A Two-Dimensional Numerical Solution for Elastic Waves in Variously Configured Rods

Abstract

The exact equations of motion governing elastic, axisymmetric wave propagation in a cylindrical rod are approximated by a first-order finite-difference scheme. This difference scheme is based on a displacement rather than a velocity formulation, thereby making it unnecessary to explicitly introduce an artificial viscosity term into the finite-difference equations. The resulting difference equations are used in conjunction with the boundary and initial conditions 10 study: (a) a pressure pulse applied to the end of a semi-infinite bar, (b) a bar composed of two materials joined together at some point along its length, and (c) a bar containing a discontinuity in cross section. The numerical results so obtained are compared to available experimental data and other analytical-numerical solutions.