PERIODIC, ALMOST PERIODIC AND CHAOTIC FORCED OSCILLATIONS OF A SHALLOW CANTILEVER SHELL WITH GEOMETRICALLY NON-LINEAR DEFORMATION

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J. of Mech. Eng., 2017, vol. 20, no. 3, pp. 25-31

DOI:   https://doi.org/10.15407/pmach2017.03.025

Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 20, no. 3, 2017 (September)
Pages 25–31

 

Authors

S. Ye. Malyshev, National Technical University “Kharkiv Polytechnic Institute” (2, Kyrpychova St., Kharkiv, 61002, Ukraine), e-mail: malsea@ukr.net

K. V. Avramov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: kvavramov@gmail.com, ORCID: 0000-0002-8740-693X

V. N. Konkin, National Technical University “Kharkiv Polytechnic Institute” (2, Kyrpychova St., Kharkiv, 61002, Ukraine)

 

Abstract

A nonlinear dynamical system with a finite number of degrees of freedom is obtained. It describes the forced oscillations of a shallow shell during its geometrically nonlinear deformation. In order to derive this dynamic system, a method of specified forms is used. In the region of the first main resonance, the Neimark-Sacker bifurcations are investigated. As a result of these bifurcations, almost periodic oscillations arise, which are then transformed into chaotic ones. The properties of these oscillations are investigated.

 

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

 

References

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Received 19 July 2017