Analysis And Experimental Research On Nonlinear Characteristics Of Coupled SD Oscillator

With the development of social economy and the progress of science and technology, the nonlinear problems are increasingly prominent in nature science and engineering. Nonlinear science research increasingly attracts the attention of researchers. The coupled SD oscillator is a kind of strong nonlinear dynamics system because of the spring’s geometrical arrangement which showed smooth and discontinuous features with the continuous variation of smooth parameters.Based on the revelant theoretical study,the paper investigates the nonlinear dynamic characteristics of coupled SD oscillator by using the combination of numerical simulation and experimental method. The exsitance of complex and rich nonlinear phenomena in the system such as multi-period, bifurcation, chaos, etc are determined by the analysis of time domain graph, spectrum diagram, phase diagram and poincaré section graph.The change law of the response status is found.The major research contents and conclusions of this dissertation are briefly summarized as follows:(1)The mechanics model of coupled SD oscillator is established and its statics analysis is researched. The experimental model with the characteristics of coupled SD oscillator is constructed, and the experiment scheme is designed.Then the damping of the experiment system is recognitioned.(2)The response status of coupled SD oscillator under different exciting frequency is studied.The response global bifurcation diagram of the oscillator is obtained. The change law of oscillator motion form is found.(3)The vibration status of coupled SD oscillator under different exciting amplitude is acquired.The vibration amplitude of the same steady state solutions will get bigger with the increase of exciting amplitude.(4)Four groups of typical smooth parameters are chosen.The response of coupled SD oscillator is analyzed from the perspective of global dynamics.It’s found that nonlinear dynamic characteristics of the system is influenced by the smoothparameters in the largest extent.Experimental results and numerical simulation results are basically identical,which indicates the exsistance of abundant nonlinear dynamic behaviors of coupled SD oscillator. The paper verifies the rationality of the physical experiment model and provides an experimental reference for the application of this system on production practice.