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弦-梁耦合系统的动力学行为分析

         

摘要

The stability and bifurcations of a string-beam coupled system at its initial equilibrium solution were investigated in detail with a combination of analytical and numerical methods.The variation of the eigenvalues versus parameters was investigated.Based on the averaged equation,the expressions for the critical bifurcation lines leading to incipient and secondary bifurcations,such as,Hopf bifurcation and 2-D tori,were obtained.Numerical simulations of these bifurcation cases were also carried out,whose results agreed well with the analytical ones,at least qualitatively.%研究了弦-梁耦合系统在初始平衡解处的稳定性与分岔情况,给出了特征值随阻尼参数的变化情况,并利用稳定性分析和特征值分析等解析方法,得到了初始平衡解、周期解和拟周期解的稳定边界以及导致Hopf分岔和2维胎面等分岔解的临界分岔曲线。最后,利用数值模拟方法研究了弦-梁耦合系统的稳定性与分岔情况。

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