Dynamic Analysis of a Composite Hollow Sphere Composed of Elastic and Piezoelectric Layers

Abstract

Dynamic analysis of a two-layered elasto-piezoelectric composite hollow sphere under spherically symmetric deformation is developed. An unknown function of time is first introduced in terms of the charge equation of electrostatics and then the governing equations of piezoelectric layer, in which the unknown function of time is involved, are derived. By the method of superposition, the dynamic solution for elastic and piezoelectric layers is divided into quasi-static and dynamic parts. The quasi-static part is treated independently by the state space method and the dynamic part is obtained by the separation of variables method. By virtue of the obtained quasi-static and dynamic parts, a Volterra integral equation of the second kind with respect to the unknown function of time is derived by using the electric boundary conditions for piezoelectric layer. Interpolation method is employed to solve the integral equation efficiently. The transient responses for elastic and electric fields are finally determined. Numerical results are presented and discussed.

Modeling and analysis of multilayer piezoelectric-elastic spherical transducers

“…All of the piezoelectric layers are polarized in the radial direction and are connected in parallel electrically. For the i th piezoelectric layer, the linear constitutive equations for spherically symmetric problem can be expressed as (Dai et al, 2010; Ding et al, 2003; Ghorbanpour et al, 2006; Li et al, 2010; Wang and Ding, 2006)…”