Propagation of a Shock Wave Front Through a Lens-Shaped Elastic Body

Ray theory is used to solve the problem of a plane pressure pulse with a discontinuous pressure front striking an elastic body whose cross section has the shape of a lens. Both plane-strain and axisymmetric motions are considered. The front and back surfaces of the lens are assumed to be circular. The velocity and acceleration at the P-wave front and the discontinuity in acceleration at the S-wave front are obtained explicitly for points along the axis of the lens and at the center of the back surface where reflections occur. The purpose of this study is to assess the effect of the curvatures of the lens on the velocity-time history at the center of the back surface of the lens which can be measured experimentally. Comparison with a laboratory test shows excellent agreement between analytical and experimental results.