Axisymmetric Elastic Wave Propagation in Bars Containing a Discontinuity

摘要

The objective of the work is to obtain a solution to the axisymmetric equations of motion in an elastic bar containing various discontinuities. The differential equations governing axisymmetric, elastic wave propagation are derived in displacement form. The resulting equations are case in an explicit finite difference scheme and integrated numerically to obtain solutions for the displacements and stresses which are valid throughout the length of the bar. The first problem considered is a pressure shock applied to the end of a constant diameter, semi-infinite bar having a free radial surface. The resulting displacements are compared to Bertholf's numerical work and Miklowitz and Nisewanger's experimental data. The next problem studied is the case of a pressure shock applied to the end of a uniform diameter bar composed of two materials fused together at some point along the bar's length. The continuity conditions on stress and displacement at the material junction are cast in finite difference form to allow the numerical integration of proceed across the material junction. The last problem examined is elastic wave transmission in a bar containing a discontinuity in cross section at some point along its length. The numerical method is used to study the case of a pressure shock applied to either the large or small end of the bar. (Author)