Propagation of spherical wave in a three-layer sphere under cyclic pressure

Abstract

In this paper, the dynamic characteristics of a three-layer sphere under a spherical wave induced by cyclic pressure are studied. Firstly, on the basis of the Lamb Decomposition and Variable Separation methods, the analytical expression of the spherical wave is conducted, which satisfies the stress equilibrium on the outer and inner surfaces of the sphere. Next, algebraic equations with respective boundary conditions are composed and solved by Legendre Polynomial expansion and effective truncation techniques. The obtained results enable us to reveal the influence on the dynamic stress concentration factor intensity under proper conditions. The conclusions of this article are verified by comparing the analytical solutions to the ones obtained by the finite element method. This paper can provide a theoretical method for the analysis of mechanical properties of multi-layered spherical structures under dynamic loading.