Transiet dynamics of a massive structure on the seismically oscillating foundation

In the present paper we study an anti-plane nonstationary (transient) problem for a massive structure above the oscillating foundation. The latter is taken as an elastic half-space with 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 analytical treatment is achieved by applying the Laplace transform over time. After that the solution in the half-space is constructed by using the Fourier transform along the horizontal coordinate. By satisfying the joining boundary conditions between the rectangle and the foundation, the problem is reduced to an integral equation along the contact zone, which contains the Laplace parameter. We propose a new numerical approach to solve the dual Volterrà-Fredholm integral equations of the arising type. Then we investigate the dynamic properties of the structure for various combinations of physical and geometric parameters.