斜拉索风雨激振面内运动的非线性分析  

Nonlinear Analysis of In-Plane Motion of Rain-Wind-Induced Vibration of Stay Cable

作　　者：李伟义[1] 张琪昌[1] 何学军[1] 

机构地区：[1]天津大学机械工程学院,天津300072

出　　处：《天津大学学报》2010年第2期156-160,共5页Journal of Tianjin University(Science and Technology)

基　　金：国家自然科学基金资助项目(10872141);教育部博士点基金资助项目(20060056005)

摘　　要：为深入研究斜拉索风雨激振面内的运动特性,依据弹性力学和气动弹性理论建立了连续斜拉索风雨激振面内非线性振动方程,利用伽辽金方法将偏微分方程转化为常微分方程.借助多尺度法得到面内一阶振动方程的平均方程和定常解,利用奇异性理论对系统进行分岔分析,确定了系统在零平衡点附近发生Hopf分岔对应的风速以及拉索发生风雨激振时对应的水线频率的范围.对拉索前四阶模态的振幅进行了数值模拟,考察了拉索以第一阶模态振动时风速、结构阻尼比等系统参数对拉索振幅的影响.研究表明,连续面内振动方程更能体现斜拉索风雨激振完整的动力学特性,同时系统中存在多种分岔行为.For in-depth study of the characteristics of in-plane motion of rain-wind-induced vibration of the stay cable,the nonlinear equation of the in-plane vibration of continuous stay cable has been presented on the basis of elastic mechanics theory and aeroelasticity theory.The partial differential equation has been diverted into ordinary differential equation with Galerkin method.The averaged equation and the steady state solution have been obtained with the method of multiple scales and bifurcation analysis has been conducted with singularity theory,which determines the wind speed as Hopf bifurcation occurs at the origin point and the range of rivulet frequency when the rain-wind-induced vibration of stay cable happens.The vibration amplitudes of the first four order modes have been numerically simulated to study the impact of system parameters,such as the wind speed and the cable damping ratio on the vibration amplitude while the stay cable is vibrating in the first order mode.Study results show that the nonlinear equation can reflect the dynamic characteristics of the in-plane motion of rain-wind-induced vibration of stay cable better,and various bifurcation behaviors exist in the system.

关 键 词：风雨激振 非线性振动 水线 GALERKIN方法 斜拉索 

分 类 号：O322[理学—一般力学与力学基础]