The transient response of a circular cylinder of arbitrary thickness, embedded in a viscoelastic medium and impinged upon by plane waves, is obtained. Dilatational and shear incident waves are considered. The solution is valid within the scope of the linear theories of elasticity and viscoelasticity. The method of solution, which circumvents the difficulties encountered in the customary transform approaches, relies upon (a) the construction of a train of incident pulses from steady-state components, where each pulse represents the time history of the transient stress in the incident wave and (b) the existence of a physical mechanism that, between pulses, restores the disturbed particles of the cylinder and the surrounding medium to an unstrained state of rest. The influence on the major stress and displacement response of variations in the viscoelastic properties of the medium is investigated for the case of incident step waves. The results for the viscoelastic media are compared with corresponding results for the limiting cases of elastic-unrelaxed and elastic-relaxed media.

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