风作用下覆冰悬索的非平面非线性动力学

主要研究侧向风载荷作用下小垂度覆冰悬索的非线性非平面运动的复杂动力学. 根据分析力学、弹性力学和空气动力学理论, 建立覆冰悬索3个自由度非线性振动的偏微分运动方程，并对其进行无量纲化，运用Galerkin方法对偏微分运动方程进行离散得到3个自由度的常微分方程，再利用多尺度法得到面内主共振2:1内共振的平均方程. 利用数值方法研究悬索的非线性运动，结果表明系统呈现周期、多倍周期、概周期和混沌运动的规律.

STUDY ON NONPLANAR NONLINEAR DYNAMICS OF ICED CABLE

In this paper, the nonlinear, nonplanar, complicated dynamics of the smallsag, iced cable subjected to side wind and movement of one support isinvestigated. Based on theories of analytical mechanics, elastic mechanicsand aerodynamics, the nonlinear partial differential equations withthree-degree-of-freedom are established. Then, the dimensionless method andthe Galerkin's method are applied to discretize the governing partialequations of a three-degree-of-freedom nonlinear system. And then, themethod of multiple scales is used to obtain the averaged equations of theiced cable system in the case of primary resonance and 2:1 internalresonances. Finally, numerical simulation is employed to find the nonlineardynamic responses of the iced cable system. It is found there exist theperiodic motion, multi-period motion, quasi-periodic and chaotic motions forthe iced cable under certain conditions.