非比例阻尼线性体系地震响应的部分平方组合(CPQC)法

A complex partial quadratic combination(CPQC) method for seismic responses of non-classically damped linear system

对于非比例阻尼线性系统,当采用基于复振型的地震反应谱振型叠加方法,即复振型完全平方组合(CCQC)方法进行动力反应分析时计算工作量较大。为此,通过分析不同振型之间的位移、速度、位移-速度相关系数随频率比和阻尼比的变化规律,给出了复振型平方和开方(CSRSS)组合方法的适用范围。同时通过分析指出在CCQC法中只需要考虑邻近振型的相关性,因此建议了一种介于CCQC法和CSRSS法之间的考虑部分相关性的复振型平方组合方法,称之为简化的CCQC法或复振型部分平方组合(CPQC)方法,用以提高计算效率。通过实例分析验证了所建议方法的适用范围、计算精度和效率。由于比例阻尼系统的地震反应谱振型组合方法是文中所述一般方法的特殊情况,因此本文提出的简化分析方法对比例阻尼系统也同样是适用的,并可以称为部分平方组合(PQC)方法。

For non-classically damped linear systems, when the complex mode superposition method based on seismic response spectrum, i.e. the complex complete quadratic combination （CCQC） formula, is used for seismic response analysis, the amount of calculation is fairly large. Hence, the applicability of the CSRSS （complex square root of the sum of squares） method is provided for studying the variations of the modal displacement, velocity, displacementvelocity correlation coefficients along with the ratios of different frequencies and damping. Based on these analyses, a simplified method, which only considers the contributions from relatively adjacent modes in CCQC method and is named as simplified CCQC or complex partial quadratic combination （CPQC） method, is proposed for reducing computational time. A numerical example is presented to analyze the applicability, computational accuracy and efficiency. The proposed simplified method is useful for classically damped linear systems as well, and may also be named as a partial quadratic combination （PQC） method.