Simplified Calculation Research on Effects of Dynamic Amplification on Soft-Upper-Rigid-Down Hybrid Structures
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摘要: 上柔下刚混合结构更易产生"鞭梢效应".在考虑刚度比、质量比对结构动力特性的影响，提出刚度质量综合比概念的基础上，假定上下部结构阻尼比相等，推导出了可用于工程应用的上柔下刚混合结构动力放大效应简化计算方法；采用1组公开发表的振动台试验数据分别以轻木-混凝土二层结构（"1+1"体系）、三层结构（"1+2"体系）、六层结构（"2+4"体系）为例共7个案例，采用振型分解法对简化计算法进行验证.研究结果表明：简化方法与振型分解法的误差均低于20%，验证了使用简化计算法计算上柔下刚混合结构动力放大效应的有效性和可靠性；当整体结构下上刚度比不小于7时，可采用简化计算法计算上部结构的动力放大效应.Abstract: Soft-upper-rigid-down hybrid structures are more susceptible to the "whipping effect". Considering the effects of stiffness and mass ratios on the dynamic characteristics of structures, a simplified calculation method which can be used in engineering to determine the effects of dynamic amplification on a soft-upper-rigid-down hybrid structure is given by proposing the concept of a stiffness mass integrated ratio and assuming that the damping ratios of the superstructure and substructure are equal. Analysis reveals that the results of the simplified calculation method correlate well with one set of published shaking table test data and the mode-superposition method. For light wood-concrete structures, which are composed of two layers ("1+1" system), three layers ("1+2" system) or six layers ("2+4" system), the results of the simplified calculation method are in good agreement with the mode-superposition method with an error lower than 20%, which verifies the validity and reliability of the simplified calculation method. It is proposed that the simplified calculation method can be used to calculate the effect of dynamic amplification of soft-upper-rigid-down hybrid structures when the stiffness ratio of the structure is not less than 7.
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图 10 质量比和刚度质量综合比参数分析
Figure 10. Parametric analysis of the mass and stiffness mass integrated ratios
图 12 顶部质点一阶振型水平位移-刚度比曲线
Figure 12. Horizontal displacement-stiffness ratio curves of upper patical
表 1 模型质量、刚度分布
Table 1. Mass and stiffness distribution based on the model
试验模型 m1/t m2/t m3/t k1/
(kN·mm-1)k2/
(kN·mm-1)k3/
(kN·mm-1)em ek β 模型4 10.5 3.5 1.1 20 2.4 3.8 0.27 10.13 2.75 模型6 10.5 3.5 1.1 30 2.4 3.8 0.27 15.19 4.12 
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表 2 放大系数对比
Table 2. Comparison of amplified coefficients
试验模型 简化计算法 Taft波 EL Centro波 SHW2波 试验结果 误差/% 试验结果 误差/% 试验结果 误差/% 模型4 1.26 1.37 8.15 1.24 -1.97 1.45 13.19 模型6 1.18 1.30 9.08 1.27 7.25 1.31 9.82
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