Abstract
In this paper, time-harmonic axisymmetric vibration of an incompressible viscoelastic half-space having shear modulus linearly increasing with depth is studied. The half-space is subjected to a vertical time-harmonic load on its surface. Numerical results concerning surface displacements due to a point force are given for the case of non-zero shear modulus at the surface. Hankel's transforms of the solutions have an infinite number of poles lying on the real axis of the complex plane in the non-dissipative case. A suitable contour of integration is used to avoid all the singularities. Calculations are performed for the dynamic as well as for the static case. In addition, vertical vibrations of a rigid disk on the considered half-space are investigated, and the influence of the non-homogeneity on the dynamic stiffness of the loaded area is demonstrated.
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