Transient Responses in a Piezoelectric Spherically Isotropic Hollow Sphere for Symmetric Problems

Abstract

By virtue of the separation of variables technique, the spherically symmetric electroelastic dynamic problem of a spherically isotropic hollow sphere is transformed to an integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of displacements, stresses, electric displacements, and electric potential are obtained. The present method is suitable for a piezoelectric hollow sphere with an arbitrary thickness subjected to spherically symmetric electric potential and radial mechanical loads, that both can be arbitrary functions about the time variable, at the internal and external surfaces.

Transient responses of a multilayered spherically isotropic piezoelectric hollow sphere

“…2. The results agree well with those presented in [9]. Thus, the validity of the present solution of the dynamic problems is clarified.…”

“…Example 1 In this example, we consider a homogeneous piezoelectric hollow sphere, of which an analytical solution has been obtained [9]. The material is taken as PZT-4 (Table 1).…”

“…The three-dimensional free vibrations of submerged and compressible fluid-filled piezoelectric hollow sphere have been further studied by Cai et al (2000) and Chen et al (2001) [6,7]. The steady-state radial vibrations of a piezoelectric hollow sphere in a compressible fluid have been investigated by Borisyuk and Kirichok [8], and the dynamic response of a piezoelectric hollow sphere in a spherically symmetric geometry have been newly obtained by Ding et al [9].…”

Dynamic responses of a functionally graded pyroelectric hollow sphere for spherically symmetric problems

“…After Á( ) is obtained, u( ; ) and ( ; ) also can be determined. It is to be noted here that we develop a similar method where a linear interpolation function is employed to approximate the unknown function in the integral equation as in [16] paper where the comments on testing and success of the numerical method are presented. In fact, the calculation accuracy of the numerical results for employing the cubic Hermite polynomial is higher than that for employing the linear interpolation function.…”

Analytical and numerical modeling of resonant piezoelectric devices in China-A review

“…Usually ceramics with radial poling are considered so that spherical symmetry is not destroyed. Similar to the case of circular cylinders, solutions for single-layered [115][116][117] and multi-layered [118,119] spherical shells and shells filled with a fluid [119,120] have been analyzed. Nonlinearity due to large extension was considered in ref.…”