平均风与气弹效应一体化的桥梁非线性后颤振分析

Nonlinear post-flutter analysis of bridge decks with the integrated mean and aero-elastic wind effects

提出了一种一体化考虑平均风效应与非线性气弹效应的桥梁后颤振时域数值算法。引入多阶段阶跃函数的概念来描述断面不同运动振幅状态下的气弹性能,即模拟了随振幅演变的非线性气弹效应。后颤振时域算法的实现需要解决两大基本问题:不同阶段的阶跃函数之间的平滑切换以及平均风效应与气弹效应之间的有效融合。为了避免不同阶段阶跃函数突然切换所引起的非物理瞬态响应,采取了平行激励的求解策略,即所有阶段的阶跃函数同时并独立地参与气动自激力的计算,得到各个阶段对应的气动自激力,任意时刻的气动自激力则通过对某相邻的两个阶段的气动自激力进行插值得到。此外,引入伪稳态效应分离法,解决了平均风荷载与气弹效应之间的不相容问题。数值算例分析表明,提出的数值算法成功地实现了一体化考虑平均风效应与非线性气弹效应的时域分析,也为大跨度桥梁的非线性后颤振性能及强健性分析提供了理论基础与求解思路。

This article puts forward a time-domain method for post-flutter analysis that can involve simultaneously the mean and nonlinear aero-elastic wind effects based on the platform of ANSYS.The concept of multi-stage indicial functions（IFs）is introduced to describe the sectional aero-elastic performances of a series of discrete motion-amplitude states,which is used for simulating the amplitude-dependent aero-elastic nonlinearity.To realize the time-domain analysis of nonlinear post-flutter,two basic issues needed to be solved：the smooth switching between two groups of IFs,and the effective integration of the mean wind loads into the flutter procedure.In order to avoid the unwanted non-physical transient responses induced by a sudden involvement of a new group of IFs,the authors put forward a strategy of parallel excitation that all groups of IFs participate in the calculation of the self-excited aerodynamic loads in the time-domain simulation,simultaneously and independently,which results in the same groups of self-excited loads.However only two adjacent groups of loads are used for expressing the aero-elastic effect at any time.In order to address the incompatibility resulted from the simultaneous simulation of the mean wind and aero-elastic loads in the procedure,a method of deduction of pseudo-steady effects from aero-elastic model is proposed.The numerical results indicate that the concepts of multi-stage IFs and pseudo-steady effects proposed in this paper can successfully implement the integrated consideration of the mean wind loads and nonlinear aero-elastic loads in the post-flutter analysis,and it also provides some theoretical basis and solution strategy for the nonlinear post-flutter analysis and robustness evaluation of long-span bridges.