Analysis Of Dynamical Behaviors Of An Oscillator With One-sided Impact On A Conveyor Belt

In mechanical engineering,discontinuous dynamical systems exist extensively.The reasons causing the discontinuousness are various,impact and friction as the most common influencing factors,have aroused many scholars' interest in research.The establishment of related mechanical models and the study of their dynamic behaviors have always been the focus of the researchers,which is of theoretical significance and practical value for the practical applications of the discontinuous dynamic systems with impact and friction in engineering.In recent years,new progress has been made in the study of discontinuous dynamical systems.The the-ory of flow switchability in discontinuous dynamical systems is gradually extended and applied,in which G-function is introduced as a new research tool to explain the transformation mechanism of motion in mechanical systems from a new per-spective.The discontinuous dynamic behavior in the system and the transition motion on the discontinuous boundary can be described more intuitively by using this theory.In this paper,the dynamical behaviors of the two-degree-of-freedom friction-induced oscillator with one-sided impact on a conveyor belt are investigated by using the theory of flow switchability in discontinuous dynamical systems.Based on the discontinuity of the system caused by impact and friction,the phase space of the system is divided into different domains and boundaries,and the possible mo-tions in the system are further discussed.And the analytical conditions of motion switching as well as the related research results of impact motion,stick motion and periodic motion are given.The main contents of this paper are as follows:In Chapter 1,the background and present situation of research on the friction-induced system with impact are introduced.The basic concept of G-function in the flow transition theory of discontinuous dynamical system and the decision the-orem of now transformation at discontinuous boundary are introduced.The basic concept of G-functions in the theory of flow switchability of discontinuous dynam-ical systems and the decision theorem of the transition of now on discontinuous boundary are given.In Chapter 2,the physical model of the two-degree-of-freedom friction-induced oscilla.tor with one-sided impact on a conveyor belt is introduced at first.Because the system is influenced by both friction and impact,all possible motions of the sys-tem are considered.When the mass m2 doesn't touch with the right-hand obstacle,the two masses m1 and m2 have the non-stick motions,one of the two masses has stick motion,and both two masses have stick motions;when the mass m2 touches with the right-hand obstacle,the mass m1 has stick or non-stick motion,and the mass m2 has impact motion or stuck motion.According to the discontinuity caused by friction and impact in the system,different domains and boundaries in the system can be divided in phase space.Because the kinetic and the static friction coeffi-cients are not equal,the vector field with flow barrier is introduced on the velocity boundary.Secondly,based on the theory of flow switchability on discontinuous dy-namical systems,the G-function is defined on the discontinuous boundaries,which is used to explain the transformation mechanism on different separation boundaries and to give the analytical conditions of the transformation of different motions in the form of theorems.In addition,based on the theory of mapping dynamics,the switching sets and four-dimensional mappings in the two-degree-of-freedom friction impact oscillator are defined,and the general structures of periodic motions and their governing equations are predicted analytically.Finally,the numerical simula-tions of passable motion,stick motion,impact motion,grazing motion and several periodic motions are carried out through MATLAB software to better explain the complex dynamical behaviors and periodic motions in the two-degree-of-freedom friction-induced oscillator with one-sided impact on a conveyor belt.In Chapter 3,the research contents of this paper are summarized,the problems further investigated and the basic theory studied in the future are put forward.