Three-dimensional free vibration analysis of a fluid-filled piezoceramic hollow sphere

This article presents an exact three-dimensional analysis of the free vibration of a piezoceramic hollow sphere filled with a compressible fluid medium. Three displacement functions are introduced to rewrite three components of the mechanical displacement in spherical coordinates. For the problem of general nonaxisymmetric free vibration, it is shown that the controlling equations are finally simplified to an uncoupled second-order ordinary differential equation and a coupled system of three such equations. Solutions to these differential equations are obtained. The coupled vibration problem of piezoceramic hollow sphere is then considered. It is found that there are two independent classes of vibrations. The first class is independent of the contained fluid and is not affected by the electric field, while the second is related to both the fluid parameter and the electric field. Exact frequency equations are derived and numerical results are finally presented.