Transient Motion of a Rigid Cylinder Produced by Elastic and Acoustic Waves

Abstract

A rigid, circular cylinder embedded in an elastic medium is subjected to a plane stress wave whose front is parallel to the axis of the cylinder. Expressions for the displacement, velocity, and acceleration of the cylinder are derived, and numerical results are presented for an incident stress wave with a step distribution in time. Formulas for the response of the cylinder produced by an acoustic wave are also presented, and it is shown that the responses from the elastic and acoustic waves are identical when the cylinder density is equal to the medium density. These results can be used as influence functions to determine the response of the cylinder produced by a plane wave with arbitrary time dependence.