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The Ishlinskii—Lavrent’ev problem at the initial stage of motion

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Abstract

The dynamic loss of stability of a thin rod with hinge-supported edges under the action of an impact constant longitudinal load at the initial stage of motion, which is restricted to the time of longitudinalwave run along the rod length, is investigated. The transverse deflection is expanded in the Fourier series. The problem is solved in the linear approximation. The additional deflection is compared with the value of the initial disturbances.

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References

  1. L. Euler, Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti, Springer, 1952.

    Google Scholar 

  2. M. A. Lavrent’ev and A. Yu. Ishlinskii, Dokl. Akad. Nauk 64 (6), 779 (1949).

    MATH  Google Scholar 

  3. V. V. Bolotin, Transverse Vibrations and Critical Velocities (Izd-vo AN SSSR, Moscow, 1953), Vol. 2 [in Russian].

    Google Scholar 

  4. H. E. Lindberg, J. Appl. Mech. 32 (2) (1965).

    Google Scholar 

  5. W. J. Hutchinson and B. Budiansky, AIAA J. 4 (3) (1966).

    Google Scholar 

  6. N. F. Morozov and P. E. Tovstik, Vestn. SPbGU, No. 2, 105 (2009).

    Google Scholar 

  7. A. K. Belyaev, D. N. Il’in, and N. F. Morozov, Mech. Solids, No. 5, 504 (2013).

    Article  Google Scholar 

  8. N. F. Morozov and P. E. Tovstik, Dokl. Phys. 58 (9), 387 (2013).

    Article  ADS  Google Scholar 

  9. N. F. Morozov, P. E. Tovstik, and T. P. Tovstik, Vestn. Yuzhno-Ural. Un-ta, Ser. Mat. Model. Progr. 7 (1), 76 (2014).

    MathSciNet  MATH  Google Scholar 

  10. N. F. Morozov and P. E. Tovstik, Dokl. Phys. 58 (11), 510 (2013).

    Article  ADS  Google Scholar 

  11. N. F. Morozov, P. E. Tovstik, and T. P. Tostik, Dokl. Phys. 59 (4), 189 (2014).

    Article  ADS  Google Scholar 

  12. B. A. Gordienko, Izv. Akad. Nauk,Mekh. Tverd. Tela, No. 1 (1969).

    Google Scholar 

  13. A. S. Vol’mir, Nonlinear Dynamics of Plates and Shells (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

  14. M. A. Il’gamov, Dokl. Phys. 59 (8), 385 (2014).

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, 199034, Russia

    N. F. Morozov & P. E. Tovstik

  2. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russia

    A. K. Belyaev & T. P. Tovstik

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

Correspondence to P. E. Tovstik.

Additional information

Original Russian Text © N.F. Morozov, A.K. Belyaev, P.E. Tovstik, T.P. Tovstik, 2015, published in Doklady Akademii Nauk, 2015, Vol. 463, No. 5, pp. 543–546.

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Morozov, N.F., Belyaev, A.K., Tovstik, P.E. et al. The Ishlinskii—Lavrent’ev problem at the initial stage of motion. Dokl. Phys. 60, 368–371 (2015). https://doi.org/10.1134/S1028335815080066

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  • DOI: https://doi.org/10.1134/S1028335815080066

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