Research On Relative Rotation Nonlinear Dynamical System Under Harmony And Random Noise Excitation

Nonlinear dynamical system of relative rotation is one of hot research subject innonlinear dynamic system research. In the process of research of the nonlinear system,stability is a critical factor. On the analysis of absorbs the domestic and foreign existing onthe basis of results, harmony and random noise excitation of the nonlinear dynamic system,stability issues are researched in this paper. Stability, bifurcation, chaos of several differentconditions are discussed, we got a very good conclusion. Finally, the purpose of thecontrol of chaos is implemented by adding cycle motive power method; it has the broadprospect and application value.The article is divided into five chapters.The first chapter: The research purpose, significance, research status and the mainresearch contents are briefly introduced.The second chapter: The principal resonance of a relative rotation nonlineardynamical system under harmony and random noise excitation is investigated.Autonomous system stability of equilibrium issues are analyzed through the tectonicLyapunov function. The method of multiple metrics is used to determine the equations ofmodulation of amplitude an phase. The approximate solution of first order is obtained.The third chapter: The principal resonance of Duffing-Van der Pol oscillator undercombined harmonic and random parametric excitations is investigated. The system torespond to the diverge curve is attained by the dynamical characteristic. Accordingly, thelinearization process is carried out to determine the steady state moments of the amplitudeof the system response. The theoretical analyses are verified with numerical simulation.The fourth chapter: Firstly, the dynamics equation of relative rotation nonlineardynamics system with nonlinear stiffness and nonlinear damping and forcing excitation isdeduced. Secondly, Based on the same lodge bifurcation, aiming at consonant withbounded incentive, concordant joint incentive, double-frequency noise to cycle motivationthree different situation, get the possible ways to produce Smale horseshoe transformunder the meaning of the necessary conditions of chaotic behaviors by Using Melnikov method.The fifth chapter: The relative rotation nonlinear dynamic system of chaotic motionwhich discussed in the fourth chapter is further researched. The system from chaosmovement into expectations low cycle sport by adding cycle motive power method, thepurpose of the control of chaos is implemented. Finally, we get the area where chaos getsinhibition.