轴向变速运动大挠度薄板的非线性动力学行为

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (11) : 11-15.

论文

轴向变速运动大挠度薄板的非线性动力学行为

刘金堂1，杨晓东1，闻邦椿2

作者信息 +

Nonlinear dynamical behaviors of axially accelerating large deflection thin plates

LIU Jin-tang1，YANG Xiao-dong1，Wen Bang-chun2

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文章历史 +

摘要

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。

Abstract

The stability and bifurcations of axially accelerating plates with large transverse deflections are investigated. The governing equations of an axially accelerating plate are derived through D’Alembert’s principle based on von Kàrmàn’s nonlinear plate theory. The Galerkin metod is employed to discretize the governing partial differential equations into a set of ordinary differential equations. By numerical method, the bifurcation diagrams are presented with respect to some parameters such as mean velocity, velocity amplitude and amplitude of exciting. The dynamical behaviors are identified based on the Poincaré 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.

导出引用

刘金堂;杨晓东;闻邦椿. 轴向变速运动大挠度薄板的非线性动力学行为[J]. 振动与冲击, 2012, 31(11): 11-15

LIU Jin-tang;YANG Xiao-dong;Wen Bang-chun. Nonlinear dynamical behaviors of axially accelerating large deflection thin plates[J]. Journal of Vibration and Shock, 2012, 31(11): 11-15