An efficient method in the 2D problem on transient oscillations of the elastic half-space interacting with a rigid structure

We propose an efficient method to study the (two-dimensional) in-plane nonstationary (transient) problem for a rigid rectangular structure above the oscillating foundation. A massive structure is perfectly coupled with the foundation, whose oscillations are caused by an oblique plane seismic wave incoming from below to the boundary surface. The structure is assumed to be considerably more rigid than the foundation. The mathematical formulation admits application of the Laplace transform over time and Fourier transform along the horizontal coordinate. By satisfying the boundary conditions over the contact zone between the rectangle and the foundation, the problem is reduced to a system of two integral equations for normal and tangential contact stress, which contain the Laplace parameter. To solve this system, we apply a numerical method to arising Volterrà–Fredholm integral equations. Then the dynamic properties of the structure is studied for various combinations of physical and geometrical parameters.