The Smooth And The Non-smooth Impacts In A Two-degree-of-freedom Vibro-impact System

This dissertation mainly presents a study on a two-degree-of-freedom vibro-impact system against a rigid surface and systematically study the dynamical phenomena of the grazing bifurcation and chaos in non-smooth dynamical systems.Surveys some recent achievements and developments of the study based on the stability of the vibro-impact system, bifurcation and chaos theory. Analyze the stability of the smooth dynamical systems. A two-degree-of-freedom impact oscillator against a rigid surface is considered. The dynamic equations of the system is established by the non-dimension equations and decoupling treatment, calculate the solution of periodic motion under the force. Time course and phase diagram is obtained through numerical simulation. Let the impact surface be the Poincare section. The stability of its periodic motion is determined by the Jacobian matrix eigenvalues of the Poincare map.Analyze the stability of the non-smooth dynamical system. A two-degree-of-freedom impact oscillator is considered when it impacts with grazing. The solutions of the grazing periodic motion is calculated. The grazing bifurcation diagram is plotted with the time Poincare mapping method.Calculate the Lyapunov exponent of the impact system through the method of continuous orthogonalization. Lyapunov exponent arranged in large to small. If there is a positive index, it means that Lyapunov attractor is chaotic.