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首页> 外文期刊>Journal of Earthquake Engineering >COMPLEX MODE SUPERPOSITION ALGORITHM FOR SEISMIC RESPONSES OF NON-CLASSICALLY DAMPED LINEAR MDOF SYSTEM
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COMPLEX MODE SUPERPOSITION ALGORITHM FOR SEISMIC RESPONSES OF NON-CLASSICALLY DAMPED LINEAR MDOF SYSTEM

机译：非经典阻尼线性MDOF系统地震反应的复模叠加算法

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This paper deals with a complex mode superposition method for the seismic: responses of general multiple degrees of freedom (MDOF) discrete system with complex eigenvectors and eigenvalues. A delicate general solution, completely in real value form, for calculating seismic time history response of the MDOF system which cannot be uncoupled by normal modes, is deduced based on the algorithms of the complex superposition method. This solution comprises of two parts which are in relation to the Duhamel integration to sine and cosine function respectively. The related term of the Duhamel integration to sine function is actually the displacement response of the oscillator with corresponding modal frequency and the damping ratio. The other can be transferred into a combination of the displacement and velocity responses of the same oscillator. In order to meet the practical needs of seismic design based on code design spectra for various kinds of structures equipped by viscous dampers, the complex complete quadratic combination (CCQC) method is deduced following similar procedures such as the well-known CQC method, in which a new modal velocity correlation coefficient, together with a new modal displacement-velocity correlation coefficient are involved besides the modal displacement correlation coefficient in normal CQC formula. The new algorithm of CCQC is not only as concise as that of the normal CQC but also has explicit physical meaning. The results obtained from complex mode superposition approaches are discussed and verified in some examples through step by step integration computation under a prescribed earthquake motion input. From these examplary analyses, it may be pointed that the CCQC algorithm normally yields conservative outcome and that the forced mode uncoupling approach has good approximation even the discussed examplary structures are strongly non-proportional.
机译：本文研究了一种复杂的地震模式叠加方法：具有复杂特征向量和特征值的通用多自由度（MDOF）离散系统的响应。基于复杂叠加方法的算法，推导了一种精确的，完全为实值形式的通用解，用于计算MDOF系统的地震时程响应，该响应不能通过常规模式解耦。该解决方案包括两个部分，分别与Duhamel对正弦和余弦函数的积分有关。 Duhamel积分与正弦函数的相关术语实际上是具有相应模态频率和阻尼比的振荡器的位移响应。另一个可以转换为同一振荡器的位移和速度响应的组合。为了满足基于规范设计频谱的粘性阻尼器配备的各种结构的抗震设计的实际需求，遵循类似的程序（例如众所周知的CQC方法）推导复杂完全二次组合法（CCQC），其中除了常规CQC公式中的模态位移相关系数外，还涉及新的模态速度相关系数以及新的模态位移-速度相关系数。 CCQC的新算法不仅与普通CQC一样简洁，而且具有明确的物理意义。在某些示例中，通过在规定的地震运动输入下进行逐步积分计算，讨论并验证了从复模叠加方法获得的结果。从这些示例分析中，可以指出，CCQC算法通常会产生保守的结果，并且即使所讨论的示例结构非常不成比例，强制模式解耦方法也具有良好的近似性。

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