Abstract
There are several theoretical models for describing longitudinal vibrations of a rod. The simplest and most common model is based on the wave equation. Less common is the model taking into account lateral displacement (Rayleigh correction). The Bishop model is considered to be superior, considering both transverse displacement and shear deformation. It would seem that the more improved the theoretical model, the better its agreement should be with experimental data. However, that turns out not to be quite the case when compared to an actual experimental spectrum of longitudinal rod vibrations over a large base of natural frequencies. Moreover, the most complex Bishop model turns out to be relatively weak. Comparisons were made for a smooth long cylindrical rod. Also discussed are the questions of specifying the velocity of longitudinal waves and Poisson’s ratio of the rod material using experimentally obtained frequencies.
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This study was supported by the Russian Foundation for Basic Research (project no. 19-01-00100).
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Translated by L.Trubitsyna
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Popov, A.L., Sadovsky, S.A. Correspondence of Theoretical Models of Longitudinal Rod Vibrations to Experimental Data. Vestnik St.Petersb. Univ.Math. 54, 162–170 (2021). https://doi.org/10.1134/S1063454121020114
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DOI: https://doi.org/10.1134/S1063454121020114