轴向变速运动大挠度薄板的非线性动力学行为

研究轴向变速运动大挠度薄板横向振动的稳定性及分岔现象。在von Kàrmàn非线性大挠度板理论基础上, 利用达朗贝尔原理建立系统的动力学模型。通过Galerkin截断, 将时间变量和空间变量、位移函数和应力函数耦合在一起的偏微分方程离散, 得到系统运动常微分方程。利用数值方法分析板随平均速度、速度脉动幅值和外激励力变化时的运动分岔行为。利用最大Lyapunov指数和Poincaré映射图识别系统的动力学行为。结果发现, 当板的某些参数变化时, 系统出现分岔现象。不同参数时, 系统呈现周期运动、倍周期运动、概周期运动, 甚至混沌运动。

Nonliear dynamic behaviors of an axially acceleratinglarge deflection thin plate

The stability and bifurcations of an axially accelerating plate with large transverse deflections were investigated.The governing dynamic equations of an axially accelerating plate were derived with D’Alembert’s principle based on von Kàrmàn’s nonlinear plate theory.Galerkin metod was employed to discretize the governing partial differential equations into a set of ordinary differential equations.With numerical method,the bifurcation diagrams were presented with respect to some parameters,such as,mean velocity,velocity amplitude and excitation amplitude.The dynamic behaviors were identified based on poincaré map and maximum lyapunov exponent.Periodic,quasi-periodic and even chaotic motions were located in the bifurcation diagram for the transverse vibration of the axially moving plate.