Dynamic Analysis Of Nonlinear Vibration Systems Under External Excitation

In nature,the non-linear phenomena are everywhere.Many complex problems are caused by nonlinear factors.With the intersections of various fields,actually most of the question's modeling is about nonlinear feature expression.Because of its deep engineering background and complex dynamic characteristics,the research on nonlinear systems with parametric excitation has always been a hot topic and widely concerned by scholars at home and abroad.This thesis mainly studies the dynamics of several nonlinear systems under external excitation.In the first part,we study the mixed mode dynamics with time delay under a kind of external excitation.Firstly,the system is calculated and analyzed by Taylor method and scale change to obtain the Hamiltonian function.By making the time history diagram and phase diagram,it is found that the system produces MMOs phenomenon.Then,the system is discretized by Euler method and the discrete equation is obtained The bifurcation of the system is analyzed by the Melnikov threshold method.When the ratio of natural frequency to excitation frequency is integer,the dynamic characteristics of the system at different time scales can be obtained by proper parameter values.Finally,the influence of time delay on the phenomenon of clustering is discussed.The second part studies the multi-steady state behavior of a kind of single-parameter external excitation under periodic excitation.The bistable dynamic behavior of chaotic attractor coexisting with periodic attractor,chaotic attractor and periodic attractor coexisting with periodic attractor and chaotic attractor is studied.The bifurcation diagram and time series diagram of the bistable dynamic system are obtained by proper parameter values.As the period of the slow variable passes the critical point,it is found that near the critical value,chaotic attractors will coexist with multiple periodic orbits or chaos,but when the parameter value exceeds the boundary value.the system will mutate,and then transfer to different types of attractors or chaos.