Reflection characteristics of torsional waves in a semi-infinite cylindrical rod connected to an elastic half-space—II

Abstract

Using the Pochhammer-Chree equation and applying Laplace transformations with respect to time and numerical inverse Laplace transformations, reflection characteristics of torsional waves in a semi-infinite rod connected to an elastic half-space are analyzed under a condition where the incident stress pulse varies proportionally with the distance from the rod axis. Time histories of surface torsional stress and circumferential displacement, and cross-sectional torsional stress and circumferential displacement distributions of the semi-infinite rod at an arbitrary point are shown. When the shear modulus ratio G R/G and the velocity ratio K are small, i.e. The half-space is hard and the rod is soft, time histories of surface stress and displacement obtained from the Pochhammer-Chree equation coincide with those obtained from the elementary equation which is derived from the assumption that each cross-section of the rod undergoes a pure rotation about the rod axis. However, when G r/G and K are not small, the curves obtained from the Pochhamer-Chree equation differ from those obtained from the elementary equation, and the difference in stress increases as the observed point approaches the interface between the rod and the half-space.