VIBRATION REDUCTION MECHANISM OF NONLINEAR ZENER SYSTEM UNDER COMBINED PARAMETRIC AND EXTERNAL EXCITATIONS

The aim is to reveal the vibration reduction mechanism of nonlinear Zener systems with different scales under the combined parametric and external excitation. With the Duffing system as the main system, low-frequency parametric excitation and external excitation are introduced, and the system is changed into a 1.5-degree-of-freedom nonlinear Zener system by coupling the viscoelastic element. After comparing the time history diagram and phase diagram before and after the change of the system, it is found that the system changes from a single large-amplitude vibration of the excited state to the bursting vibration of the excited state and the silent state, the vibration amplitude is greatly reduced, and the vibration reduction effect is obvious. Then analyze the stability and bifurcation of autonomous systems. The stability of the generalized autonomous system, the close relationship between the imperfect bifurcation and the vibration behavior of the non-autonomous system are analyzed based on the idea that there is a maximum value of the external excitation in the range of the excitation amplitude change by using the method of envelope fast and slow analysis, which defines the parameter excitation term as a slow-varying parameter. It is found that the autonomous system has an obvious regulating effect on the non-autonomous system, which is manifested in the enhanced stability of the equilibrium point of the autonomous system after coupling viscoelastic elements, the type of equilibrium point changes from center to stable focus, the enhanced attraction of the equilibrium line to the system track line, and at the same time, multiple stabilized equilibrium lines limit the vibration region of the non-autonomous system, which are the fundamental reasons for vibration reduction. In addition, based on the analysis of dual parameter bifurcation, it was found that adjusting parameters can control the occurrence of the system imperfect bifurcation, thereby improving the system's vibration reduction performance.