Authors: Hedrih, Katica (Stevanović) 
Simonović, Julijana D.
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Non-linear dynamics of the sandwich double circular plate system
Journal: International Journal of Non-Linear Mechanics
Volume: 45
Issue: 9
First page: 902
Last page: 918
Issue Date: 1-Nov-2010
Rank: M22
ISSN: 0020-7462
DOI: 10.1016/j.ijnonlinmec.2009.12.007
Abstract: 
Multi-frequency vibrations of a system of two isotropic circular plates interconnected by a visco-elastic layer that has non-linear characteristics are considered. The considered physical system should be of interest to many researches from mechanical and civil engineering. The first asymptotic approximation of the solutions describing stationary and no stationary behavior, in the regions around the two coupled resonances, is the principal result of the authors. A series of the amplitudefrequency and phasefrequency curves of the two frequency like vibration regimes are presented. That curves present the evolution of the first asymptotic approximation of solutions for different non-linear harmonics obtained by changing external excitation frequencies through discrete as well as continuous values. System of the partial differential equations of the transversal oscillations of the sandwich double circular plate system with visco-non-linear elastic layer, excited by external, distributed, along plate surfaces, excitation are derived and approximately solved for various initial conditions and external excitation properties. System of differential equations of the first order with respect to the amplitudes and the corresponding number of the phases in the first asymptotic averaged approximation are derived for different corresponding multi-frequency non-linear vibration regimes. These equations are analytically and numerically considered in the light of the stationary and no stationary resonant regimes, as well as the multi-non-linear free and forced mode mutual interactions, number of the resonant jumps.
Keywords: Circular plates | Hybrid sandwich non-linear system | Multi-frequency | Mutual interaction | Resonance | Resonant jumps | Stability | Trigger | Visco-non-linear elastic layer
Publisher: Elsevier
Project: Theoretical and Applied Mechanics of the Rigid and Solid Bodies. Mechanics of Materials 

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