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Buckling problem for a rod longitudinally compressed by a force smaller than the Euler critical force

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Abstract

It was earlier shown that a rod can buckle under the action of a sudden longitudinal load smaller than the Euler critical load. The buckling mechanism is related to excitation of periodic longitudinal waves generated in the rod by the sudden loading, which in turn lead to transverse parametric resonances. In the linear approximation, the transverse vibration amplitude increases unboundedly, and in the geometrically nonlinear approach, beats with energy exchange from longitudinal to transverse vibrations and back can arise. In this case, the transverse vibration amplitude can be significant. In the present paper, we study how this amplitude responds to the following two factors: the smoothness of application of the longitudinal force and the internal friction forces in the rod material.

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Authors and Affiliations

  1. Institute for Problems inMechanical Engineering, Russian Academy of Sciences, Bol’shoy pr. 61, St. Petersburg, 199078, Russia

    A. K. Belyaev & T. P. Tovstik

  2. Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034, Russia

    N. F. Morozov & P. E. Tovstik

Authors
  1. A. K. Belyaev
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  2. N. F. Morozov
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  3. P. E. Tovstik
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  4. T. P. Tovstik
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Corresponding author

Correspondence to A. K. Belyaev.

Additional information

Original Russian Text © A.K. Belyaev, N.F. Morozov, P.E. Tovstik, T.P. Tovstik, 2016, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2016, No. 3, pp. 28–39.

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Belyaev, A.K., Morozov, N.F., Tovstik, P.E. et al. Buckling problem for a rod longitudinally compressed by a force smaller than the Euler critical force. Mech. Solids 51, 263–272 (2016). https://doi.org/10.3103/S0025654416030031

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