Abstract
We use numerical-analytic methods to study the influence of the length of a thin inhomogeneous rod on its natural frequencies and the shapes of its plane transverse vibrations. We found that the existence of an external elastic medium described by the Winkler model can lead to an anomalous effect, i.e., to an increase in the natural frequencies of the vibration lower modes as the rod length increases continuously. We discovered rather subtle properties of this phenomenon in the case of variations in the length, the mode number, and the fixation method. We separately studied vibrations for the standard boundary conditions: fixation, hinged fixation, tangential fixation, and free end. We calculated several simple examples illustrating the anomalous dependence of the frequency of the rod natural vibrations in a strongly inhomogeneous elastic medium with different boundary conditions.
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Original Russian Text © L.D. Akulenko, S.V. Nesterov, 2010, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2010, No. 2, pp. 126–133.
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Akulenko, L.D., Nesterov, S.V. Anomalous dependence of the vibration frequencies of a rod in an elastic medium on the rod length. Mech. Solids 45, 257–263 (2010). https://doi.org/10.3103/S0025654410020111
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DOI: https://doi.org/10.3103/S0025654410020111