Analysis Of Nonlinear Dynamics In Nonsmooth Mechanical System

In the producing, manufacturing and assembling of our daily machines, due to someirresistible factors, mechanical equipments always have clearance, thus, a series ofvibro-impact arise. If these vibrations last too long or cannot be solved for a long time, it willbring a series of rather prominent problems such as equipment failure, strain aggravation,shorter life span of the equipment. Hence, vibro-impact system widely exist in dailymanufacture in engineering practice, the study for it has important project guidingsignificance. This article makes specific study on four kinds of two-degree-of-freedomvibro-impact models.1. Firstly, a typical two-degree-of-freedom vibro-impact system is given. This chapterwill study the dynamic response of two-degree-of-freedom vibro-impact system withclearance, obtain of the system according to collision condition and engagement conditiondecided by collision rules, the stability and local bifurcation of the fixed point in the mappingis discussed. The effectiveness of the two-degree-of-freedom vibro-impact system withclearance is stated, the bifurcation and the routes to chaos behaviors of the class of symmetryperiodic vibro-impact motion is analyzed.2. The second vibration system in this article is also a two-degree-of freedom model.Based on the existing system, the dynamic behavior of two-degree-of freedom vibro-impactsystem is analyzed, decoupling first, solve the differential equations through boundaryconditions of the periodic motion of the system, and then deduce the Poincaré mapping,theoretical analyze the stability of the periodic motion in different systems. Study theexistence and stability of the sub harmonic periodic motion by analytical method, throughnumerical modeling method, further study the influence of system parameter to the periodicmotion.3. In the chapter four，simulate some simple vibration model using the system simulationsoftware Simulink, thereby get the phase diagram, time history diagram, and find out thefrequency of the system occurring chaos. In practical, it is of great significance, it alsoconduct simple simulation to some vibro-impact models using the new simulation software.By selecting some parameters to do simulation study, quasi-periodicity condition and chaoscondition of the practical system can be utilized or avoided, it offers theoretical foundation forthe chaos vibration machine, and it in flavor of the beginners to understand and grasp thecharacteristics of chaos as soon as possible.