Study On Periodic Solutions And Chaos Movement Of Relative Rotation Dynamics System

The transmission of relative rotation power is the basic content of large and complex mechanical system, and one of the most important ways of mechanical power transmission system. the relative rotation of the drive shaft for power transmission signals and state prediction become a significantvmeans to eliminate accidents, ensure the rotation system's security, reliable and efficient operation.This thesis discusses the relative rotation system of nonlinear differential dynamic system model of unified, chaotic performance, qualitative analysis and exact method for finding periodic solutions.First, the thesis discusses the first two types of relative rotation of the unified model of nonlinear dynamic system, proves that under certain conditions there is a Poincarébifurcation in the unified model of autonomous systems, and studies the performance of a unified chaotic system.Subsequently, the thesis studies of under the harmonic excitation force two elastic end relative rotational axis primary resonance, gets the steady asymptotic periodic solution, harmonic resonance system solutions and subharmonic resonance solution.What's more, the thesis proves that under certain conditions,there is harmonic and periodic solution in the double flexible shaft end relative rotation system for nonlinear dynamic equations, and gets the approximate steady-state periodic solution.Finally, for a class of linear stiffness and nonlinear damping force and the strong force of forced periodic force term cycles of relative rotation nonlinear dynamic system, the writer gets existence, boundedness and uniqueness of periodic solutions and the necessary condition of limit cycles of stability of a class of autonomous system through qualitative analysis. Besides, in this thesis, a sort of exact periodic solutions is available under periodic signal disturbance.