Some features of nonlinear interaction of vibration modes of thin circular cylindrical shells

Abstract

The paper deals with the problem on forced flexural vibrations of a thin infinitely long circular cylindrical shell (thin circular ring under plane deformation) with large amplitudes. The equations of ring motion are obtained from equations of the nonlinear theory of flexible shallow shells. A new approach to the construction of a nonlinear finite-dimensional model of a ring is proposed.

Three statements that make it possible to specify a series of fundamental notions of nonlinear flexural vibrations of circular cylindrical shells of finite length are formulated and proved.

About the authors

N. A. Taranukha

Komsomolsk-na-Amure State Technical University

Author for correspondence.
Email: taranukha@knastu.ru

Doctor of Technical Sciences, Professor

Head of the Department of Shipbuilding

Russian Federation

G. S. Leyzerovich

Komsomolsk-na-Amure State Technical University

Email: yahad@kmscom.ru

Candidate of Technical Sciences, Assistant Professor

Professor of the Department of Mechanics and Analyses of Processes and Structures

Russian Federation

References

  1. Volmir, A. S. Nonlinear dynamics of plates and shells / A. S. Volmir. – M.: Nauka, 1972. – 432 p.
  2. Kubenko, V. D. Nonlinear problems of oscillations of thin shells (Survey) / V. D. Kubenko, P. S. Kovalchuk // Appl. Mech. – 1998. – 34. – No. 8. – PP. 3-31.
  3. Kubenko, V. D. Nonlinear interaction of modes of flexural vibrations of cylindrical shells / V. D. Kubenko, P. S. Kovalchuk, T.
  4. S. Krasnopolskaya. – Kiev: Naukova. dumka, 1984. – 220 p.
  5. Varadan, T. K. Nonlinear free flexural vibrations of thin-walled circular cylindrical shells / T. K. Varadan, G. Prathap, H. V. Ramani // AIAA J. – 1990. – No. 5. – PP. 21–24.
  6. Leyzerovich, G. S. Nonlinear modes of motion of thin circular cylindrical shells // J. of Appl. Mech. and Techn. Physics. – 2001. – Vol. 42. – No. 4. – PP. 161-164.
  7. Taranukha, N. A. Dynamics of "irregular" shells / N. A. Taranukha, G. S. Leyzerovich. – Vladivostok: Dalnauka, 2005. – 423 p.
  8. Taranukha, N. A. New solutions in the dynamics of "irregular" shells / N. A. Taranukha, G. S. Leyzerovitch. – Vladivostok: Dalnauka, 2007. – 203 p.
  9. Leyzerovich, G. S. Non-obvious features of the dynamics of circular cylindrical shells / G. S. Leyzerovich, N. A. Taranukha // Bulletion of the Russian Academy of Sciences. Mechanics of rigid bodies. – 2008. – No. 2. – PP. 96-105.
  10. Evensen, D. A. Nonlinear flexural vibrations of thin circular rings / D. A. Evensen // Trans ASME. J. Appl. Mech. E. – 1965. – Vol. 33. – No 3. – PP. 553-560.

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