Axisymmetric time-harmonic Lamb's problem for a system comprising a viscoelastic layer covering a viscoelastic half-space

Abstract

The axisymmetric time-harmonic Lamb's problem for a system comprising a viscoelastic covering layer and viscoelastic half-space is studied. The investigation is carried out within the scope of the piecewise homogeneous body model with the use of the exact field equations of the linear theory of viscoelasticity. The mechanical relations of the materials are described through fractional exponential operators. The corresponding boundary value problem is solved by utilizing the Hankel integral transformation. Parameters characterizing the influence of the viscosity of the constituents of the considered system on the frequency response of the amplitudes of the stresses acting on the interface plane are introduced. Numerical results on these frequency responses are presented and discussed. In particular, it is established that in the case where the material of the covering layer is stiffer than that of the half-space material an increase in the values of the aforementioned parameters leads to parametric resonance.