Bifurcation Characteristics Of Periodic Motions Of Impact Systems With Clearance

The research on the mechanism of vibro-impact is of great practical significance to the design of non-smooth mechanical vibration systems with clearance,the optimization of dynamic parameters,reliability and operational safety,reduction of noise and prolongation of service life.Non-smooth systems are generally multi-parameter high-dimensional systems,and the change of parameters will cause qualitative changes in the dynamic characteristics of the system,which directly affects the overall function and performance indicators of the system,and is the key factor to determine whether the system can operate safely and efficiently.In this paper,several Impact vibration systems with clearance are considered by multi-parameter and co-simulation analysis.Dynamic characteristics of impact vibration systems with clearance are studied from the system level through two-dimensional parameter bifurcation diagram,single parameter bifurcation diagram,phase diagram and Poincaré map,so as to provide theoretical reference for parameter optimization design.The main research contents are as follows:The dynamic model of a single-degree-of-freedom vibro-impact system with a symmetric gap is firstly considered,and analyzes the relationship between the system's dynamic characteristics and various parameters in detail.As the two important parameters of the system,the gap ? and the frequency ? of the excitation force,the influence of the change of they on the system dynamics are studied preferentially.In the two-parameter plane,adjacent basic movements pass through two special areas when transferring between each other: hysteresis domain or tongue-shaped domain.The distribution of various types of periodic motion and the transition process of adjacent periodic motion through the hysteresis and tongue-shaped domains are analyzed in detail.The difference in the direction of increase and decrease of the bifurcation parameters may lead to different types of boundary lines in the adjacent motion occurrence areas and produce hysteresis domains.In the hysteresis domain,two adjacent movements are stable and coexist.In the low-frequency and small-gap area,when the bifurcation parameter ? or ? is continuously reduced,the grazing bifurcation will continue to occur,and the number of times the mass block impacts the elastic constraints on both sides will continue to increase.Based on the value range of each dimensionless parameter,the influence of each parameter on the type of periodic motion,emergence law and impact velocity is analyzed.Next,the dynamic model of vibro-impact system under asymmetric excitation is considered.Obtaining the types and occurrence regions of periodic motion by numerical methods in a double-parameter plane.The types of basic motions and subharmonic motions in the low frequency regions and the distribution regularity in the double-parameter plane are revealed.The bifurcation characteristics between non-impact motions and basic motions are studied.The regularity and bifurcation characteristics of the subharmonic motions in tongue-shaped regions and hysteresis caused by the irreversibility of grazing bifurcation are studied.The effects of system parameters on the types,occurrence regions and impact velocity of periodic motion are discussed.Finally,the dynamic model of the progressive vibro-impact system is considered.Based on two types of Poincaré projection,the Runge-Kutta method was used to numerically simulate the type,existence domain and distribution of the system's periodic motion in the two-dimensional parameter plane,and revealed the diversity of the system's periodic motion types.The influence of each parameter on the system dynamics is studied,and the parameter matching range that makes the system work in a stable single-cycle impact motion is determined.Through analysis,it can be seen that in the double-parameter plane of the frequency-static force,the maxiamum impct velocity and progressive amount occur in the area of the basic motion 1 / 1.In the frequency-amplitude double-parameter plane,the smaller ?,the larger the impact velocity and the progressive amount of the basic motion 1/1.