The Application Of The Time-delay Damping Technology In The Nonlinear Vibration System

Delay vibration is a new kind of vibration suppression technology,it has the advantages of the real time control, wide vibration frequency band, good effect of vibration,simple structure of the vibration damper etc..Due to the delay dynamic system is quite complex, and its theory is not mature, and most of the research is on linear system,there is few research on delay vibration in nonlinear system.This paper mainly studies the application of the time-delay vibration technology in the nonlinear system, and analyses the effect of the delay and feedback gain factor on vibration of the system in emphasise.In this paper,it begins with a single degree of vibration system as the research object. By exerting harmonic external motivation on the vibration system, delay feedback control is used to study the influence on the system vibration. Perturbation analysis of the movement differential equation of the system is developed.We found the approximate analytic value of the nonlinear vibration system using multi-scale method, and analyzed the system stability using the Routh – Hurwit criterion. Then we analyzed the effect of the system of nonlinear stiffness coefficient and damping coefficient on the system main resonance amplitude frequency curve.At last,we analyzed the effect of the time delay and feedback gain factor on the main resonance amplitude frequency curve of the system under the state of time delay feedback control.On the basis of the above research, by coupling on a pendulum with parametric excitation namely from the parameters of vibration system to the system, the parameters of vibration system saturation phenomenon happens when the primary resonance and 1:1 internal resonance occur together, then the effect of the delay feedback control on the parameters of vibration system is studied.The influence of time delay and feedback gain coefficient in a certain range can reduce the vibration of the primary system, and on the basis of the feedback gain factor to delay adjustment, can reduce the vibration of the system to a great extent. We can reduce the vibration of the primary system to a great extent using time delay feedback control.Compared to the parameters of the vibration,it can be reduced the biggest dynamic vibration absorber which is used to around 20%,35%55%.At last, we also studied the first-order vibration mode of the beam controled by the nonlinear saturated controller in this paper, and analysed the effect of time-delay on the delayvibration frequency drift and the impact of bandwidth, thus solved the problem of vibration frequency drift of the delay control system.This paper mainly studies the application of the time-delay damping technology in the nonlinear vibration system, and the results show that there is obvious damping effect of the time-delay damping technology on nonlinear vibration system,and simple and convenient in control.