On the conformity of theoretical models of longitudinal rod vibrations with ring defects experimental data

Abstract

The paper considers a number of theoretical models for describing longitudinal vibrations of a rod. The most simple and common is based on the wave equation. Next comes the model that takes into account the lateral displacement (Rayleigh correction). Bishops 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 agree with the experimental data. Nevertheless, when compared with the actually determined experimental spectrum of longitudinal vibrations of the rod on a large base of natural frequencies, it turns out that this is not entirely true. Moreover, the most complex Bishops model turns out to be a relative loser. The comparisons were made for a bar with small annular grooves that simulate surface defects, which is considered as a stepped bar. The questions of refinement with the help of experimentally found frequencies of the velocity of longitudinal waves and Poisson's ratio of the rod material are also touched upon.

Keywords

• stepped bar
• longitudinal vibrations
• rayleigh correction
• bishop correction
• wave equation
• experimental data