THEORY AND EXPERIMENT OF EQUAL-PEAK OPTIMIZATION OF TIME DELAY COUPLED PENDULUM TUNED MASS DAMPER VIBRATING SYSTEM

Pendulum tuned mass damper is widely used in structural vibration suppression because it is easy to install, maintain, replace economically and practically. The vibration of the primary system could be suppressed by tuning the natural frequency of the pendulum. The vibration of the pendulum is opposite to primary system by tuning the natural frequency of the pendulum to or close to the control frequency of the primary system. The multi-objective optimization designs are analyzed for both passive system when primary system without damping and time delay feedback active system when primary system with damping. It is realized equal-peak control of the amplitude-frequency response curve of the primary system and difference control between the resonance peak and the anti-resonance point. First, the mechanical model and vibration differential equation of the time-delay coupled pendulum tuned mass damper are established. The optimal frequency ratio of system and the optimal damping ratio of the pendulum tuned mass damper are obtained by equal-peak optimization for the passive system when primary system without damping. For the passive system when primary system with damping, equal-peak phenomenon of the amplitude-frequency response curve for the primary system is destroyed under these optimization parameters. Secondly, for the time delay feedback active optimal control system when primary system with damping, the stability region of feedback gain coefficient and time delay are obtained by using the CTCR method. The equal-peak control of the amplitude frequency response curve for primary system could be realized by adjusting the two control parameters of the feedback gain coefficient and time delay under the conditions of system is stable. Thirdly, the time delay sensitivity and feedback gain sensitivity of the primary system amplitude amplification factor at the resonance point are analyzed. It is shown that the resonance point amplitude is more sensitive to the feedback gain coefficient than to the time delay. Finally, the theoretical results are verified by experiments in frequency domain and time domain. The research shows that the amplitude of the primary system is suppressed in a wide frequency range by using the time delay feedback equal-peak optimization. The flatness of the amplitude-frequency response curve is ensured by controlling the difference between the resonance peak and the anti-resonance point. © 2023 Chinese Journal of Theoretical and Applied Mechanics Press. All rights reserved.