Two Simplified Models for Human-Structure Vertical Interaction
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摘要: 基于质量-刚度-阻尼（mass-spring-damper，MSD）和质量-刚度-阻尼-附加质量（mass-spring-damper-rigid mass，MMSD）两类简化分析模型，采用正则化结构振型函数建立简化的人-结构竖向相互作用动力方程. 针对具有非比例阻尼特性的动力方程，采用状态空间法求解耦合系统瞬时频率和阻尼比，讨论两种耦合动力方程的区别以及结构在人行荷载作用下频率和阻尼比的变化规律，分析人-结构耦合状态下结构加速度响应的差异. 结果表明：考虑人-结构竖向相互作用时，两类动力方程的结构阻尼比显著增大，结构瞬时频率略有减小，瞬时阻尼比峰值平均提高31.67%，瞬时频率峰值平均仅减小0.29%； 结构人致振动分析时应考虑人-结构竖向相互作用；MSD和MMSD两种模型分析情况下，结构动力响应差异很小，均方根加速度值的差异仅为0.34%.
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关键词:
- 人-结构竖向相互作用 /
- 人致振动 /
- 模态分析 /
- 简化分析模型 /
- 振动分析
Abstract: Based on a mass-spring-damper（MSD）model and a mass-spring-damper-rigid mass（MMSD）model, which are two kinds of pedestrian simplified models, the equations of vertical dynamic interaction pertaining to a simplified human-structure were deduced by the regularization structure modal function. Using the dynamic equation with non-proportional damping characteristics, the state-space method was used to solve the instantaneous frequency and damping ratio of the system equations; the difference between the two coupled dynamic equations and the change regularity of frequency and damping ratio of the structure under walking load were discussed, and the difference in the structural acceleration response in a human-structure coupled state was analysed. The results show that the structural damping ratio between the two kinds of equations is significantly different; however, the instantaneous frequency of the structure is only slightly distinct, considering the vertical interaction between a human and a structure. The instantaneous damping ratio peak increases by an average of 31.67%, and the instantaneous frequency reduces by an average of 0.29%. Human-structure vertical interaction must be considered in response to human-induced structural vibration analysis. The difference in structural dynamic responses between the MSD and MMSD models is very small, and the difference in the root mean square acceleration is only 0.34%. -
图 3 MMSD模型和MSD模型下结构瞬时阻尼比变化曲线
Figure 3. Instantaneous structural damping ratio of the two models
表 2 不同附加刚性质量下的结构加速度值
Table 2. Structural acceleration with different rigid masses
最大加速度
/（m•s–2）${m_0}$/kg 4 5 6 7 8 ${a_{\max}}$ 1.631 1 1.632 2 1.633 2 1.634 3 1.635 3 ${a_{\max {\text{-}} {\rm s}}}$ 1.976 2 1.977 0 1.977 9 1.978 7 1.979 5 
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