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| 大跨度桥梁地震随机振动响应极值分析的半解析方法 |
| Semi-analytical Method for Peak Analysis of Seismic Random Vibration Response of Long Span Bridges |
| 投稿时间：2025-02-25 修订日期：2025-05-13 |
| DOI： |
| 中文关键词: 桥梁抗震 首次穿越破坏 虚拟激励法 随机振动 半解析方法 |
| 英文关键词: Bridge seismic resistance First excursion failure Virtual incentive method Random vibration Semi analytical method |
| 基金项目:国家自然科学基金 |
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| 摘要点击次数: 11 |
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| 中文摘要: |
| 提出了一种大跨度桥梁地震随机振动响应极值分析的半解析方法。桥梁结构受地震作用的动力可靠度分析是典型的基于首次穿越破坏问题，其可转化为在某一时间间隔内结构响应随机过程的绝对最大值问题。将应力响应谱矩从物理空间解耦到模态空间，并利用留数定理和虚拟激励法，由模态空间中的响应获得桥梁任意位置的应力谱矩。进一步结合随机振动首次穿越破坏的极值概率统计规律，可得到桥梁应力响应极值的均值和方差半解析表达式，避免了大量的物理空间下的谱矩数值积分运算，大大提高了求解效率和计算精度。数值算例中，采用半解析方法对受到地震随机作用下的某斜拉桥进行应力响应极值期望进行计算，并与传统方法进行比较，验证了所建立方法的效率和精度。 |
| 英文摘要: |
| A semi-analytical method for the extreme value analysis of the random vibration response of long-span bridges under earthquakes is proposed. The dynamic reliability analysis of bridge structures under seismic action is a typical problem based on the first-passage failure, which can be transformed into the problem of the absolute maximum value of the random process of the structural response within a certain time interval. The stress response spectrum moments are decoupled from the physical space to the modal space. By using the residue theorem and the pseudo excitation method, the stress spectrum moments at any position of the bridge can be obtained from the response in the modal space. Furthermore, by combining with the extreme value probability statistical laws of the first-passage failure in random vibration, the semi-analytical expressions of the mean value and variance of the extreme value of the bridge stress response can be obtained, avoiding a large number of numerical integrations of the spectrum moments in the physical space and greatly improving the solution efficiency and calculation accuracy. In the numerical example, the semi-analytical method is used to calculate the expected value of the extreme value of the stress response of a certain cable-stayed bridge under random seismic action, and the results are compared with those obtained by the traditional method, which verifies the efficiency and accuracy of the established method. |
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