Dynamical Analysis And Experiment Of Variable Mass SD Oscillator

Geometric nonlinear solution in the nonlinear vibration is one of important research field. With the development of the nonlinear vibration, these problems has been widespread concern. Based on SD(smooth and discontinuous) oscillator, consider the actual quality of experimental design spring design, we will propose variable mass SD oscillator model,and analyze the nonlinear dynamic behavior from simulation experiments and theoretical perspectives.We will establish variable mass SD oscillator geometrically nonlinear dynamics model. We will analyze the variation of SD oscillator’s mass, restoring force and stiffness. From the perspective of qualitative analysis, we will discuss the dynamics of variable mass SD oscillator in the free vibration. Consider non-conservative system, we will analyze the problem of domain of attraction when the free vibration damping. From the quantitative analysis, we will research the variable mass SD oscillator amplitude-frequency characteristics and phase-frequency characteristics and their variation with specific parameters.We will design variable mass SD oscillator experimental device and observe experimental phenomena. We will measure compression performance of experimental spring device, and calculate the stiffness of the spring means. We will collect acceleration data of damping free vibration, and estimate equivalent viscous damping coefficient of the system by fitting the data. We will collect oscillator acceleration signal data for research and analysis when it’s in forced vibration, and get its displacement and velocity by frequency domain integration. Taking into account the Poincare section and vibration phase trajectory. We will identify the vibration characteristics of experiment such as period and Chaotic vibration phenomena. Though numerical simulation, we will analyze the dynamic behavior of the theoretical model in the state of vibration parameters; see bifurcation diagram and the largest Lyapunov exponent, study the vibration characteristics of this case. We find period-one, period-two, paroxysmal, and Chaotic vibration phenomena in variable mass SD oscillator, and there are c two typical road(paroxysmal and period-doubling bifurcations) from period to chaotic vibration...