Waves generated at the lateral surfaces of an elastic block due to a time-varying homogeneous external pressure applied to its frontal surface

The influence of the Rayleigh surface waves on the transient motion of a rectangular block under the action of a uniform external pressure, which begins to act on one of its surfaces (the frontal surface) at time t = 0, while the other surfaces are free, is evaluated. The problem is reformulated in terms of moving surface loads applied to the lateral surfaces of the block, which are considered as independent, so that the problem is reduced to a problem for an elastic quarter-space. Using the Cagniard–de Hoop method, an analytical solution is obtained for the displacement of material particles on the free lateral surfaces of the block, which makes it possible to study the coupling between the body waves and the Rayleigh surface waves. By expanding the solution to the problem in powers of the Poisson ratio, which is considered as a small parameter, we obtain an approximate solution that describes with sufficient accuracy the motion not only near the lateral surfaces but also at any point in the block. To assess the accuracy of the approximate solution, the particle displacements on the lateral surface obtained from this solution were compared with those determined from the analytical solution.