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 Regul. Chaotic Dyn.: Year: Volume: Issue: Page: Find

 Regul. Chaotic Dyn., 2016, Volume 21, Issue 4, Pages 437–454 (Mi rcd87)

Chaos Control for the Plates Subjected to Subsonic Flow

Hamed Norouzia, Davood Younesianab

a School of Railway Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
b Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720, USA

Abstract: The suppression of chaotic motion in viscoelastic plates driven by external subsonic air flow is studied. Nonlinear oscillation of the plate is modeled by the von-Kármán plate theory. The fluid-solid interaction is taken into account. Galerkin’s approach is employed to transform the partial differential equations of the system into the time domain. The corresponding homoclinic orbits of the unperturbed Hamiltonian system are obtained. In order to study the chaotic behavior of the plate, Melnikov’s integral is analytically applied and the threshold of the excitation amplitude and frequency for the occurrence of chaos is presented. It is found that adding a parametric perturbation to the system in terms of an excitation with the same frequency of the external force can lead to eliminate chaos. Variations of the Lyapunov exponent and bifurcation diagrams are provided to analyze the chaotic and periodic responses. Two perturbation-based control strategies are proposed. In the first scenario, the amplitude of control forces reads a constant value that should be precisely determined. In the second strategy, this amplitude can be proportional to the deflection of the plate. The performance of each controller is investigated and it is found that the second scenario would be more efficient.

Keywords: chaos control, von-Kármán plate theory, Melnikov’s method, Lyapunov exponent, bifurcation

DOI: https://doi.org/10.1134/S1560354716040043

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Bibliographic databases:

MSC: 35L75, 37D45, 74H65
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Citation: Hamed Norouzi, Davood Younesian, “Chaos Control for the Plates Subjected to Subsonic Flow”, Regul. Chaotic Dyn., 21:4 (2016), 437–454

Citation in format AMSBIB
\Bibitem{NorYou16} \by Hamed~Norouzi, Davood~Younesian \paper Chaos Control for the Plates Subjected to Subsonic Flow \jour Regul. Chaotic Dyn. \yr 2016 \vol 21 \issue 4 \pages 437--454 \mathnet{http://mi.mathnet.ru/rcd87} \crossref{https://doi.org/10.1134/S1560354716040043} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380679700004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84980348220} 

• http://mi.mathnet.ru/eng/rcd87
• http://mi.mathnet.ru/eng/rcd/v21/i4/p437

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Norouzi H., Younesian D., “Nonlinear Vibration of Laminated Composite Plates Subjected to Subsonic Flow and External Loads”, Steel Compos. Struct., 22:6 (2016), 1261–1280