Random Response of a Rigid Sphere Embedded in a Viscoelastic Medium and Related Problems

Abstract

Random and harmonic responses are considered for a rigid movable sphere embedded in a viscoelastic medium. The solution takes into account the filtering effect of the viscoelastic medium on the traveling random waves. The sphere can be also randomly located with respect to a plane at which the spectral density of incident stochastic waves is prescribed. For a Maxwellian medium with small losses the exact stationary response is derived. The results regarding the nonstationary response of the sphere embedded in a Kelvin-Voight medium are obtained numerically. It is shown that the results obtained are applicable to the prediction of mechanical properties of composite materials, as well as to those of buried structures, when these objects are excited by incompletely known or random disturbances.