Research On Dynamics Of High-dimensional Vibro-impact System

A suspension vibro-impact system model and two three-degree-of-freedom complicatednonlinear system models are studied in this paper, analyzed several kinds of main parametersexcitation frequency, and its influence for periodic motion in non-smooth dynamical system.Find that excitation frequency is sensitive in high-dimensional vibro-impact system.Especially for the small changes of the excitation frequency in the critical point, which lead toa qualitative change of the system periodic motion. Through the analysis the influence ofsystem parameter for vibro-impact dynamics behavior, select the appropriate system optimalparameters in order to optimize the movement of the system. It offered a theoretical basis forthe optimization design of vibro-impact system in the application of engineering.In the first chapter, illustrate the engineering background of high dimension vibro-impactsystem, then simply analyzed the theoretical tools of vibro-impact system. Finally, list theapplication of vibro-impact system in engineering practice in recent years, elaborate part ofthe research achievement under the corresponding engineering background, and illustrate theexisting main problems in vibro-impact system, at the same time outlook the developmenttrend of vibro-impact system dynamics.In the second chapter, build a suspension vibro-impact system model first, judging fromthe condition of periodic motion in the system, deducing the expression of fixed point andanalytical solution of the suspension vibro-impact system. And analyze the periodic solutionunder the disturbance movement of the system, and then build Poincaré four-dimensionalmaps. By selecting a collision cross section as Poincaré map, the suitable system parameterconditions, through numerical simulation find the dynamics behavior of doubling bifurcation,Hopf bifurcation of the system, and the variation trend of linearization matrix eigenvalue isgiven out on the unit circle.Dynamics behavior of a three-degree-of-freedom relative vibro-impact system is studiedin the third chapter, specific parameter values when doubling bifurcation and Hopf bifurcationtake place of the system are given. Making analysis of the movement and deduce, andestablish six-dimensional mapping. Selecting the collision cross section as Poincaré mappingsection, using the numerical simulation to find the process of the road to bifurcation and chaosin the system and studies its evolution regular pattern.In the last chapter, comprehensive analyze the dynamics behavior of athree-degree-of-freedom vibro-impact system. First analyze the periodic motion of the system,then deduced the analytical solution according to the boundary condition of the system, anddetermine six-dimensional Poincaré map of the system, then numerical simulated the complex dynamic behavior to the bifurcation and chaos of the system.