Analysis On Global Periodic Motions Of Piecewise Linear System

This thesis concentrates on the piecewise smooth dynamic system with gap based on the mapping method.The global dynamic motions of the system are discussed.The analytical solutions obtained from the Poincaré mapping method are compared with the numerical solutions,and the effects of the system parameters on the periodic motion of the piecewise smooth system are discussed.The thesis is mainly focused on the following issues:Firstly,based on the gear transmission system,the physical model and the mechanical model are obtained.Applying the Poincaré mapping method to the symmetric gear transmission system with elastic constraint and gap,the periodic solutions of the system and the influence of the parameters on the periodic solutions can be obtained from the mapping method.The analytical solution is compared with the results by Runge-Kutta numerical method,and the switching velocity and time can be obtained based on different Poincaré sectionsSecondly,based on the study on the symmetric piecewise smooth system with elastic constraint and gap,the asymmetric smooth system is studied.The same Poincaré mapping method is used to discuss the periodic solutions of the asymmetric system.The periodic motions under different damping values are also discussed.The comparisons between analytical solution and numerical solution are good.The results of the asymmetric system are compared with the symmetric model and the periodic motions under zero damping situation are also discussed.Based on the studies above,the periodic motions of symmetric system and asymmetric system respectively under different damping parameters are studied,and the Poincaré method is applied to determine the analytical solutions and the periodic motions for each system.The results between the analytical solution and the numerical solution are good.The relationships of switching velocity and switching time versus damping parameters are obtained.At last,a summary of the whole thesis is obtained and some suggestions for the future study are represented.