Time-harmonic response of transversely isotropic multilayered half-space in a cylindrical coordinate system

With the aid of the analytical layer-element method, a comprehensive analytical derivation of the response of transversely isotropic multilayered half-space subjected to time-harmonic excitations is presented in a cylindrical coordinate system. Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the Fourier expansion, Hankel and Laplace integral transform, analytical layer-elements for a finite layer and a half-space are derived. Considering the continuity conditions on adjacent layers׳ interfaces and the boundary conditions, the global stiffness matrix equations for multilayered half-space are assembled and solved. Finally, some numerical examples are given to make a comparison with the existing solution and to demonstrate the influence of parameters on the dynamic response of the medium.