Transient torsional vibrations of a rigid mass connected to an elastic half-space by an elastic circular rod

Abstract

Applying Laplace transformations with respect to time and numerical inverse Laplace transformations, the transient torsional vibrations of a rigid mass connected to an elastic half-space by an elastic rod are analyzed under two specific incident pulse loads. The time histories of the rigid mass rotation are presented. Application of the numerical inverse Laplace transformations enables us to obtain the time histories of the rigid mass rotation accurately and fairly quickly by utilizing a digital computer. This method is applicable to the transient problem of a rigid mass connected to a half-space by an elastic medium or a finite elastic medium on a half-space, e.g. machines such as a press or a pile driver footed on a foundation, if the shape of the incident pulse is not very complicated and the maximum time T max is not too long. When the slenderness ratio of the rod is small, the damping effect of the half-space on the rigid mass rotation due to waves radiating to infinity is small, regardless if the shear modulus ratio of the half-space and the rod is large or not. The amplitude of the rigid mass roation increases and its period lengthens as the shear modulus ratio increases.