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Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification

Abstract : A system composed of two cubic nonlinear oscillators with close natural frequencies, and thus displaying a 1:1 internal resonance, is studied both theoretically and experimentally, with a special emphasis on the free oscillations and the backbone curves. The instability regions of uncoupled solutions are derived and the bifurcation scenario as a function of the parameters of the problem is established, showing in an exhaustive manner all possible solutions. The backbone curves are then experimentally measured on a circular plate, where the asymmetric modes are known to display companion configurations with close eigenfrequencies. A control system based on a Phase-Locked Loop (PLL) is used to measure the backbone curves and also the frequency response function in the forced and damped case, including unstable branches. The model is used for a complete identification of the unknown parameters and an excellent comparison is drawn out between theoretical prediction and measurements.
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Submitted on : Friday, May 15, 2020 - 12:39:25 PM
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Arthur Givois, Jin-Jack Tan, Cyril Touzé, Olivier Thomas. Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification. Meccanica, Springer Verlag, 2020, 55 (3), pp.481-503. ⟨10.1007/s11012-020-01132-2⟩. ⟨hal-02586115⟩

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