Transient Response of Cylinders to Shear Waves

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Abstract
The response of a hollow cylinder of arbitrary thickness, embedded in an elastic medium, to a transient plane shear wave is presented. The solution is valid within the scope of the linear theory of elasticity. The technique for obtaining the solution relies on (1) 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 (2) 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 validity of the technique, demonstrated previously in the case of a dilatational wave, is further demonstrated in the present case by (1) comparisons with published data for limiting cases, and (2) results obtained for a broad range of values of cylinder and surrounding medium parameters. The influence of the cylinder thickness and cylinder-medium impedance mismatch on the response, when the incident wave is a step pulse, is investigated. The natures of the differences between the responses to dilatational and shear waves is also examined.

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