Analysis Of Discontinuous Dynamics Behaviors Of Several Oscillators On Conveyor Belts

Discontinuous dynamical systems exist extensively in the field of mechanical engineering and daily life.In general,people are accustomed to using continuous models to analyze motions in discontinuous dynamical systems.However,continu-ous models do not describe discontinuous dynamical systems very well.The friction between the contact surfaces of the two masses and the switching control law in system will cause discontinuity and make the research more complicated.In order to provide better analysis prediction and optimal design of the mechanical engineer-ing system,in this paper,the two physical models in mechanical engineering and the complex dynamic behaviors of oscillators are analyzed by using the theories of discontinuous dynamical systems,which provides a theoretical basis for the design of the corresponding mechanical system and reference for the selection of system design parameters.This paper is divided into three chapters.In chapter 1,we present the research background and significance of the dis-continuous dynamical systems,and give the relevant concepts,several lemmas of the corresponding flow switchability theories.In chapter 2,we introduce the model of the friction-induced oscillator with elliptic control law on the conveyor belt.The discontinuity of the system is mainly caused by the friction between the oscillator and the conveyor belt and the elliptic control law.And the different domains and boundaries of this system are defined by the discontinuity of friction and elliptic control law.Based on the division of domains and boundaries,the analytical conditions for the appearance or disappear-ance of stick or sliding motions,grazing motions,and stick or sliding motions are predicted analytically.Moreover,by constructing the basic mapping structures,periodic motions in such a discontinuous system are predicted analytically.Finally,the motions of the oscillator at different boundaries are illustrated by numerical simulations.In chapter 3,we investigate the model of the linear impact oscillator on the conveyor belt.The dynamical behaviors of this system are analyzed by the flow switchablility theories in discontinuous dynamical systems,which is mainly caused by the friction between the mass and the conveyor belt and collision between the masses.The domains and the boundaries of this system are defined according to the displacement of the mass and the speed of the conveyor belt,and the analytical conditions of the passable,sliding and grazing motions are obtained based on the division of the domains and the boundaries.The basic mappings and switching sets are defined to describe the motions of the oscillator.And then the analytical prediction of periodic motion is given by the mapping structures.Finally,the appropriate parameters axe selected to illustrate the passable and grazing motions.