Electroelastic fields in layered piezoelectric spheres

Abstract

Analytic and discrete-layer models are used to study the displacement and electrostatic potential fields in the static and free vibration response of layered piezoelectric spheres. The analytic solution is developed for the lowest harmonic for purposes of comparison. The discrete-layer model is based on approximations to the variational form of the equations of motion and the charge equation. The displacements and electrostatic potential are separated into functions in the radial direction of the sphere and those for spherical surfaces. General expressions are given for arbitrary approximation functions. For purposes of numerical examples, piecewise quadratic Lagrange interpolation polynomials are used in the radial direction, with spherical harmonics in the circumferential and azimuthal directions. The results from these numerical models are compared with earlier studies for elastic spheres, and several new results are presented for layered piezoelectric spheres.