Propagation of Axisymmetric Waves in a Circular Semiinfinite Elastic Rod

Abstract

The Mindlin-McNiven equations for axially symmetric waves are used to determine the radial strains in a circular, semiinfinite, isotropic, elastic rod for both pure and mixed end conditions when a constant pressure is suddenly applied to its end. Using double integral transforms, the solution is obtained in terms of three Fourier integrals, each one representing one mode of propagation. These integrals are too complex to be evaluated exactly and, therefore, an asymptotic solution, valid for large distance of travel, is obtained for the head of the pulse by using the method of steepest descent. The results predict the existence of edge resonance and further demonstrate its influence on the strain field. © 1964, Acoustical Society of America. All rights reserved.