留数定理在多维多点反应谱法耦合系数求解中的应用

为解决目前多维多点反应谱法研究中耦合系数积分求解繁琐的问题，基于留数定理提出了一种高效的解析求解方法。该解析求解公式不仅可以考虑行波效应，还可以同时考虑动力与拟静力的耦合、相干效应和方向交叉项等多种耦合效应。将考虑多种效应的耦合系数求解公式转化为解析的形式，不仅其计算结果等价，而且计算效率是积分法的100倍以上，进一步凸显了在多维多点求解问题中反应谱法相较于时程分析法的应用优势，并且使多维多点反应谱法应用于现行结构设计软件变为了可能。基于现行规范的模型假设，提出两种简化算法，使效率优势得到进一步提高。利用多维多点反应谱法，对某高铁站房的工程实例进行计算，并同时程分析法的结果进行对比。两种方法所得结果基本吻合，验证了反应谱法的合理性，且多维多点反应谱法的求解效率远高于多维多点时程分析法的。

Application of residue theorem in cross-correlation coefficients on multi-support and multi-component response spectrum method

Based on current research, in order to avoid the complicated integral calculation in getting the accurate value of cross-correlation coefficients of multi-component and multi-support response spectrum method, residue theorem was applied to this issue so that the representation of the formulas can be transformed to efficient analytical expression. The analytical formulas of cross-correlation coefficients considering multi-component and multi-support seismic excitations can take the factors of the response coupling dynamic and static component, incoherence effect and cross directions as well as wave passage effect into account. The analytical formulas are equivalent to integral expression. Meanwhile, this transformation leads to 100 times increase of efficiency at least which leads to a great advantage of the response spectrum method compared to the time history analysis method and makes it possible to achieve multi-component and multi-support response spectrum method by current structural design software. Based on the current code, two simplified methods which are more efficient were proposed. With the response spectrum method under multi-component and multi-support seismic excitations, structural response characteristics of a high-speed railway station were discussed. Compared with the result from time history analysis, the accuracy of the method can be verified. Meanwhile, the efficiency of the response spectrum method is much higher.