Analysis Of The Characteristics Of Non-smooth Dynamic Mechanical Systems

Under the promotions of actual demand,more and more mathematicians and mechanics have begun to focus on non-smooth dynamic mechanical systems,especially in engineering applications,and attach importance to the research and practice of non-smooth dynamic system theories,in recent years.Currently,many scholars have studied a large number of theoretical analysis methods to analyze and solve the complex dynamics in a non-smooth mechanical systems.The Melnikov method is a very practical analytical method for the global analysis of dynamical systems.Although it has made great progress and improvement in smooth dynamical systems,the classical Melnikov method can not be directly applied to non-smooth dynamical systems.The analysis results will be very inaccurate,so it is necessary to modify and supplement the Melnikov method to study the non-smooth system.In order to explore the application of Melnikov method to non-smooth dynamical systems,the generalized Melnikov's method applied to two type of nonsmooth nonlinear dynamic mechanical systems has been derived from the classical Melnikov method.The following research is carried out in this paper.1.The Melnikov method is an effective analytical method for the study of homoclinic bifurcations,heteroclinic bifurcations and subharmonic bifurcations for non-smooth systems.This paper mainly introduces the basic theory of Melnikov method,giving out the simple derivation of the Melnikov function applied to homoclinic orbits and heteroclinic orbits and subharmonic orbits.The generalized Melnikov's function for a class of discontinuous system and rigid collision system with clearance is derived through perturbation analysis and Poincare mapping.2.A non-smooth dynamics model with 2-DOF for high speed cutting system is established,according to the characteristics of tool vibration coupling with workpiece.Classical stability analysis method-Hopf bifurcation and a generalized Melnikov's method are used to analyze the dynamic characteristics of the model respectively.Then the critical conditions of existence of stable periodic motion(chatter)are determined and the validity of the results are verified by numerical method.3.By the generalized Melnikov method,the characteristics of periodic motions with double-impact of the system with 2-dof are studied,and the existence condition of period-2 motions with double-impact is determined,that is,a critical curve in the parameter domain.The validity of the generalized Melnikov method is proved by numerical simulation.