Periodic, almost periodic and chaotic forced oscillations of the sloping cantilever shell under geometrically nonlinear deformation

Authors

  • С. Е. Малышев National Technical University 'Kharkiv Polytechnic Institute', Kharkiv, Ukraine
  • К. В. Аврамов Institute of Mechanical Engineering Problems. AN Podgorny National Academy of Sciences of Ukraine, Kharkiv, Ukraine
  • В. Н. Конкин National Technical University 'Kharkiv Polytechnic Institute', Kharkiv, Ukraine

Keywords:

nonlinear periodic oscillations of a shallow shell, stability of oscillations, almost periodic oscillations, chaotic oscillations

Abstract

A nonlinear dynamical system with a finite number of degrees of freedom is obtained, which describes the forced oscillations of the shallow shell for its geometrically nonlinear deformation. To derive this dynamic system, the method of given forms. In the region of the first fundamental resonance, the Neumark-Sacker bifurcations are investigated. As a result of these bifurcations, almost periodic oscillations arise, which are transformed into chaotic oscillations. The properties of these oscillations are explored.

Author Biographies

К. В. Аврамов, Institute of Mechanical Engineering Problems. AN Podgorny National Academy of Sciences of Ukraine, Kharkiv

Doctor of Technical Sciences, Professor

В. Н. Конкин, National Technical University 'Kharkiv Polytechnic Institute', Kharkiv

PhD

References

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Avramov, K. V., 2013, Vibrations of shallow shells rectangular in the horizontal projection with two freely supported opposite edges Mechanics of Solids, 48, (№ 2), 186–193.

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Published

2017-10-05

Issue

Vol. 20 No. 3 (2017)

Section

Dynamics and Strength of Machines

License

Copyright (c) 2017 С. Е. Малышев, К. В. Аврамов, В. Н. Конкин

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