Analytical solution for a vibrating rigid sphere with an elastic shell in an infinite linear elastic medium

The analytical solution is given for a vibrating rigid core sphere, oscillating up and down without volume change, situated at the center of an elastic material spherical shell, which in turn inside infinite (possible different) medium. based on symmetry considerations continuity displacement both shell - outer medium boundaries as well stress edge shell. Furthermore, separation into longitudinal transverse waves used. Analysis shows that surprisingly complex range physical phenomena can be observed when frequency changed while keeping parameters same, especially compared to case any With careful choice materials, thickness vibration frequency, it possible filter out most generate pure tangential domain (and vice-versa, we waves). When applied different frequencies with help fast Fourier transform (FFT), pulsed shown exhibit (L) (T) (often called P- S-waves earthquake terminology).