Chaotic Dynamics Of Typical Vibro-impact Systems

The research of chaotic motion of the vibro-impact system is one of the hot topics in the dynamics of non-smooth system.Melnikov method is an effective analytical method of chaotic dynamics.The analytical results of chaos for three typical vibro-impact models are obtained by Melnikov method,and the analytical results are verified by numerical simulations.Chapter 1 Introduction.The research background?significance and status for vibro-impact system are introduced.Chapter 2 The chaotic motion of a single potential well vibro-impact system with bounded noise excitation.The necessary conditions are obtained and verified by numerical method,the effect of bounded noise on chaos is discussed.The results show that the larger the amplitude of bounded noise,the easier chaos will be generated,while the increase of the intensity of bounded noise can restrain chaos generation under certain conditions.Chapter 3 Chaotic motion of shape memory alloy beams with bilateral constraints.The analytical results obtained by Melnikov method,then maximum Lyapunov exponent and phase diagram are carried out.The graph of maximum Lyapunov exponent via the parameter of collision is given.The results show that larger parameter of collision is helpful to suppress chaos,while larger harmonic excitation amplitude can promote the generation of chaos under certain conditions.Chapter 4 Chaotic motion of shape memory alloy beams with bilateral constraints excited by white noise.The analytical results and numerical simulations are carried out.Moreover,the influences of white noise amplitude on chaos are investigated.The results reveal that the increase of the amplitude of white noise can accelerate the generation of chaos under certain conditions.Chapter 5 Conclusions and Prospects.The conclusions are summarized and the further problems are discussed.