Study On Nonlinear Dynamic Behavior Of Two Kinds Of Complex Impact Vibration Systems With Bilateral Constraint

The impact vibration system widely exists in engineering field and daily life,and it is a common piecewise smooth system.With the development of mechanical engineering,the structure of impact vibration system is becoming more and more complex.Therefore,this thesis considers two kinds of complex bilateral restraint impact vibration systems,namely,a twodegree-of-freedom bilateral mixed restraint impact system under the influence of Coulomb friction and an N-DOF asymmetric bilateral rigid constraint impact vibration system.The main research contents of this thesis are as follows:Firstly,for a class of two-degree-of-freedom bilateral mixed constraint collision system under the influence of Coulomb friction,all possible motion states of the system are classified,and the conditions for the mutual conversion between the vector field and motion states of each motion state are analyzed.Then,the motion states of the collision-caused grazing bifurcation and friction-caused adding-sliding bifurcation are analyzed emphatically,and the analytical conditions of all possible bifurcations of the system in this state are given.Finally,the special bifurcation point in the state space obtained by the analysis of the above analytical conditions are analyzed by using the path-following method.The results show that this analytical condition can successfully find the special bifurcation point where one oscillator has a grazing bifurcation while the other oscillator has an adding-sliding bifurcation,and the two bifurcations influence each other.Secondly,for a class of N-DOF asymmetric double-sided rigid impact vibration system,the existence condition of the double-sided grazing periodic solution is discussed by using the zero-time discontinuous mapping method,and the calculation formula of the fixed point corresponding to the N-DOF asymmetric double-sided grazing periodic solution is given.Furthermore,the conditions of saddle-node bifurcation and period-doubling bifurcation in the double-sided edge-wiping system are derived.In order to verify its generality,a kind of threedegree-of-freedom double-sided rigid impact vibration system is selected for analysis,and the parameters are selected for numerical simulation based on the general solution obtained by decoupling.The conditions of simultaneous occurrence of grazing bifurcation,period doubling bifurcation and saddle-node bifurcation in the system are obtained,and a number of grazing codomensional-two bifurcation points are found.In order to analyze the dynamic phenomena near the bifurcation point,using Lyapunov exponent,local partial bifurcation diagram and time history diagram,it is found that periodic motion and chaotic phenomena appear alternately near bifurcation point.And the simulation verifies the correctness of the theoretical analysis.Finally,the pulse method is used to control the chaotic system,and the chaos in the system is controlled as periodic motion.