A Semi-Analytical Method for Peak Response Analysis of Bridge Stochastic Vibration Under Seismic Excitation
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摘要: 提出了一种随机地震激励下线性结构首次穿越破坏的极值响应半解析分析方法. 基于多模态正交分解策略实现时空变量的有效解耦，将结构物理应力响应转化到模态空间的高效求解. 借助虚拟激励法推导了地震谱作用下的模态响应谱矩解析表达式，结合首次穿越破坏机制的响应峰值概率密度函数，构建了振动峰值响应的高精度快速计算模型. 以典型大跨斜拉桥为工程背景，对关键构件应力响应峰值进行对比分析. 数值实验结果表明：与传统方法相比，该文方法在保证计算精度的同时，计算效率提升两个数量级，为大型工程结构的抗震可靠度评估提供了有效工具.Abstract: A semi-analytical method for peak response analysis of first-passage failure of linear structures under stochastic seismic excitation was presented. Based on a multi-modal orthogonal decomposition strategy, the effective decoupling of temporal and spatial variables was achieved, to transform the structural physical stress response into the efficient modal space solution. The pseudo excitation method was employed to derive analytical expressions for modal response spectral moments under seismic spectrum excitation. Combined with the probability density function of response peaks according to the first-passage failure mechanism, a high-precision and rapid computational model for vibration peak responses was established. In the engineering case of a typical long-span cable-stayed bridge, comparative analysis of stress response peaks for critical components was conducted. Numerical results demonstrate that, compared with conventional methods, the proposed approach maintains computational accuracy while improving computational efficiency by 2 orders of magnitude, providing an effective tool for seismic reliability assessment of large-scale engineering structures.
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Key words:
- seismic response spectrum /
- random vibration /
- pesudo excitation method /
- first passage failure
edited-byedited-by1) (我刊编委赵岩来稿) -
图 1 大跨度斜拉桥有限元模型(单位: m)
Figure 1. The finite element model for a long span cable-stayed bridge (unit: m)
图 3 不同方法计算的桥梁截面正应力(σ+y)极值期望
Figure 3. Peak expectations of normal stress (σ+y) of the bridge section calculated with different methods
图 4 不同方法计算的桥梁截面正应力(σ-y)极值期望
Figure 4. Peak expectations of normal stress (σ-y) of the bridge section calculated with different methods
图 5 不同方法计算的钢索轴向应力极值期望
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 5. Peak expectations of the cable axial stress calculated with different methods
图 6 应力极值期望最大的单元位置
Figure 6. The expected maximum positions of stress peaks in elements
图 7 不同模态截断数下的桥梁单元17截面应力极值期望
Figure 7. Peak stress expectations of the bridge element 17 section under different modal truncation numbers
图 8 桥梁单元17截面的应力极值概率分布和期望
Figure 8. The probability distribution and expectation of stress peaks in the bridge element section 17
图 9 不同方法计算的桥梁截面正应力(σ+y)极值标准差
Figure 9. Peak standard deviations of normal stress (σ+y) of the bridge section calculated with different methods
图 10 不同方法计算的桥梁截面正应力(σ-y)极值标准差
Figure 10. Peak standard deviations of normal stress (σ-y) of the bridge section calculated with different methods
图 11 不同方法计算的钢索轴向应力极值标准差
Figure 11. Peak standard deviations of the cable axial stress calculated with different methods
图 13 不同阻尼比下的钢索单元截面轴向应力极值期望
Figure 13. Expectations of the peak sectional axial stress of the cable element under different damping ratios
图 14 不同阻尼比下桥梁单元截面+y端正应力极值期望
Figure 14. Expected normal stress peaks at the +y end of the bridge element section under different damping ratios
图 15 不同阻尼比下桥梁单元截面-y端正应力极值期望
Figure 15. Expected normal stress peaks at the -y end of the bridge element section under different damping ratios
图 16 钢索单元轴向应力极值期望敏感度
Figure 16. Expected sensitivities of the peak axial stress of the cable element
图 17 桥梁单元截面+y端正应力极值期望敏感度
Figure 17. Expected sensitivities of the peak normal stress at the +y end of the bridge element section
图 18 桥梁单元截面-y端正应力极值期望敏感度
Figure 18. Expected sensitivities of the peak normal stress at the -y end of the bridge element section
图 19 钢索单元轴向应力极值标准差敏感度
Figure 19. Sensitivities of the standard deviation of the peak axial stress of the cable element
图 20 桥梁单元截面+y端正应力极值标准差敏感度
Figure 20. Sensitivities of the standard deviation of the peak normal stress at the +y end of the bridge element section
图 21 桥梁单元截面-y端正应力极值标准差敏感度
Figure 21. Sensitivities of the standard deviation of the peak normal stress at the -y end of the bridge element section
表 1 不同阻尼比下的计算时间
Table 1. Calculation time costs under different damping ratios
modal damping ratio ζ=0.01 ζ=0.03 ζ=0.05 calculation time 0.830 s 0.815 s 0.802 s 
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