On the correspondence of theoretical models of longitudinal vibrations of a rod with experimental data

Abstract

A number of theoretical models are known for describing longitudinal vibrations of a rod. The simplest and most common is based on the wave equation. Next comes a model that takes into account lateral displacement (Rayleigh correction). The Bishop model is considered to be more perfect, taking into account both transverse displacement and shear deformation. It would seem that the more perfect the theoretical model, the better it should be consistent with experimental data. Nevertheless, when comparing with a really defined experimental spectrum of longitudinal vibrations of a rod on a large base of natural frequencies, it turns out that this is not quite so. Moreover, in the relative loss is the most complex Bishop model. Comparisons were made for a smooth long cylindrical rod. The questions of refinement with the help of experimentally found frequencies of the velocity of longitudinal waves and the Poisson’s ratio of the rod material are also touched.