Doklady Physics

, Volume 58, Issue 9, pp 387–391 | Cite as

Transverse rod vibrations under a short-term longitudinal impact

Mechanics

Abstract

Transverse vibrations of a thin rod caused by a short-term longitudinal impact are considered. After the impact, a system of compression-tension waves, which causes transverse vibrations, appears in the rod. Parametric resonance, which leads to an unbounded rise in the amplitude of transverse vibrations, is investigated in the linear approximation. With a nonlinear approach, beats appear in the resonance vicinity, in which the mutual exchange of the energy of longitudinal and transverse vibrations occurs. The influence of viscoelastic resistance forces is investigated.

Keywords

Longitudinal Wave Parametric Resonance Transverse Vibration Instability Region Nonlinear Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. Euler, Method for Finding the Curves Possessing the Properties of the Maximum or the Minimum, or the Solution of the Isoperimetric Problem Taken in the Most Common Sense (Gostekhizdat, Moscow, 1934) [in Russian].Google Scholar
  2. 2.
    M. A. Lavrent’ev and A. Yu. Ishlinskii, Dokl. Akad. Nauk 64(6), 779 (1949).MATHGoogle Scholar
  3. 3.
    A. S. Vol’mir, Stroit. Mekh. Raschet Sooruzh., No. 1, 6 (1960).Google Scholar
  4. 4.
    V. V. Bolotin, Transverse Vibrations and Critical Velocities (AN SSSR, Moscow, 1953), Vol. 2 [in Russian].Google Scholar
  5. 5.
    N. F. Morozov and P. E. Tovstik, Vestn. SPbGU, No. 2, 105 (2009).Google Scholar
  6. 6.
    A. M. Lyapunov, General Problem on Motion Stability (Gostekhizdat, Moscow, 1950) [in Russian].Google Scholar
  7. 7.
    V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients and Their Applications (Nauka, Moscow, 1972) [in Russian].Google Scholar
  8. 8.
    V. A. Pal’mov, Vibrations of Elastoplastic Bodies (Nauka, Moscow, 1976) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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