Energy Partition Oscillator and Necessary and Sufficient Conditions of Energy Localization
Wayne State University, Detroit, Michigan, U.S.A
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A strongly nonlinear conservative oscillator describing the dynamics of energy partition between two identical linearly coupled Duffing oscillators is introduced and analyzed. Temporal shapes of such oscillator are close to harmonic when the initial energy disbalance between the interacting Duffing oscillators is relatively small. However the oscillator becomes strongly nonlinear as the amplitude of energy exchange increases. It is shown nevertheless that the oscillator is exactly solvable and, as a result, the entire first order averaging system, describing the dynamics of coupled Duffing oscillators, admits exact analytical solution. Based on the first integral of the energy partition oscillator, necessary and sufficient conditions of energy localization are obtained in terms of the initial states of original system.
© Owned by the authors, published by EDP Sciences, 2012