Model of Torsional Waves Based on Transverse and Layered One-Dimensional Component of Infinite Length

Abstract

The dispersion of torsional wave in transverse and layered one-dimensional component of infinite length is investigated. The study is carried out by treating the one-dimensional component as a cylinder of infinite length firstly, Then put forward a way that the component is divided into a multilayer to analyze torsional wave propagation, the model is constructed in cylindrical coordinates for homogeneous and layered component, the governing equation of torsional wave was derived based on one-dimensional elastic theory and Whittaker's function, obtain harmonic wave solution of the governing equation by making use of the boundary and continuity conditions of adjacent layers. Finally the result of numerical simulation illustrated the influence of component's density and shear module on torsional angels and phase velocity. It has been observed the velocity is changing as the change of parameters of shear module and density according to the curve. The conclusion made shown the consistency with the classical theory, and the effective on model such as bearings, engineering mechanics and displacement of particles.