Radial vibration of piezoelectric/magnetostrictive composite hollow sphere

The radial vibration of a multilayered piezoelectric/magnetostrictive composite hollow sphere is investigated. In terms of the Gaussian equations, two unknown time functions are first introduced to complete the solution of electric displacement and magnetic induction. The solution for mechanical field involving two unknown time functions is obtained by means of the superposition method, the state space method as well as the separation of variables method. By means of the electric and magnetic boundary conditions and continuity conditions, two Volterra integral equations of the second kind with respect to two time functions are derived. The interpolation method is employed to solve the Volterra integral equations. The present solution is suitable for analyzing the transient responses of composite hollow sphere composed of piezoelectric and magnetostrictive layers with arbitrary composite sequence. Numerical results are presented and discussed.