摘 要:根据桥梁断面的试验颤振导数,采用阶跃函数模拟了自激力的时域表达式,并推导了便于时域分析的自激力递推公式.采用APDL语言编制了颤振时域分析的程序并在ANSYS中实现.时域分析表明,几何非线性效应对桥梁颤振临界状态影响甚微,而对其后颤振性能影响很大.线性理论揭示的后颤振响应是一种典型的发散现象,而计入几何非线性效应后,后颤振响应最终演变为小振幅的极限环振动(LCO).此外,能量分析表明,线性发散振动的结构储能不断增加,而考虑几何非线性时,结构储能维持在一个较低水平(LCO状态).相比线性发散造成的灾难性毁灭而言, LCO只会对结构产生累积损伤;鉴于此,还需要综合考虑材料的强度及疲劳特性等因素,才能进一步评估桥梁结构的安全性与稳定性.
关键词:后颤振;时域分析;极限环;几何非线性;能量
中图分类号:U448.25 文献标志码:A
Limit Cycle Oscillation of Bridge Post-flutter with
Geometric Nonlinearities Included
WU Changqing, ZHANG Zhitian†, ZHANG Weifeng, CGEN Zhengqing
(Wind Engineering Research Center, Hunan University, Changsha 410082, China)
Abstract: According to experimental sectional flutter derivatives, indicial functions are applied to simulate the self-excited loads of a bridge deck section, and their recursive formulas which are essential in the implementation of FE analysis procedure are given. The procedure of time-domain flutter analysis, which is achieved by APDL language, is performed by the ANSYS software. Numerical results show that geometric nonlinearities have a negligible effect on the flutter threshold, but a significant effect on the post-flutter properties. When geometric nonlinearities are included, the post-flutter ultimately leads to a limit cycle oscillation (LCO) with a very small amplitude compared to a formidable divergence resulted from a linear method. Furthermore, the analysis shows that, in the case of linear analysis, the energy stored in the structure increases continuously as time progresses; however, this energy is limited in a quite low level (LCO state) when geometric nonlinearities are involved. Compared with the traditional divergence and catastrophic collapses, LCO results in cumulative damage that is of much more moderate; in view of this, other factors, such as the material strength and fatigue properties, are indispensable for further evaluation of the security and stability of the bridge structure.
Key words: post-flutter; time-domain analysis; limit cycle; geometric nonlinearities; energy
大跨度橋梁风致失稳现象包括静力失稳与动力失稳两类,其中静力失稳表现为侧向屈曲与扭转发散[1-2],而动力失稳则表现为颤振、涡激共振、驰振及抖振等引起的失稳现象.颤振问题是大跨度桥梁风致振动研究中的热点问题之一.多年来,抗风设计者围绕颤振临界风速这一问题进行了广泛地研究,建立了一套成熟的颤振频域分析方法[3-7].然而,这类方法属于线性理论的范畴,局限于颤振临界问题的分析,无法准确地分析与评估大跨度桥梁结构的后颤振特性.基于线性理论可知,当风速高于颤振临界风速时,结构将会出现大变形的发散振动,这显然是一种非线性振动.然而,对于非线性颤振研究而言,频域法不再适用.因此,要准确地评估桥梁后颤振性能,必须建立一套非线性颤振的分析方法.近年来,机翼气动问题的相关研究表明,当同时考虑结构及气动力非线性或者只考虑其中之一时,机翼的后颤振行为最终表现为极限环振动(LCO)[8-10].然而,至今为止,大跨度桥梁的非线性颤振与后颤振研究的相关报道较少.究其原因主要有以下两点:第一,抗风设计者目前最关心的问题依然是结构的颤振临界问题,而这一问题在线性范围内即可得到很好地解决;第二,建立一套成熟的桥梁非线性气动弹性理论存在很大困难,目前这方面的研究还处于起步阶段.