Abstract
The dynamics of a system consisting of a nonlinear primary oscillator, subjected to a harmonic external force, and a nonlinear energy sink (NES) are investigated. The analytical solutions for the steady-state responses are obtained by the complexification-averaging method and the analytical model is confirmed by numerical simulations. The results indicate that the introduction of the NES can effectively suppress the vibrations of the primary oscillator. However, as the excitation amplitude increased, the NES may lose its efficiency within certain frequency range due to the appearance of the high response branches. Following the results analysis, it is concluded that this failure can be eliminated by reducing the nonlinear stiffness of the NES properly. The effects of nonlinear stiffness of the primary oscillator on the corresponding responses are also studied. The increase in this nonlinear stiffness can reduce the response amplitude and alter the frequency band where the high branches exist.
Highlights
The nonlinear energy sink, consisting of a small mass and a pure nonlinear spring, constitutes an effective solution for vibration suppression over a broad frequency range [1,2,3]
The results indicate that the introduction of the nonlinear energy sink (NES) can effectively suppress the vibrations of the primary oscillator
Comparing the responses of the primary oscillator without the NES, which are demonstrated in Figures 4(a), 8(a), 9(a), and 10(a), it is indicated that the value of the resonance peak decreases and the frequency which corresponds to the resonance peak increases with the raise of the nonlinear stiffness k1
Summary
The nonlinear energy sink, consisting of a small mass and a pure nonlinear spring, constitutes an effective solution for vibration suppression over a broad frequency range [1,2,3]. It can result in a one-way irreversible energy transfer from the primary system to the NES. Compared to traditional linear and weakly nonlinear absorbers, the NES has the higher suppression efficiency under many conditions [4, 5]. Majority of cases, the controlled primary systems were linear models These researches contributed significantly to the characteristics of the nonlinear TET. The effects of the nonlinear stiffness of both the NES and primary oscillator on the vibration suppression are analyzed and compared
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