Time delay vibration reduction control for suspension cable under multi-frequency excitation

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (17) : 182-187.

XIA Hui1, PENG Jian1,2, LI Luxin1, SUN Hongxin1,2, YU Jianda1,2, SHAO Hongli1

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Abstract

Suspension cable is a typical flexible structure. It has the characteristics of light weight, large flexibility and small damping. Under the action of multi-frequency excitation, it is easy to produce large vibration, which is easy to cause the fatigue failure of structure and the occurrence of engineering disaster. Therefore, the vibration control of suspension cable is an urgent problem to be solved in practical engineering applications. The time-delay velocity feedback control strategy is used to reduce the vibration of the suspension cable under multi-frequency excitation. Based on Hamilton variational principle, a nonlinear vibration control model of a controlled suspension cable under multi-frequency excitation is established. The delay differential equation is obtained by Galerkin method. The multiscale method is used to solve the amplitude-frequency response equations when the superharmonic and subharmonic resonance occurs in the controlled suspension structure, and the stability of the steady-state solution is determined. The nonlinear dynamic behavior of the controlled cable and the influence of the parameters of the control system on the resonance response are analyzed. The results show that the response of superharmonic resonance and subharmonic resonance occurs simultaneously in the multi-frequency excitation system. The distance between different branches decreases with the increase of time delay. As the control gain decreases, the phases of stable and unstable solutions of the branches tend to approach. By adjusting the control gain and time delay, the resonance range, response amplitude and phase can be changed, so as to achieve the optimal control effect.

Key words

delay feedback / the resonant response / suspension cable / multi-frequency excitation

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XIA Hui1, PENG Jian1,2, LI Luxin1, SUN Hongxin1,2, YU Jianda1,2, SHAO Hongli1. Time delay vibration reduction control for suspension cable under multi-frequency excitation[J]. Journal of Vibration and Shock, 2023, 42(17): 182-187

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