STUDY ON VIBRATION REDUCTION OF DYNAMIC VIBRATION ABSORBER FOR TWO-SCALE DUFFING SYSTEM

Duffing system with two-scale coupling generally will behave in complex vibration, because of the characteristics of large amplitude and high frequency, then the harm from complex vibration cannot be ignored. The vibration control problem of linear vibration absorber for Duffing system with low frequency parameter excitation is studied. By comparing the time history diagram and phase diagram of the system before and after coupling the linear dynamic vibration absorber, the system with dynamic vibration absorber shows mixed vibration mode (bursting vibration), and the vibration amplitude is suppressed significantly, especially for the high frequency vibration part. Using the slow-fast analysis method, the corresponding autonomous system is obtained when the parameter excitation is a slowly varying process. It is found that the stability and bifurcation behavior of the autonomous system can obviously regulate the vibration response of the non-autonomous system. The results show that although fork bifurcation occurs in the autonomous system before and after the coupled dynamic vibration absorber, the stability of the autonomous system changes after the dynamic vibration absorber is added. Comparing to the stable center in the original system, the attractor of the autonomous system coupled linear dynamic vibration absorber changes to asymptotically stable focus. The attractive force of the stable equilibrium line of autonomous system to trajectory of non-autonomous system is enhanced, which reduces the vibration amplitude of the non-autonomous system. In addition, the reduction about hops times of trajectory between different attractors is another reason for the decrease of the vibration amplitude. Based on the analysis of vibration reduction effect with relevant parameters of parametric excitation, it is found that the dynamic vibration absorber can suppress the vibration of the system in a large vibration amplitude and frequency range. It provides a theoretical basis for the research on vibration reduction of two-scale system coupled linear dynamic vibration absorber.