Plane strain dynamic response of a transversely isotropic multilayered half-plane

• Analytical layer-element solution for dynamic response of transversely isotropic multilayered half-plane is presented.
• Analytical layer-elements are derived by the Fourier transform and the corresponding algebraic operations.
• The global stiffness matrix equation is assembled by considering the continuity conditions between adjacent layers.
• Examples are given to portray the influence of anisotropy, the depth of load, stratification and the frequency of excitation.

A semi-analytical method is developed to analyze the plane strain dynamic response of a transversely isotropic multilayered half-plane subjected to a time-harmonic surface or buried load. On the basis of the governing equations of motion in Cartesian coordinates, the analytical layer-elements of a single layer with a finite thickness and a half-plane are obtained through the Fourier transform and the corresponding algebraic operations. The analytical layer-element solution for the multilayered half-plane in the transformed domain can be derived in combination with the continuity conditions between two adjacent layers. After the boundary conditions are introduced, the corresponding solution in the frequency domain is recovered by the inverse Fourier transform. The comparison with an existing solution for an isotropic half-plane confirms the accuracy of the proposed method. Several examples are given to portray the influence of material anisotropy, the depth of external load, material stratification and the frequency of excitation on the vertical displacement and vertical normal stress.