Forced Axisymmetric Vibrations of an Electrically Excited Hollow Sphere Made of a Continuously Inhomogeneous Piezoceramic Material*

Abstract

The forced axisymmetric vibrations of a hollow sphere made of a functionally graded radially polarized piezocelectric material are studied using the spatial theory of electroelasticity. The properties of the material vary continuously as a power function along the radial coordinate. The vibrations are excited by applying a varying electrostatic potential to the sphere surface. Solid and split electrodes are considered. After separation of variables and expression of the components of displacement and electric-flux density, electrostatic potential, and the stress tensor in terms of spherical functions, the original three-dimensional problem is reduced to a boundary-value problem for ordinary differential equations. The problem is solved by the effective method of discrete orthogonalization. The numerical solution is analyzed. Particularly, the distributions of the mechanical and electric parameters in the first modes of forced electroelastic vibrations of the sphere made of homogeneous and inhomogeneous piezoceramic materials are compared and analyzed. The effect of the loading caused by applying a variable electrostatic potential to the sphere surface on the distribution of forced vibration characteristics is studied.