General three-dimensional scattering and dynamic stress concentration of Lamb-like waves in a spherical shell with a spherical inclusion

Abstract

Three-dimensional scattering and dynamic stress concentration of Lamb-like waves around a spherical inclusion (inhomogeneity and a cavity) in a thick spherical shell are investigated theoretically and numerically. Two spherical coordinates, located at the spherical shell center and the inclusion center, are established to express the incident and scattered wave potential functions. By a kind of addition formulas, all the potential functions can be transformed into the same coordinate, then the analytical solution of the displacements and stresses are derived, and all the undetermined coefficients are solved by satisfying the boundary condition and the interface condition. In order to describe the 3-D stresses concentration, multiple DSCFs are employed and the 3-D distributions are depicted. The results reveal the influences of inclusion material and the cavity on the distributions of DSCFs, and the influence of incident wave frequency and inclusion position are also calculated. This research is expected to provide theoretical understanding on dynamic analysis and mechanical properties evaluation of the spherical shells.