横向风荷载作用下轴向运动弦线自激振动和稳定性分析  

ON SELF-EXCITED VIBRATION ANALYSIS FOR AXIALLY MOVING STRINGS WITH TRANSVERSE WIND EXCITATIONS

作　　者：吕乐丰[1] 王跃方[1] 刘迎曦[1] 

机构地区：[1]大连理工大学工程力学系,大连116023

出　　处：《工程力学》2008年第2期40-45,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(10472021,10421202);教育部留学回国人员科研启动基金项目(教外司留[2004]527)

摘　　要：研究了横向定常风荷载作用下轴向运动弦线的非线性自激振动问题。将风荷载模型化为平均风速的非线性函数,建立动力学微分方程。采用Galerkin方法,将运动弦线简化为离散的二维系统并进行线性化,分析弦线平衡构型的稳定性,根据Routh-Hurtwitz判据确定了平衡点的稳定域。确定了多参数下Hopf分岔点及产生稳定极限环的条件。使用增量谐波平衡(IHB)法求解了自激振动的周期响应,按照Floquet理论确定了周期解的稳定性。最后,讨论了运动速度和平均风速稳定性的影响,并给出相应的稳定性条件。There exist axially translating string structures, e.g. string cars that operate under wind loadings in outdoor environments. The wind excitation may cause severe vibrations and jeopardize the safety of the strings. In this paper the authors investigate the nonlinear vibration of the translating strings with small sag-to-span ratios under wind excitations. The governing partial differential equation is obtained by modeling the wind excitation as a nonlinear function of the transport speed. The Galerkin approach is adopted to reduce the string to an approximate system with a few numbers of DOFs. After linearization of the system the stability of the equilibrium configuration is investigated through an eigenvalue analysis. Explicit conditions arc provided for loss of stability based on the Routh-Hurwicz criterion as well as for generation of stable limit cycles via the Hopf bifurcation, both taking transport speed and wind speed as the controlling parameters. The periodic motion of the string is determined using incremental harmonic method, with stability analyses carded out by eigenvalue computation for the Floquet multipliers. Various stability conditions arc presented considering the transport speed, wind speed and the viscous damping as operation parameters.

关 键 词：非线性振动 轴向运动弦线 自激振动 风荷载 HOPF分岔 

分 类 号：O322[理学—一般力学与力学基础] O323[理学—力学]