Impedance functions for a rigid foundation on a layered medium

Abstract The problem of the harmonic forced vibrations of a massless rigid disc supported on an elastic layered medium is studied. The elastic medium consists of a layer of constant thickness placed on an elastic half-space. The contact between the layer and the underlying half-space is such that continuity of displacements and stresses at the interface is secured. Forced vertical, rocking and horizontal vibrations with harmonic time dependence are considered under the assumption of relaxed bonding between the rigid disc and the surface layer. The resulting mixed boundary value problems are reduced to sets of Fredholm integral equations that are solved numerically for a wide range of frequencies. The force—displacement relationships thus obtained present several differences with the corresponding results for a homogeneous half-space. In general, the rocking impedances are the least affected by layering, while the vertical impedances are the most affected. The impedances for a layered medium show a stronger frequency dependence than the impedances for the half-space. For intermediate and high contrast between the elastic properties of the layer and those of the half-space there is a considerable reduction of the radiation damping for low frequencies.