Competitive energy transfer between a two degree-of-freedom dynamic system and an absorber with essential nonlinearity

The background of this work is related to passive vibration control of a two degree-of-freedom master system attached to an essentially nonlinear slave absorber aimed to attenuate vibrations by irreversibly transferring energy to a localized nonlinear normal mode (nonlinear normal modes should be considered here according to the definition from Rosenberg in J. Appl. Mech., 28:275–283, 1961). Such a nonlinear absorber which has no preferential frequency is theoretically able to capture several nonlinear resonances. The main purpose is here to bring insight in what is actually going on when two linear modes are in competition for energy transfer. An original asymptotic analysis using two small parameters enables one to build a scenario that improves the understanding of resonance mechanisms and to forecast which mode will be first attenuated by means of energy transfer. Numerical benchmark simulations corroborate the reliability of obtained scenario.

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