Dynamic responses of a multilayer spherically isotropic pyroelectric hollow sphere

The dynamic solution of a multilayer spherically isotropicpyroelectric hollow sphere for spherically symmetric problem is obtained. Bythe principle of superposition, the solution is divided into two parts: Oneis quasi-static and the other is dynamic. The quasi-static part is obtainedin an explicit form by the state space method, and the dynamic part isderived by the initial parameter method coupled with the separation ofvariables method as well as the orthogonal expansion technique. By using theobtained quasi-static and dynamic parts and utilizing the electric boundaryconditions as well as the electric continuity conditions, a Volterraintegral equation of the second kind with respect to a function of time isderived, which can be solved successfully by means of the interpolationmethod. The displacements, electric potentials and stresses can be finallydetermined. The present method is suitable for a multilayer sphericallyisotropic pyroelectric hollow sphere consisting of arbitrary layers andsubjected to arbitrary spherically symmetric thermal loads. Numericalresults are presented and discussed at the end.