非线性参数激励系统的动力分叉研究

本文针对弹性梁动力曲屈分叉问题,建立了系统的非线性Mathiue方程,较全面地讨论了此类参数激励系统的1/2亚谐分叉特性,指出以往对此类问题的研究得到的只是一种退化情形下的分叉特性,阐述了分叉方程的截断对分叉结果的影响,得到了一些新的结果。文中还介绍了一个模型弹性梁系统分叉响应特性的实测结果,证实了理论分析的可靠性。

INVESTIGATION ON DYNAMICAL BIFURCATIONS OF A NONLINEAR PARAMETRIC EXCITATION SYSTEM

In order to study dynamical bucking and bifurcations of an elastic beam, we establish nonlinear Mathieu equation of this beam and discuss thoroughly the characteristic of 3/2 subharmonic bifurcation in parametrically excited system. Our studies show that researchers only got bifurcating characteristic of a degenerate case when they investigated these problems. We analyse influence of truncation in bifurcating equation on bifurcation set, and obtain some new results. Finally, we give result of experiment on bifurcating response curves of elastic beam and examine theoretical results by experiment.