Research On Dynamics Of Multiple-degree-of-freedom With Clearance In Vibro-impact System

Along with the mechanization, some of the terminology is more widely been mentioned, such as elastic impact, rigid impact, impact, vibration, wear, fatigue aging, fracture, etc., The thesis selects the rigid impact in above phenomenon as the research object, studies dynamic behavior of a collision and rigid and methods to reduce and avoid rigid impact. Research on the rigid impact system its essence is the study of nonlinear dynamical behavior of the system.This paper selects a horizontal rigid impact of two-degree-of-freedom, a horizontal rigid impact of three-degree-of-freedom and a vertical rigid impact of three-degree-of-freedom model as examples study the process of rigid impact, the research ideas of three models are as follows: Firstly, build the dynamic model of the impact vibration system by derive, establishment the differential equations of motion of the model based on Newton's second law, and then get the system dimensionless equations of motion by dimensionless. Next, use the normal mode theory to decouple the system equation and obtain its general solution. Then under the precondition of the existence of periodic motion of system create a system perturbation equation, combined with periodic boundary conditions of motion, based on numerical analysis method to solve differential equations of motion of the system, next establish the appropriate Poincaré map, find the eigenvalues of the system and analyze the conditions for the existence of periodic motion and study its stability. Finally use the programming software MATLAB and win-TC simulate the dynamic behavior of the system, analysis of the influence of the change of control parameters on the system dynamic behavior.In the first model, first of all analyze the system dynamics behavior by the contrast analysis of four global bifurcation diagram and conclude that the change of the stiffness of the linear spring ?kand the strength of the linear damping ?con the system dynamic behavior is more significant than that of the clearance B under the condition of constant base parameters. Then with the help of the Poincaré section analyses the influence of the change of control parameters on the system dynamic behavior, find the pitchfork bifurcation and a invariant circles ? torus doubling ? phase lock ? winding deformation ? torus doubling ? chaos two roads leading to the chaos. In the second model, find a fixed point ? pitchfork bifurcation ? hopf bifurcation ? expand ? phase lock ? chaos road and a invariant circles ? torus doubling ? torus doubling ? winding deformation ? chaos road and a fixed point ? hopf bifurcation ? expand ? torus doubling ? phase lock ? chaos road three roads leading to chaos. In the third model,firstly established the three-dimensional phase diagram, analysis the change of control parameters ? not only affect oscillator motion path, also affect the oscillator motion on the number of cycles per unit time cycle.