Energies of the dynamics in a double circular plate nonlinear system

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.