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- Title
H<sub>∞</sub> optimization of cubic stiffness nonlinear energy sink attached to a linear system.
- Authors
Zheng, Zhiwei; Huang, Xiuchang; Su, Zhiwei; Yang, Yong
- Abstract
Nonlinear energy sinks (NESs) have become a research hotspot due to their frequency robustness, but the optimization problem under harmonic excitation has not been adequately addressed. In this paper, the response of a single-degree-of-freedom system with a cubic stiffness NES attached under harmonic excitation is simplified to 1:1 internal resonance through the harmonic balance method, and H∞ optimization is carried out on this basis. By comparing the frequency response curves (FRCs) of the system and the response of the system under the chirp excitation, the reliability of this approximation method is verified. Through the analysis of the fold bifurcations, the variation trend of the FRCs changing with the external excitation and the conditions for detached resonance curves to appear are obtained. The performance in three special cases is analyzed analytically, while the optimal parameters in general cases are analyzed numerically and fitted to obtain empirical formulas. The results show that the NES will fail applied on the undamped system due to a fixed point tending to infinity. When the external excitation is too large, the NES will amplify vibration of the linear system, and the damping of the NES has a very important influence on the vibration control if the damping of the system is relatively high. Finally, the performance of the NES is compared with the traditional linear vibration absorber (LVA). Although the best performance of the NES is not as good as the LVA, it can achieve multi-mode control under certain conditions.
- Subjects
VIBRATION (Mechanics); SINGLE-degree-of-freedom systems; VIBRATION absorbers; RESONANCE; VIBRATION tests; LINEAR systems
- Publication
Nonlinear Dynamics, 2023, Vol 111, Issue 17, p15653
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-023-08690-6