Authors: Hedrih, Katica (Stevanović) 
Simonović, Julijana D.
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Energies of the dynamics in a double circular plate nonlinear system
Journal: International Journal of Bifurcation and Chaos
Volume: 21
Issue: 10
First page: 2993
Last page: 3011
Issue Date: 1-Jan-2011
Rank: M22
ISSN: 0218-1274
DOI: 10.1142/S0218127411030301
Abstract: 
This paper presents an analytical and numerical analysis of the transfer energy between plates for free and forced transversal vibrations of a visco-nonlinear elastically connected double circular plate. The analysis showed that the connection of VoigtKelvin type with the nonlinearity of third order between plates caused the appearance of two-frequency-like regime of time function, which corresponds to one eigen amplitude function of one nonlinear mode. Furthermore, the time functions of different vibration nonlinear modes are coupled, as well as energy transfer between plates in one eigen mode appear. More than two resonant jumps in the amplitude-frequency as in phase-frequency curves appear and cause more than two resonant jumps of the energy modes and the corresponding influence between nonlinear modes, as nonlinear interactions phenomena. Using the analytical results for the first asymptotic approximation of the amplitudes and phases of multifrequency particular solutions of such dynamics, it is possible to analyze the transfer energy between nonlinear modes in stationary and nonstationary regimes. A few numerical results from the analysis are presented in this paper together with the conclusions on the influence of nonlinearity in coupling layer on the dynamics and transfer of energy in such systems.
Keywords: amplitude-frequency and phase-frequency curves | Double circular plate system | energy transfer | interaction between nonlinear modes | nonlinear dynamics | resonant jumps
Publisher: World Scientific
Project: Theoretical and Applied Mechanics of the Rigid and Solid Bodies. Mechanics of Materials 

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