Analysis Of Dynamic Behavior Of A Type Of Fricional Vibrator

In the study of frictional vibration,the conveyor belt model has been extensively investigated.Although there are many researches on stick slip vibration,it is rare to get the analytical expression of the system in steady state.If a particular approximate solution can be given,it is of great value for analyzing viscous sliding motion,which helps to observe the effect of parameters on vibration effectively.Because of the three motion states of pure sliding,viscous and viscous sliding,the piecewise nonsmooth friction increases the difficulty of studying the dynamic behavior of the mass conveyor belt.Therefore,the research of mass conveyor belt has become one of the hotspots of nonlinear dynamics.The main contents of the research on mass conveyor belt are as follows:1.Firstly,the periodic solution of the oscillator and the concrete expression is obtained by theoretical analysis in the stick-slip state of a class of systems with velocity dependent friction function.And the results are explained more intuitively by numerical simulation.Secondly,the control rate is designed,the stability analysis is carried out,and the stick and flutter motion is eliminated successfully.The system is stable in a single motion state with only pure sliding,and the feasibility of this method is verified by numerical simulation.2.Firstly,the conditions of switching-sliding bifurcation of the oscillator are discussed.Secondly,by constructing the zero time discontinuous mapping,the specific expression of the switching-sliding bifurcation point is obtained.Using local mapping PDM and ZDM to construct the Poincare global discontinuous mapping of the system.This lays the foundation for further analysis of the stability of the system.Then the specific value of the switching-sliding bifurcation point is given and verified by switching-sliding bifurcation condition.Finally,the phase diagram of the periodic motion and local motion of the oscillator is given.