Propagation of Elastic Waves in a Finite Length Bar with a Variable Cross Section

Abstract

The present paper is concerned with the propagation of elastic waves in a finite length bar with a variable cross section subjected to an arbitrary longitudinal impact loading. The solution is obtained by the application of the Laplace transform. The results of this analysis can be applied only to a thin bar with small changes of area and to waves which are long compared to the lateral dimensions of the bar. Numerical calculations are carried out for the case of truncated cones, and strain wave histories at various stations along the bar are shown for two kinds of impact loading. The corresponding experiments are also performed for two different truncated cones. The theoretical predictions are found to be in good agreement with the experimental results.