RAYLEIGH PROBLEM FOR VISCOELASTIC MATERIALS

Discussion of the Rayleigh problem for viscoelastic waves is simplified by using the convolution square roots of the modulus and compliance, g(t) and j(t) respectively. The wave speed is found to be g(t). Comparison theorems, to the effect that the displacement approaches equilibrium faster in a stiffer material, are proved. One of these theorems is used in conjunction with certain exact solutions to obtain bounds on the displacement, including an upper bound valid for all materials. Lower bounds are also obtained. An elementary approximate solution, applicable to any form of material response, is obtained. This approximation is in good agreement with the exact solution in cases on which it has been tested.