BEM approach to protection of structures from seismic waves by a viscoelastic stratum

In the context of the anti-plane problem, we study harmonic oscillations of an elastic rectangle whose base is isolated from the foundation by a viscoelastic stratum of finite thickness. Such a (viscoelastic) medium is embedded in the ground, which is simulated as a homogeneous isotropic elastic half-space. By using the fundamental representation of solution through single and double layer potentials, the problem is reduced to a set of integral equations. The main practical aspect of this investigation is connected with seismic base isolation. We thus estimate the wave attenuation, which results in the decrease of the vibration amplitude for the rectangular construction, provided by the viscoelastic stratum.