准周期激励非线性隔振系统的混沌研究

Study on the chaos of the nonlinear vibration isolation system under quasi-periodic excitation

建立了准周期激励下非线性隔振系统的模型;应用Poincare映射方法对系统进行降维处理后,在Poincare截面上分析了系统稳定流形和不稳定流形的行为。应用Melnikov方法确定了系统产生混沌的参数区域。结果表明双曲不变环面的稳定流形和不稳定流形之间同宿横截相交是导致该系统产生混沌的根本原因,并给出了系统出现混沌时的相图、Poincare截面图,计算了Lyapunov指数。

The derivative equation of motion for the nonlinear vibration isolation system is provided in this paper. After reducing the system dimension with the Poincare map, the behaviour of the stable and unstable manifold is analyzed on the Poincaxe cross section.The chaotic parameter regime of this system is defined by the Melnikov method.The results show that the transverse intersection between the stable and unstable manifolds of the hyperbolic invariant torus is the essential reason for chaos. The classic phase plane, Poineare section and spectra are shown, and the Lyapunov exponent is calculated.