Doklady Physics

, Volume 59, Issue 4, pp 189–192 | Cite as

Again on the Ishlinskii-Lavrentyev problem

  • N. F. Morozov
  • P. E. Tovstik
  • T. P. Tovstik


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.


DOKLADY Physic Parametric Resonance Transverse Vibration Deformation Pattern Longitudinal Force 
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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • N. F. Morozov
    • 1
  • P. E. Tovstik
    • 2
  • T. P. Tovstik
    • 2
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute of Problems in Machine ScienceRussian Academy of SciencesSt. PetersburgRussia

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