VIBRATION THEORY OF NON-HOMOGENEOUS, SPHERICALLY ISOTROPIC PIEZOELASTIC BODIES

In this paper, three displacement functions are introduced to simplify the basic equations of a radially polarized, spherically isotropic, piezoelectric medium with radial inhomogeneity. For the general non-axisymmetric free vibration problem, it is shown that the controlling equations are finally reduced to an uncoupled second order ordinary differential equation and a coupled system of three second order ordinary differential equations. Solutions to these differential equations are given for the case that material constants are of power functions of the radial co-ordinate. For free vibrations of multilayered piezoelastic spherical shells, it is shown that there are two separated classes of vibrations. The first class is independent of the electric effect and is identically the same as that for pure elasticity, while the second is affected by the electric field. Numerical results are given for the non-axisymmetric free vibration of a single-layered, inhomogeneous piezoelastic spherical shell and effects of some involved parameters are discussed.