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

[+] Author and Article Information
J. L. Habberstad

Lawrence Radiation Laboratory, University of California, Livermore, Calif.

J. Appl. Mech 38(1), 62-70 (Mar 01, 1971) (9 pages) doi:10.1115/1.3408768 History: Received August 08, 1969; Revised February 04, 1970; Online July 12, 2010


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.

Copyright © 1971 by ASME
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