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Again on the Ishlinskii-Lavrentyev problem

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Abstract

The problem of deformation and transverse vibrations of a thin rectilinear rod under a longitudinal force is considered. It is established in the classic Ishlinskii and Lavrentyev paper in the linear statement that with the longitudinal force essentially exceeding the Euler critical force, the stability loss generates one of the upper buckling modes. Below, the evolution of post-critical rod deformations is considered for long-term force excitation in the nonlinear statement and the relation of the deformation pattern is noted both with the Ishlinskii-Lavrentyev effect and with the Euler elasticas.

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199804, Russia

    N. F. Morozov

  2. Institute of Problems in Machine Science, Russian Academy of Sciences, Bol’shoi pr. 61, Vasil’evskii Ostrov, St. Petersburg, 199178, Russia

    P. E. Tovstik & T. P. Tovstik

Authors
  1. N. F. Morozov
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  2. P. E. Tovstik
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  3. T. P. Tovstik
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Corresponding author

Correspondence to P. E. Tovstik.

Additional information

Original Russian Text © N.F. Morozov, P.E. Tovstik, T.P. Tovstik, 2014, published in Doklady Akademii Nauk, 2014, Vol. 455, No. 4, pp. 412–415.

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Morozov, N.F., Tovstik, P.E. & Tovstik, T.P. Again on the Ishlinskii-Lavrentyev problem. Dokl. Phys. 59, 189–192 (2014). https://doi.org/10.1134/S102833581404003X

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  • DOI: https://doi.org/10.1134/S102833581404003X

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