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Modal interactions between a linear oscillator and a nonlinear vibration absorber: fast-slow dynamics

Lan HuangXiaodong Yang
Jan 2024
Considerable attention has been given to the use of a nonlinear energy sink (NES) as a nonlinear vibration absorber. The NES is an efficient passive control device, that has been the focus of extensive research. In this paper, the modal interactions between a linear oscillator subjected to a harmonically external excitation and a grounded NES are studied. By applying the complexification-averaging method, the system is reduced from the four-dimensional (4D) real vector fields to the two-dimensional (2D) complex vector fields, namely the fast-slow system. Based on the fast-slow analysis, the fast subsystem, a one-dimensional (1D) complex vector field, is obtained from the fast-slow system, in which the linear oscillator's complex amplitude can be considered a bifurcation parameter. With the change of the bifurcation parameter, the critical manifold, obtained from the fast subsystem, presents distinct structures, that capture diverse types of modal interactions between the linear oscillator and the NES, verified by the numerical simulation results. The results indicate that the critical manifold can well predict the modal interactions on multiple time scales. The Hilbert spectrums verify that there is energy transfer at different time scales in the system. Additionally, the two special types of oscillations, namely the point-type oscillations and the ring-type oscillations, cannot be captured by the critical manifold.
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