Nonlinear Dynamics Of Collisional Vibration Systems

In various types of machine components that contain gaps,shock vibration often occurs due to the presence of gaps.There are more and more institutions with gaps around us,and the system movement with gaps will inevitably produce vibrations.Therefore,it is more and more meaningful to study the dynamic behavior of such systems.This paper takes the engineering machinery system as the research object,establishes a dynamic model of a two-degree-of-freedom collision vibration system and a dynamic model of a three-free collision-containing vibration system,and lists the dynamic differential equations of the system model based on Newton's second law.And it is non-dimensionalized,and the corresponding analytical solution is obtained by modal analysis method,and the existence condition of the system periodic response and the expression of Poincaré mapping are deduced and calculated.The numerical simulation of the system is performed through MATLAB programming,and the dynamic behavior of these two dynamic model systems is analyzed.The third chapter,taking the bearing rotor system as the research object,establishes a two-degree-of-freedom impact vibration system with gap impact,and deduce the relevant differential equations of the system.Then,the relevant dynamic behavior of the system is simulated by MATLAB programming.Four groups of parameters are selected to obtain the four groups of bifurcation diagrams and the corresponding Poincar e section projection of the system,and analyze the process of single period motion,multi cycle motion,periodic doubling,torus doubling and how to chaos evolution under different control parameters.The fourth chapter takes the linear vibrating screen as the research object,and establishes a three-degree-of-freedom collision-vibration system.Establish the corresponding differential equations of motion to calculate its associated periodic solution and Poincaré map.Then,the relevant dynamic behaviors of the system are calculated by MATLAB simulation.Four groups of parameters are selected to simulate the system's four-component diagram and Poincaré cross-section projection diagram to analyze the different motion characteristics of the system under different control parameters and how it evolves to chaos.