Dynamic responses of a functionally graded pyroelectric hollow sphere for spherically symmetric problems

The spherically symmetric thermoelastic problem of a functionally graded pyroelectric hollow sphere is considered. The functionally graded material is restricted to the variations of density and other material constants as a certain power of the radial distance. By virtue of the introduction of a dependent variable as well as the separation of variables technique, a Volterra integral equation of the second kind related to a function with respect to time is derived, which is solved successfully by using an interpolation polynomial to approximate the unknown function. The corresponding recursive formulae are derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently and is suitable for a functionally graded pyroelectric hollow sphere with an arbitrary thickness and subjected to arbitrary spherically symmetric thermal loads. Numerical results are finally presented.