Bifurcation Analysis And Chaos Control Of Collision Vibro-impact System

In engineering practice,when there is a gap between parts and components of mechanical system,the vibro-impact phenomenon will occur under the action of external excitation,which makes the system speed jump before and after vibration.Therefore,this kind of system is non-smooth and strongly nonlinear.Under certain parameter conditions,bifurcation phenomenon and even chaotic motion will occur.However,the most chaos movement can cause the mechanical structure to fail or even damage,so it has important social practical significance and engineering application value to eliminate the chaos movement through control.Based on this,the bifurcation phenomenon and chaotic motion of a rigid vibro-impact system with single degree-of-freedom are analyzed,and the chaotic motion control problem of the vibro-impact system is explored and studied in this dissertation.The main content of this dissertation is organized in the following manner:Firstly,the double-period bifurcation behavior and grazing bifurcation behavior of single-degree-of-freedom rigid vibro-impact system model are analyzed.For the study of double-period bifurcation,the excitation frequency?of the system is taken as the bifurcation parameter,and the bifurcation diagram of the system state x?5?under certain parameter configuration is obtained by numerical simulation.On this basis,the phase diagram of the system,Poincarécross section diagram,time course diagram and spectrum diagram are further obtained,so as to qualitatively judge whether chaotic motion appears in the system.In addition according to the conditions of double-period bifurcation in the system and the Jacobi matrix,the characteristic value of periodic double-period bifurcation is obtained,so as to quantitatively judge whether the system has double-period bifurcation.For the study of the grazing bifurcation,the critical frequency?0 of the system,the excitation frequency?and the critical gap d0 are used as the bifurcation parameters,and the distribution map of the edge wiping bifurcation in the??,d₀?parameter plane is numerically simulated.Moreover,according to the condition that the system has grazing residual dimension dichotomy,combined with the Jacobi matrix expression at the grazing point₀x,the phase diagram and Poincarécross section diagram of the system at the bifurcation point are used to qualitatively judge whether the system has periodic motion of the edge until it leads to chaos.Secondly,due to the need of chaos controller parameter Optimization,PSO algorithm was improved and named IPSO algorithm?IPSO?.Because the research problem is a kind of minimum problem,four typical optimization test functions are used to simulate the performance of IPSO algorithm.The results show that IPSO algorithm has great advantages in convergence speed and avoiding falling into local optimum performance compared with PSO algorithm and dragonfly algorithm?DA?.Finally,an intelligent optimal control strategy based on radial basis function neural network?RBFNN?is proposed to control chaotic motion of a single-degree-of-freedom rigid vibro-impact system.RBF three-layer network structure is used to design the chaotic controller,and the collision surface is selected as the Poincarésection,and the fitness function is established based on the distance between adjacent two points on the section.The fitness function is used to guide the IPSO algorithm to optimize the parameters of the chaos controller.The simulation results show that the control strategy has a good effect on chaotic motion control of rigid vibro-impact system with single-degree-of-freedom.At the same time,the effects of different initial control time and different number of hidden nodes on the control effect are also studied in this dissertation,which lays a foundation for further improving the chaotic motion control of vibro-impact system in the future.