多点输入反应谱中耦合系数的研究

Research on the Coherency Coefficients in the Multi-Support Response Spectrum

首先利用虚拟激励法推导了仅考虑行波效应下多点输入反应谱表达式,重点对多点输入反应谱中动位移耦合系数ρijpq及拟静位移耦合系数ρSpq的计算方法及其特性进行了研究。为了避免繁琐的积分运算,提出了一种"拟合+插值"的耦合系数计算方法,不但精度高,而且大大提高了计算效率。研究表明,ρijpq相对于地震波到达支座点的时差Δt具有明显的三角函数的关系;从总体趋势上看,ρijpq绝对值基本随ωj/ωi的增大而减少,这一点与一致输入时的振型耦联系数ρij相同。在仅考虑行波效应的情况下,可以认为,各支座点的拟静力位移完全相关,即ρSpq=1,结构拟静力位移谱与地震动的位移谱相同。

By means of the pseudo - excitation method, the expression of multi - support response spectrum is developed only considering the traveling wave effect. The calculation and characteristic of dynamic displacement coherency coefficient ρijpq and ρpq^S is focused on the research. For reducing integration work, a new coherency coefficient calculation method, called ＂fitting ＋ interpolation＂, is presented, which has high precision and efficiency. The study shows that ρiipq has the relationship of trigonometric function with △t - the earthquake wave arrival time difference between each support. In general, the absolute value of ρijpq decreases with increasing ωj/ωi, which is the same as the modal coupling coefficient ρij in simple support excitation. If only considering the traveling wave effect, the pseudo static displacement caused by each support can be thought of being completely correlation. It means that pseudo static displacement spectrum of structure is identical with that of ground motion, that is ρpq^S = 1.