Dynamic responses of a multilayered pyroelectric hollow cylinder of crystal class 2Â mm for axisymmetric plane strain problems

The dynamic solution of a multilayered pyroelectric hollow cylinder of crystal class 2 mm in the state of axisymmetric plane strain is obtained. By the principle of superposition, the solution is divided into two parts: One is quasi-static and the other is dynamic. The quasi-static part is obtained in an explicit form by the state space method, and the dynamic part is derived by the separation of variables method coupled with the initial parameter method as well as the orthogonal expansion technique. By using the obtained quasi-static and dynamic parts and the electric boundary conditions as well as the electric continuity conditions, a Volterra integral equation of the second kind with respect to a function of time is derived, which can be solved successfully by means of the interpolation method. The displacements, stresses and electric potentials can be finally determined. The present method is suitable for a multilayered pyroelectric hollow cylinder of crystal class 2 mm consisting of arbitrary layers and subjected to arbitrary axisymmetric thermal loads. Numerical results are finally presented and discussed.