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

Abstract

Reflection characteristics of torsional waves in a semi-infinite rod connected to an elastic half-space are analyzed under two specific incident pulse loads, applying Laplace transformations with respect to time and numerical inverse Laplace transformations. The time histories of the torsional stress and rotation of the semi-infinite rod at an arbitrary point are shown. The advantage of this method, i.e., applying the numerical inverse Laplace transformations, is that it is simpler than using Fourier analysis and synthesis, and applicable to any incident pulse load except where the rise time interval of the incident pulse load is too short. In the case of a step pulse load, the stress curves approach that of the fixed boundary condition and the rotation curves approach asymptotically the static rotation value of each given shear modulus ratio GR/G and velocity ratio K. In the case of a half-sine pulse load, the reflected stress peak values decrease and those of the rotation increase with an increase in GR/G and K. A cross−over effect occurs when GR/G≳1 and K≳1; it becomes pronounced as GR/G and K increase.