Impact on a transversely anisotropic half-space

Abstract

An analysis is presented of the linear wave propagation problem in a transversely isotropic half-space, with the axis of symmetry located in the free surface when subjected to arbitrary concentrated normal loading on the boundary, using a mixed Laplace and two-dimensional Fourier transform as well as a modified Cagniard-de Hoop technique. The solution for the displacement resulting from a step load is obtained in integral form from which the response to an arbitrary force history is obtained by convolution; corresponding results for the strains were derived analytically. A computer program was then developed to evaluate the field variables. The procedure can be applied for the determination of these quantities both in the interior and near the surface of the medium, and can also be utilized to predict the results for an isotropic solid by approximating this material as a slightly anisotropic body. Comparisons of the predictions of the analysis both with the results of a finite element procedure and experimental measurements in large blocks of an isotropic and a transversely isotropic material show good correlation.