Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space

• The analytical layer element is an exact and symmetric stiffness matrix without positive exponential functions.
• The analytical layer-element of a single layer is obtained in the Hankel transform domain.
• The analytical layer element method is used to study axisymmetric dynamic response of transversely isotropic multilayered half-space.
• The influence of transversely isotropic and stratified character on the dynamic response of the medium is remarkable.

Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the corresponding algebraic operations and the Hankel transform, the analytical layer-elements of a finite layer and a half-space are obtained in the transformed domain. According to the continuity conditions between adjacent layers, the global stiffness matrix equation is obtained by assembling the analytical layer-element of each single layer. The solutions in the transformed domain are acquired by introducing the boundary conditions into the global stiffness matrix equation, and thus, the corresponding solutions in frequency domain are achieved by taking the inversion of Hankel transform. Finally, some numerical examples are given to illustrate the accuracy of the proposed method, and to study the influence of properties and the frequency of excitation on the dynamic response of the medium.