Abstract: In order to make clear the value principle of each parameter in the weighted amplitude wave superposition (WAWS) method based on FFT technique, the particular attention was paid on the time step Δt and its influence on the following dynamic calculation results. Aiming at the SDOF spring oscillator model and the lightning rod high-rise structure of a transformer substation, a variety of parameters were used to simulate the fluctuating wind time history and calculate the time history dynamics. The value principle of parameters of WAWS, including the cut-off frequency fu, period T0, frequency point N, ratio of time point to frequency point M/N and the time step Δt, was given by comparing the results and analyzing the principle of WAWS and combining the characteristics of wind spectrum and modal force spectrum. The research results show that: in random field simulation based on WAWS with single index frequency, if the ratio of time-frequency points is taken as the commonly used value M/N=2, there are only two time points in each period of the harmonic wave corresponding to the maximum frequency fu. So the obtained broken line can't accurately reproduce the simulation target of the original cosine curve, moreover, the corresponding Δt may not be able to accurately account for the resonance effect of the structure in the dynamic time history calculation. In order to accurately account for the resonance effect in the dynamic calculation, fu and M/N can be increased to decrease Δt, and the effect of increasing fu or M/N is the same. The spring oscillator model has the most stringent requirements for Δt, which can be regarded as the upper limit of ordinary structure. And the specific value of Δt of ordinary structure can be determined reasonably through trial calculation under the guidance of the upper limit value.

Key words: bridge engineering, weighted amplitude wave superposition (WAWS) method, fluctuating wind field, cut-off frequency, time-frequency point ratio, time step, resonance effect

摘要： 为明确基于FFT技术的谐波合成法(WAWS)中各参数的取值原则，尤其关注时间步长Δt以及对后续动力计算结果的影响，针对单自由度弹簧振子模型和某变电站避雷针高耸结构，采用多种参数进行脉动风时程模拟和时程动力计算，经结果对比和WAWS原理分析，并结合风谱和模态力谱特征，给出WAWS的参数，包括截止频率fu、周期T0、频率点N时频点比值M/N和时间步长Δt的取值原则。研究结果表明：基于单索引频率的WAWS进行随机场模拟时，如果时频点比值取常用值M/N=2，最大频率fu对应谐波的每个周期里只有两个时间点，得到的折线无法准确再现原余弦曲线的模拟目标，并且对应的Δt可能在动力时程计算无法准确计入结构的共振效应；为使动力计算准确计入共振效应，可通过增加截止频率fu和M/N来减小Δt，并且增加fu或增加M/N的效果一致；弹簧振子模型对Δt的要求最为苛刻，其Δt可作为普通结构的上限，普通结构对Δt的具体取值，可以上限值为指导再通过试算合理确定。

关键词: 桥梁工程, 谐波合成法, 脉动风场, 截止频率, 时频点比值, 时间步长, 共振效应