The response of a hollow cylinder of arbitrary thickness, embedded in an elastic medium, to a transient plane pressure wave is presented. The solution is valid within the scope of the linear theory of elasticity. The technique for obtaining the solutions 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 which, between pulses, restores the disturbed particles of the cylinder and the surrounding medium to an unstrained state of rest. The validity of the technique is demonstrated by (a) comparisons with published data for limiting cases and (b) results obtained for a broad range of values of cylinder and surrounding medium parameters. The influence on the cylinder response of liner thickness and cylinder-medium impedance mismatch, when the incident wave is a step pulse, is investigated.

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