RADIAL VIBRATION OF ELASTO-PIEZOELECTRIC COMPOSITE CYLINDER WITH AN ISOTROPIC ELASTIC CORE

Abstract

The transient responses of infinite elasto-piezoelectric composite hollow cylinder with an isotropic core under radial vibration are obtained. According to the charge equation of electrostatics, the expression of electric displacement for piezoelectric layer is first expressed by a product of a known function about radial distance and an unknown function about time. Then the governing equations for mechanical field of the piezoelectric layer, involving the unknown time function, are derived. By the method of superposition, the dynamic solutions for both elastic and piezoelectric layers are divided into two parts named as quasi-static and dynamic parts. The quasi-static part is obtained in an explicit form and the dynamic part is solved by the separation of variables method. Both the quasi-static and dynamic parts thus obtained involve the undetermined time function. By means of the electric boundary conditions, a Volterra integral equation of the second kind with respect to the unknown time function is derived. Interpolation method is introduced to solve the integral equation efficiently. The displacements, stresses and electric fields are finally determined. Numerical results are presented.