对应地震反应谱的当量功率谱密度函数的数值算法

A Numerical algorithm for equivalent power spectral density functions corresponding to seismic response spectra

提出根据地震反应谱曲线求解当量功率谱密度函数曲线的一种数值算法,为结构随机地震反应分析中确定和计算地面运动功率谱密度提供依据。在相对位移谱与结构相对位移响应峰值的均值之间建立联系;在现有迭代方法的基础上,对算法公式作进一步的推导和整理,将迭代计算转变为线性方程组的求解计算,进而避免迭代方法的不收敛。通过对数值计算结果的分析发现,由于规范反应谱曲线存在斜率突变,采用本文算法计算出的功率谱密度曲线在规范反应谱曲线的两端和分段转折点处会出现倍周期分岔甚至混沌现象。为此建议适当增加低频范围内离散频率点的数目,且采取整体光滑的反应谱曲线,从而提高计算结果的稳定性。

A numerical algorithm, by which the seismic power spectral density can be determined according to the response spectrum, is proposed in this paper. It is used to calculate the power spectral density of ground motions in structural random seismic response analysis. A connection is established between the relative displacement spectrum and the mean value of the peak relative displacement responses： Based on the existing iterative method, the formulas are further developed, and the traditional iterative calculation procedure is replaced by solving a linear system of equations to avoid non-convergence problem. It is found from the numerical results that because of the slope sahation of the response spectrum, period doubling bifurcation, and even chaos occur at piecewise points and endpoints of the seismic power spectral density curves obtained from the proposed algorithm. Therefore, suggestions are made that appropriately increasing the number of discrete frequency points in low frequency range and adopting global smooth response spectrum curves during calculation can improve the stability of the results.