摘要
索结构在表面覆冰后在横截面上引起偏心,在风荷载作用下面内、面外两个横向振动与扭转振动会耦合在一起,动力学状态较为复杂。该文建立了悬索风致振动的三维耦合振动模型,将风荷载表示为攻角的非线性函数,通过Hamilton原理导出动力学方程。采用Galerkin法将控制方程离散化,根据Routh-Hurwitz判据得到索平衡构形在参数空间内的稳定域,确定了发生Hopf分岔的临界风速,并且用数值解验证了稳定性条件。在给定的Hopf分岔设计点附近,采用近似解析方法确定了稳定域的边界形状,节省了一定的计算工作量。
The dynamic behavior of an ice-covered cable is complicated because of the eccentricity over the cable＇s cross-section, which makes the in-plane and out-of-plane vibrations coupled with the torsion vibration. A three-dimensional coupling model of a suspension cable loaded by wind excitation is developed, with the wind force expressed as a nonlinear function of the angle of attack. The governing partial differential equation of motion is derived through the Hamilton＇s principle and discretized using the Galerkin approach. The stability region in the parametric space of the cable＇s equilibrium configuration is obtained using Routh-Hurwitz criterion. The critical wind speed of the Hopf bifurcation is determined and later verified numerically. The boundary shape of the stability region is obtained through an approximately analytical method in the vicinity of a given Hopf bifurcation point, by which a fair amount of computational cost is saved.
出处
《工程力学》
EI
CSCD
北大核心
2012年第8期14-21,共8页
Engineering Mechanics
关键词
偏心索
风荷载
耦合振动
HOPF分岔
稳定域
eccentric cables
wind excitation
coupling motion
Hopf bifurcation
stability region
