Analysis Of Dynamical Behaviors In A Vibro-impact System Under Periodic Excitations

Discontinuous dynamical systems widely exist in the field of mechanical engi-neering.Due to the possible gaps between two or more interconnected components,friction and impact phenomena occur in mechanical systems,which results in com-plex discontinuous dynamic behaviors in mechanical systems.Impact systems as one kind of discontinuous dynamic systems,scholars at home and abroad have done a lot of researches on dynamical behaviors of vibro-impact systems,and the study on the impact system has important theoretical and practical value.In recent years,the research on discontinuous dynamic systems has made great progress;especially using the flow switchability theory of discontinuous dynamical systems,a lot of dis-continuous dynamical models have been studied by regarding impact phenomena as the discontinuous dynamic behavior occurring in time-varying dynamic domains and time-varying dynamic boundaries.The G function is used as a research tool to study complex motion switchability in the mechanical system,which help us better explain the discontinuous dynamic behaviors in mechanical systems.Based on this theory,this paper studies the discontinuous dynamical behaviors of a class of impact systems in periodic excitations.The main contents of this paper are as follows:The first chapter introduces the research background of discontinuous dynamic systems,and gives the corresponding concepts of flow switchability theory and the related lemmas used in this paper.In the second chapter,the physical model studied in this paper is firstly in-troduced,which is a kind of impact system under periodic excitations.Since two masses touch and interact,all possible motions for the two masses m1 and m2 in the impact system are eonsidered:free-fly motion;sliding-stick motion;impaet motion;side-stick motion.In addition,according to the discontinuity caused by friction and impact,different motion domains and discontinuous boundaries are defined in absolute coordinates and relative coordinates,respectively.Secondly,based on the flow switchability theory for discontinuous dynamical systems,the G-functions are defined on the discontinuous boindaries,and further the analytical conditions of the passable motion and sliding-stick motion a.ppearance and disappearance are obtained by such G-functions.The necessary and sufficient conditions of side-stick motion and the analytical conditions of grazing motion are also given,and the corresponding physical explanat.ions are given.After that,the switeching sets and mapping structures of the impact system are definedjand then the general struc-tures and governing equations of predicting simple periodic motions are analyzed.Finally,the numerical simulations of the displacement-time history,velocity-time history,phase trajectory and G-function-time history in the impact system are car-ried out by using MATLAB software,which better explains the complex motions in the impact system under periodic excitationsThe third chapter summarizes the research content in this paper,and the future research topics.