Longitudinal Waves in Elastic Rods with Discontinuous Cross Sections

Abstract

In this paper longitudinal impact waves in an elastic rod with discontinuous cross section struck by a rigid sphere are studied numerically and experimentally. In a rod with finite length, waves move back and forth along the rod; therefore, it may happen that two incident waves cross a discontinuity interface simultaneously. Thus, the reflected and transmitted waves induced at the interface will influence the incident waves due to the wave reflection at both ends of the rod. For these general cases, to the authors’ knowledge, there are no computational methods for the transmitted and reflected waves. This problem will be addressed in this paper in some detail. In the numerical simulations, the classical Hertzian contact law and the wave equation are combined to compute impact responses. In the experimental setup, advanced instruments like Laser-Doppler-Vibrometers for measuring the high frequency impact responses are used. It is shown that numerical results computed by this approach agree very well with experimental results.