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A.K. Belyaev, N.F. Morozov, P.E. Tovstik, and T.P. Tovstik, "Buckling Problem for a Rod Longitudinally Compressed by a Force Smaller Than the Euler Critical Force," Mech. Solids. 51 (3), 263-272 (2016)
Year 2016 Volume 51 Number 3 Pages 263-272
DOI 10.3103/S0025654416030031
Title Buckling Problem for a Rod Longitudinally Compressed by a Force Smaller Than the Euler Critical Force
Author(s) A.K. Belyaev (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, vice.ipme@gmail.ru)
N.F. Morozov (Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, morozov@nm1016.spb.edu)
P.E. Tovstik (Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, peter.tovstik@mail.ru)
T.P. Tovstik (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, tovstik_t@mail.ru)
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.
Keywords rod, longitudinal impact, lateral bending, parametric resonance
References
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Received 11 October 2015
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