Study On The Dynamics Of Geometrically Nonlinear Dry Friction Vibrators

The problem of nonlinear vibration is an important subject in the field of physics and technology.Abundant research achievement has been obtained at present.However,as the production and technology are improving,there are still a lot of questions needed to be explored and further studied.The main methods of nonlinear vibration theory include the qualitative method,analytic method and the numerical method.Nonlinear vibration theory has been applied widely in physics,electronics,biology,the modern fluid mechanics,the space technology,etc.In this dissertation,various nonlinear dynamics behavior of a class of geometric nonlinear dry frictional oscillator are discussed.The first chapter introduces the engineering background,the research purpose and significance of geometric nonlinear oscillator,survey the recent achievements of this class of system,Moreover,we briefly recall the basic notions and methods which will be used in what follows.In the second chapter,the motion equation for a class of geometrical nonlinear oscillator with dry friction is established,and the periodic of different kinds of the systems are demonstrated by numerical.The third chapter considers the chaotic motion of the geometrical nonlinear dry friction oscillator.We calculate the analytic expression of the homoclinic orbit and apply the Melnikov method to obtain the critical conditions of the dry friction oscillator appearing chaotic motions.Besides,the validity of the analytical method is verified by numerical simulation,and the roads of the oscillator towards to chaotic state by period doubling bifurcation is revealed.In chapter 4,the effects of external excitation on the global dynamics of the system are discussed.The phenomena of coexistence of periodic motions,coexistence of periodic motions and chaotic motions are found.Moreover,the evolution rules of the basin of attraction are studied when the external excitation change.