轴向运动大挠度板的非线性动力学行为

NONLINEAR DYNAMICAL BEHAVIORS OF AXIALLY MOVING LARGE DEFLECTION PLATES

该文研究了受周期激励轴向运动大挠度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轴向运动速度、外激励力幅值、长宽比和轴向拉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。

The stability and bifurcations of axially moving plates with large transverse deflections are investigated. The governing equations of an axially moving plate are derived through the D＇Alembert＇s principle based on von Karman＇s nonlinear plate theory. The Galerkin metod is employed to discretize the governing partial differential equations into a set of ordinary differential equations. By a numerical method, the bifurcation diagrams are presented with respect to some parameters such as transport speed, amplitude of exciting, the ratio of the length to the width of plates and the longitudinal tension. The dynamical behaviors are identified based on the Poincare map and the Largest Lyapunov Exponent. Periodic, quasi-periodic and even chaotic motions are located in the bifurcation diagram for the transverse vibration of the axially moving plate.