Multi-objective optimization design of a grounded stiffness time delay feedback dynamic vibration absorber with inerter

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (23) : 133-143.

YANG Liuqing,ZHAO Yanying

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Abstract

The vibration of the vibrating system can be suppressed partly by using inerter and grounded stiffness components. The natural frequency of the vibrating system could be changed by inerter and grounded stiffness. Delayed feedback control technology is a simple and effective active vibration control technology. Delayed feedback control is commonly coupled to passive control systems to suppress vibration. In this paper, the multi-objective optimization design of the grounded stiffness coupled delayed feedback dynamic vibration absorber system with inerter is studied. The amplitude of the resonance peaks and anti-resonance peak, anti-resonance frequency band can be effectively controlled by optimizing the system structure parameters and control parameters. Firstly, the optimal structural parameters of the inerter and grounded stiffness system are obtained by the fixed-point theory. Secondly, the stability analysis of the control system is analyzed by the Cluster Treatment of Characteristic Roots (CTCR) method. The stable region of the feedback gain and delayed coefficient are obtained. Thirdly, the optimal inerter coefficient is obtained according to the symmetry of the anti-resonance frequency band in the perspective of satisfying the optimization criteria. Finally, the region of control parameters satisfying optimization goal is obtained considering optimal structural parameters and criteria. The research shows that for a certain external excitation frequency, there is a pair of optimal parameters of feedback gain coefficient and time-delay in control parameter region. The amplitude of the primary system can be suppressed to the minimum by selecting this pair of optimal parameters of feedback gain coefficient and time-delay. The numerical simulation results of amplitude frequency response curve and time history response curve are agree with the analytical results well. The reliability of the results in this paper is approved from the above results. The theory foundation of optimization and design is provided for active delayed feedback control system.

Key words

dynamic vibration absorber / inerter / grounded stiffness / delayed feedback control / multi-objective optimization

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YANG Liuqing,ZHAO Yanying. Multi-objective optimization design of a grounded stiffness time delay feedback dynamic vibration absorber with inerter[J]. Journal of Vibration and Shock, 2023, 42(23): 133-143

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