The Generation of Stress Pulses at the Junction of Two Noncollinear Rods

Abstract

The reflection of a stress pulse at the junction of two elastic rods which are not collinear, results, in general, in the generation of four separate pulses. A longitudinal pulse and a flexural pulse are reflected back along the first rod, and a pulse of each type is also transmitted into the second rod. For a given incident wave shape Fourier techniques may be employed to predict the shapes of these four pulses. In this paper the analytic relations between the incident pulse and the four generated pulses are derived both for an incident longitudinal pulse and an incident fluxural pulse. The simple one-dimensional theory is used to describe the propagation of longitudinal waves, and the Timoshenko equation is used for flexural propagation. The equations derived were solved numerically for a rectangular longitudinal pulse propagated along a system consisting of two rods of the same material (carbon steel) at an angle to each other, and these results were tested experimentally by impact experiments. The agreement was found to be very satisfactory for all the angles that were tried.