Free vibration analysis of laminated piezoceramic hollow spheres

Abstract

This paper presents an exact three-dimensional analysis of the general nonaxisymmetric free vibration of a piezoceramic hollow sphere by employing a state-space approach. By introducing three displacement functions and two stress functions, the basic equations of a spherically isotropic piezoelectric medium are eventually turned into two separated state equations with variable coefficients. The solutions of these two equations are then obtained by virtue of Taylor’s expansion theorem. Relationships between the state variables at the inner and outer surfaces of a laminated hollow sphere are established. Exact frequency equations corresponding to two independent classes of vibrations are then derived from the free conditions at the spherical boundary surfaces. Numerical results are finally presented.