The concept of standard deviation spectrum of structural response is firstly introduced. Taking the conditions as rational criteria that the standard deviation spectra of the steady-state displacement, velocity and acceleration of structures are minimized, the basic idea of optimal selection of frequencies in the spectral representation method is delineated. On this basis,two types of approaches are proposed to select deterministic and randomized frequencies, respectively, for the harmonic components. Taking the Clough-Penzien spectrum as an example, numerical analyses are carried out. The investigations show that for the structures with fundamental period in 0～3 s, 7 harmonic components are adequate, whereas for the structures with fundamental period in 0～6 s, 50 harmonic components are adequate. These results are in obvious contrast to the cases in the classical spectral representation method, where usually 500～600 harmonic components are necessary. The optimal selection of frequencies will greatly reduce the number of the random variables involved in the spectral representation method and hence will improve the efficiency greatly in the stochastic response analysis of structures.%首先阐述了结构响应标准差谱的基本概念.以结构位移、速度和加速度稳态响应标准差谱误差最小为准则,阐明了对谱表达方法谐波分量频率进行优选的基本思想.在此基础上,提出了确定性频率和频率随机化两类频率优选方法.以Clough-Penzien谱为例,进行了数值实例分析.研究表明,当结构基本周期在0～3 s之间时,随机激励选取7个谐波分量即可,而对于基本周期在0～6 s的结构,随机激励含有50个谐波分量已经足够.这与经典谱表达方法中采用均匀频率取点时通常需要500～600个谐波分量相比,极大地降低了随机变量个数,有效地提高计算分析效率.
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