过滤白噪声地震动模型的CQC振型相关系数计算

深圳大学土木工程学院,广东深圳 518060

工程抗震; 振型相关系数; 完全二次型组合; 振型分解反应谱法; Lyapunov方程; 过滤白噪声

Calculation of CQC mode correlation coefficients under filtered white noise model of earthquake ground motion
WANG Gang and ZHOU Xiaoqing

College of Civil Engineering, Shenzhen University, Shenzhen 518060, Guongdong Province, P.R.China

seismic engineering; modal correlation coefficient; complete quadratic combination; mode-superposition response spectrum analysis; Lyapunov equation; filtered white noise

DOI: 10.3724/SP.J.1249.2018.02128

备注

当地震动模型为过滤白噪声时,通过频域有理分式积分,求完全二次型组合(complete quadratic combination,CQC)振型相关系数的闭合表达式将变得困难和不实用.本研究提出将传递函数转化为状态空间方程,通过求解Lyapunov方程得到振型相关系数的方法,且通过用Kanai/Tajimi模型验证了方法的有效性.该方法可推广到常见的过滤白噪声地震动模型,避免了频域有理分式积分闭合解的冗长公式,计算量小,可靠性好,是精确解.

When filtered white noise is used to model ground motion, the computation of complete quadratic combination(CQC)modal correlation coefficients by integration of rational function becomes difficult, and the closed-form formulas become tedious and impractical. We propose a new method to obtain modal correlation coefficients by transforming transfer function model into state space model and then by solving a Lyapunov equation. This method can be extended to the situation where filtered white noise ground motion models are used. Kanai/Tajimi model is used to verify the correctness of the proposed method. It is not only concise, reliable and numerical efficient but also can avoid solving tedious closed-form formulas of integration of rational functions.

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