A solution method using realistic (broad-band) viscoelastic response characteristics covering approximately ten decades of logarithmic time is presented for wave propagation in two-dimensional geometries. A Dirichlet series representation of the viscoelastic mechanical properties and a numerical collocation inversion procedure overcome many of the computational difficulties associated with the Laplace-transform approach to dynamic linear viscoelasticity and also afford a complete time solution. Stress distributions are given for two complementary cases, (a) the viscoelastic half-space subjected on the upper surface to the steady motion of a step pressure load moving supersonically relative to any wave speed in the material, and (b) the semi-infinite thin plate similarly loaded on its edge.

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