考虑几何非线性的桥梁后颤振极限环特性

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.
According to experimental sectional flutter derivatives, indicial functions are used to simulate the self-excited loads of a bridge deck section, and their recursive formulas that 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 show 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 very small amplitude compared with a formidable divergence resulted from a linear method. Furthermore, the analysis results show 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 significant cumulative damage. 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 bridge structures.