate of crystal class 6mm was investigated in [2±4]. In order to reduce the applied electric potential, the same piezothermoelastic problem concerning multiple piezoelectric plates of crystal class 6mm was investigated in [5]. The shape control of a cylindrical panel or a rectangular hybrid plate with some piezoelectric layers under thermomechanical load were reported in [6,7], however, these papers are restricted to three-dimensional steady state piezothermoelastic problems.It is well known that thermal stress distributions in transient states signi®cantly differ from those in steady states. Therefore, we recently analyzed the three-dimensional transient piezothermoelastic problem for a rectangular composite plate composed of cross-ply and piezoelectric laminae, [8], and functionally graded rectangular plate bonded to a piezoelectric plate [9]. The numerical results for the temperature change, displacement, stress, electric potential and electric displacement distribution in a transient state under nonuniform heat supply were showed.In the present paper, we analyze the transient three-dimensional piezothermoelastic problem of the control of thermoelastic displacements of a two-layered comp...

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