The Research On Cell-Mapping Method And Sticking Motion Of Nonsmooth Dynamic Systems

This thesis aims at the application of cell-mapping method in nonsmooth dynamic systems, as well as the sticking phenomenon in multi-degree of freedom nonsmooth systems. The global analyses of some typical nonsmooth systems are carried out.On the global analyses of general smooth nonlinear dynamic systems, cell-mapping method is a commonly used tool. In chapter two, the cell-mapping method and some relative conceptions are introduced at first. Then the means of pullback integral is introduced into the impact process base on the cell-mapping method, and satisfy the requirement of both velocity and precise of calculation, in view of the characteristics of non-smooth dynamic systems. Whereafter, a vibro-impact system and a piecewise smooth system are served as examples to validate the cell-mapping method of nonsmooth systems, and the sensitivity with damper of domains of attraction in this vibro-impact system is also found.Subsequently in chapter three, the basic ideology of Poincarémap, which is a dispensable theory tool for analyzing nonsmooth dynamic systems, is introduced. The stability of a one-degree of freedom system with two-sided amplitude constraints is considered by setting up Poincarémap. Furthermore, the multi-solutions'coexistence and domain of attraction variate with parameter are researched by using cell-mapping method of nonsmooth systems, and it is found that this variation has relation to the leap phenomenon after comparing with Poincarémap figures.Sticking motion can be found in multi-degree-of-freedom vibro-impact systems, especially when coefficient of restitution is relatively small. Through analyzing two movement states, sticking and non-sticking, the Poincarémapping of 1-sticking-period-1 motions is set up by using the end of sticking plane as Poincarésection, and the analytical expressions of Jacobi matrix are determined at the corresponding fix points of the Poincarémapping. Therefore, the eigenvalue analyses for the stability of 1-sticking period-1 motions can be discussed based on the Jacobi matrix. It is shown that our method is valid through the numerical simulation, from which, the max proportion of sticking motions in one period is found as well. Finally, the rising phenomenon of this system are given by using the constrained plane as Poincarésection, and the condition expression of sticking motion can be use to explain this phenomenon.