桥梁自激力脉冲响应函数及颤振时域分析

Impulse Response Functions of Self-excited Force and Flutter Analysis in Time Domain for Bridge

为探讨基于自激力脉冲响应函数卷积积分列式的颤振时域分析中存在的问题,使用颤振导数的有理函数近似式推导出了自激力脉冲响应函数的具体形式,建立了基于自激力脉冲响应函数的桥梁颤振运动方程并给出了2种时域求解方案,通过讨论自激力脉冲响应函数的性质解决了颤振时域分析中结构初始响应失真以及积分时间步长如何设定的问题。通过对具有理想平板断面的简支梁的颤振分析发现:结构初始响应失真的现象是自激力中非线性卷积积分项的初始条件未知造成的,通过限定与自激力非定常特性相关的气动系数的下限可以有效解决该问题;时间积分步长会影响到基于自激力递推列式的颤振分析结果的精度,可以根据自激力时域模型中气动力系数及桥梁结构颤振形态估算所需的时步。

In order to explore the problems in time-domain flutter analysis based on the formulation of self-excited forces expressed in terms of convolution integrals of impulse response function, governing equation of bridge flutter was established based on this impulse response function. Two solution schemes for this governing equation were also proposed. The critical issues in time-domain flutter analysis, such as how to reduce initial response distortion and how to set integral time step, were cleared up by analyzing the characteristics of impulse response function of self-excited force. Flutter analysis of a simply supported beam with idealized thin plane section adopting the two procedures was provided. The results show that the distortion of initial response is caused by the unknown initial conditions of nonlinear convolution integral terms of self-excited force, which can be avoided by restricting the lower limit of the aerodynamic coefficients related to the unsteady property of self-excited force, and integral time step may affect precision of flutter analysis results based on recursive formula of self-excited force, which can be evaluated by aerodynamic coefficients and flutter mode shape of the bridge.