Seismic oscillations of an elastic rectangular structure protected by a viscoelastic stratum: in-plane problem

We study the problem of seismic protection of a rectangular elastic construction by mean of a viscoelastic stratum made of material of Kelvin-Voigt type. In particular we consider the in-plane problem. By using the standard boundary integral equations method (BIEs), the dynamic problem is reduced to a system of BIEs over the set of boundary lines. In order to reduce the dimension of the problem in its discrete form, for wave processes in the stratum and in the half-space foundation we use a special Green's function satisfying the stress-free boundary conditions over the boundary of the half-space. A numerical algorithm is used to solve the problem after discretization and finally we discuss the physical meaning of the results and the efficiency of the seismic protection by the viscoelastic stratum.