Study On Nonlinear Dynamics Of A Class Of Friction And Impact Systems With Rigid Constraints

In the field of mechanical engineering,discontinuous dynamical?systems are u-biquitous.Impact and friction are inevitable and can not be ignored in the process of mechanical structure design,which have great influence on the dynamic behavior of the system.Because of the gap and the rigid constraint,the vector field of the rigid impact vibration system with friction is discontinuous.In recent years,people have gradually realized that discontinuous models can provide better prediction for mechanical engineering systems.In addition,the theory of flow transformation and flow barrier of discontinuous dynamic system in dynamic domain has laid a founda-tion for the research of actual dynamic system,and the G-functions are introduced to analyze the singularity of discontinuous dynamical systems in such theory.In order to better study the dynamic mechanism of complex discontinuous dynam-ical systems,the analytical conditions of motion transformation at discontinuous boundary are given.Based on the dynamics theory,the 2-DOF(two-degree-of-freedom)bilateral rigid constraints impact system with nonlinear friction is studied in this paper,the transition conditions at the discontinuous boundary under dif-ferent motion states and the research results of periodic motions are given.The study of the impact vibration system with friction and constraint is of theoretical significance and practical value to understand its motion mechanism and analyze its global performance,service life and other factors.The main contents of this paper are as follows:In Chapter 1,the background and current status of research on the 2-DOF bilateral rigid constraints impact system with nonlinear friction are described.And the basic concept and correlation lemmas of flow transformation theory in discon-tinuous systems are briefly introduced.In Chapter 2,the physical model and friction model of the 2-DOF bilateral rigid constraints impact system with nonlinear friction are introduced.The external controlled force acting on the object in such system has a negative feedback in the form of a constant force,and in the case that the dynamic friction coefficient and the static friction coefficient are not equal,the nonlinear dynamic friction will be described by the piecewise linear dynamic friction.In addition,all motion states of the objects in the system are analyzed in Chapter 2.Since the friction forces exist in the two masses of the 2-DOF impact system with bilateral rigid constraints,the phase space of the system is divided into several different boundaries and domains,and the state vector and vector field of the system are introduced.Based on the theory of flow switchability in discontinuous dynamical systems and the difference of dynamic and static friction coefficients,the G-functions are defined on the corre-sponding velocity and displacement boundaries and in the vector field with a flow barrier,the appropriate methods and basic criteria for the research of the discon-tinuous dynamical systems with flow barriers are presented,and the conditions of the motion switching,especially the more important conditions for the appearance and disappearance of stick motion,are explained in physics and illustrated in detail.Due to the existence of stuck state,the onset and vanishing conditions for stuck motion are developed,from which it can be seen that such oscillator has more com-plicated and rich dynamical behaviors.The four-dimensional switching sets and the mapping structure of the system are defined on the basis of the theory of mapping dynamics,the governing equations of periodic motion and the local stability analy-sis are given in order to further analyze and predict the complex periodic motions.In the end,the passable motion,stick motion,grazing motion,impact motion and two periodic motions are numerically simulated by using MATLAB software,so as to explain the motion transformation mechanism of the system more intuitively.Chapter 3 summarizes this paper and looks forward to the future research problems and the basic theory of learning.