Elastodynamic solution for spherically symmetric problems of a multilayered hollow sphere

Abstract

The elastodynamic solution of a multilayered hollow sphere for spherically symmetric problems is obtained by decomposition into two parts, one being the quasi-static and the other the dynamic solution. The quasi-static solution is firstly derived by means of the state-space method, and the dynamic solution is obtained by utilizing the separation of variables method and the orthotropic expansion technique. The solutions for displacement and stresses are obtained in result. The present method is suitable for a multilayered spherically isotropic hollow sphere, with arbitrary thickness of each of the layers and arbitrary initial conditions, subjected to arbitrary form of a spherically symmetric dynamic load at the internal and external surfaces. Numerical results are finally presented.

Transient responses of a multilayered spherically isotropic piezoelectric hollow sphere

“…(25) into Eqs. (20), (21), (23), (24) and (14), and with the aid of Eqs. (26)-(29), we can derive the following equations, form which the dynamic solution u (i) d , (i) rd and (i) θd can be determined.…”

“…By virtue of the orthogonal property of R (i) m (ξ ), [21,25], we can derive the following equation from Eq. (41).…”

“…The stress-wave propagation in a laminated thick-walled hollow sphere has been investigated [20], while the procedure presented there is not very strict and has been improved [21]. Due to the special electro-mechanical coupling effect, the search for the solution of elasto-dynamic problems involving multilayered piezoelectric hollow spheres is difficult.…”

“…In this paper, a method for solving the elasto-dynamic problem of multilayered elastic hollow spheres [21], is extended to solve the dynamic responses of their multilayered piezoelectric equivalents. The dynamic solution of a multilayered spherically isotropic piezoelectric hollow sphere in spherically symmetric problems is first divided into two parts by the method of superposition: one is quasi-static and the other is dynamic.…”

Elastodynamic response of bonded solids using the method of eigenfunction expansion

“…Du and Cheng [17] investigated the propagation of laser-generated guided waves in bonded plates with a weak interface using the two-layer normal mode expansion method. Ding et al [18] obtained the elastodynamic solution of a multilayered hollow sphere for spherically symmetric problems using the EEM. Yin and Yue [19] investigated the transient plane-strain response of multilayered elastic cylinders to axisymmetric impulses using the same method.…”