Dynamic of an inhomogeneous three-layer sphere under cyclic pressure

Abstract

In this paper, the dynamic characteristics of inhomogeneous three-layer spheres under spherical wave induced by cyclic pressure are studied. The density is assumed to have a square of inverse proportional function distribution along the radius. Firstly, on the basis of Lamb decomposition and variable separation method, the analytical expression of spherical wave is conducted, which satisfies the stress equilibrium on the outer and inner surfaces of the sphere, and the Euler equation is obtained due to inhomogeneity. Next, algebraic equations with respective boundary conditions are composed and solved by effective truncation techniques. Finally, a comparison and discussion are conducted between the model presented in this article and the homogeneous model obtained by the Legendre polynomial expansion. Obtained results enable 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 finite element method. This paper can provide a theoretical method for the analysis of mechanical properties of inhomogeneous multilayered spherical structure under dynamic loading.