基于模态叠加法的公路简支梁桥动力放大系数研究

周勇军; 薛宇欣; 高徐军; 李冉冉; 王业路; 赵煜

doi:10.19818/j.cnki.1671-1637.2023.06.008

基于模态叠加法的公路简支梁桥动力放大系数研究

doi: 10.19818/j.cnki.1671-1637.2023.06.008

1.
长安大学公路学院，陕西西安 710064
2.
中国电建集团西北勘测设计研究院有限公司，陕西西安 710065
3.
济南城市建设集团有限公司，山东济南 250014

基金项目:

国家重点研发计划 2021YFB2601000

国家自然科学基金项目 51978063

陕西省自然科学基础研究计划项目 2021JLM-47

中央高校基本科研业务费专项资金项目 300102282108

详细信息

作者简介:
周勇军(1978-), 男, 湖北孝感人, 长安大学教授, 工学博士, 从事桥梁结构分析与智能检测研究

中图分类号: U441.3
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- 文章访问数: 160
- HTML全文浏览量: 31
- PDF下载量: 54
- 被引次数: 0
出版历程
- 收稿日期: 2023-06-15
- 刊出日期: 2023-12-25

Research on dynamic amplification factor of highway simply supported girder bridge based on modal superposition method

1.
School of Highway, Chang'an University, Xi'an 710064, Shaanxi, China
2.
Northwest Engineering Corporation Limited, Xi'an 710065, Shaanxi, China
3.
Jinan City Construction Group Co., Ltd., Jinan 250014, Shandong, China

Funds:

National Key Research and Development Program of China 2021YFB2601000

National Natural Science Foundation of China 51978063

Natural Science Basic Research Project of Shaanxi Province 2021JLM-47

Fundamental Research Funds for the Central Universities 300102282108

More Information

Author Bio:
ZHOU Yong-jun(1978-), male, professor, PhD, zyj@chd.edu.cn

摘要

摘要: 为研究模态阶数对挠度和弯矩动力放大系数分析的影响，以标准跨径的简支T梁桥、箱梁桥和空心板桥为研究对象，基于模态叠加法推导了简支梁在三轴车作用下的动力放大系数表达式；采用MATLAB软件编制了车桥耦合振动分析程序进行数值计算，研究了桥面不平整度、车辆速度与车辆质量3种因素下挠度和弯矩动力放大系数随模态截断阶数的变化规律，分析了不同模态阶数下两者的比值关系，对一座30 m简支箱梁桥进行了实桥动载试验验证。研究结果表明：挠度动力放大系数受模态阶数影响较小，1阶模态对挠度动力放大系数的贡献率为99%，选取前5阶模态时，可以获得完整桥梁结构响应信息；弯矩动力放大系数受模态阶数影响较大，1阶模态对弯矩动力放大系数的贡献率为86%，前5阶模态贡献率为90%；当考虑前25阶甚至更多模态时能够得到弯矩动力放大系数可靠结果；车辆速度在一定程度上影响模态阶数对动力放大系数的贡献率，桥面不平整度与车辆质量对动力放大系数收敛阶数影响不甚显著；弯矩动力放大系数小于挠度动力放大系数，当取1阶模态时，两者比值为0.86，取前15阶模态时，两者比值为0.95；建议相同测试条件下采用挠度动力放大系数。
- 桥梁工程 /
- 简支梁桥 /
- 动力放大系数 /
- 模态叠加 /
- 模态截断阶数
Abstract: To explore the effect of modal orders on analyzing dynamic amplification factors (DAFs) of deflection and bending moment, simply supported T-girder bridges, box girder bridges, and hollow slab bridges with standard spans were selected as the research objects, and based on the modal superposition method, the DAF formula of simply supported girders under the action of three-axle vehicle was derived. The vehicle-bridge coupling vibration analysis program was compiled by using MATLAB software for numerical calculation, and the relationship of the DAFs of the deflection and bending moment with the order of modal truncation was studied under the influence of three factors, such as deck roughness, vehicle speed, and vehicle mass. In addition, the ratio relationship between two DAFs under different modal orders was analyzed and verified by the dynamic field test of a 30 m simply-supported box girder bridge. Research results show that the DAF of deflection is less affected by the modal order, and the contribution rate of the first-order mode to the DAF of deflection is 99%. When the modes at the first five orders are selected, the complete structural response information of the bridge can be obtained. However, the DAF of bending moment is greatly affected by the modal order, and the contribution rate of the first-order mode to the DAF of bending moment is 86%, while the contribution rate of the modes at the first five orders is 90%. Reliable results of DAF of bending moment are obtained when the modes at the first 25 orders or more are considered. The contribution rate of modal orders to the DAFs is affected by vehicle speed to some extent. The influences of deck roughness and vehicle mass on the convergence of the DAFs are not significant. The DAF of bending moment is less than that of deflection. When the first-order mode is selected, the ratio of the two is 0.86. When the modes at the first 15 orders are selected, the ratio of the two is 0.95. It is suggested to use the DAF of deflection under the same test condition. 2 tabs, 10 figs, 29 refs.
- bridge engineering /
- simply supported girder bridge /
- dynamic amplification factor /
- modal superposition /
- modal truncation order

HTML全文

图 1 匀速移动常量力作用的简支梁模型

Figure 1. Simply supported girder model under constant moving forces

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图 2 挠度和弯矩动力放大系数

Figure 2. Dynamic amplification factors of deflections and bending moments

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图 3 车辆模型

Figure 3. Vehicle model

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图 4 桥面不平整度对动力放大系数的影响

Figure 4. Effects of deck roughnesses on dynamic amplification factors

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图 5 车辆速度对动力放大系数的影响

Figure 5. Effects of vehicle speeds on dynamic amplification factors

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图 6 车辆质量对动力放大系数的影响

Figure 6. Effects of vehicle masses on dynamic amplification factors

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图 7 模态阶数对挠度及弯矩动力放大系数的贡献率

Figure 7. Contributions of modal order to deflection and bending moment dynamic amplification factors

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图 8 动力放大系数比值

Figure 8. Ratios of dynamic amplification factors

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图 9 实桥动载试验

Figure 9. Bridge dynamic field test

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图 10 实测应变和挠度时程曲线

Figure 10. Time history curves of measured strains and deflections

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表 1 简支梁主要参数

Table 1. Primary parameters of simply supported girders

结构类型	跨径/m	单位长度质量/ (kg·m^-1)	抗弯刚度/ (10¹⁰ N·m²)
T梁	20	9 755	3.37
	30	11 122	7.46
	40	13 673	15.76
箱梁	20	10 469	2.48
	30	12 349	5.22
	40	14 467	9.50
空心板	10	11 156	0.59
	13	12 304	0.90
	16	13 452	1.30
	20	15 173	2.06

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表 2 实测结果

Table 2. Measured results

v/ (km·h^-1)	y_{d, max}/ mm	y_{j, max}/ mm	ε_{d, max}	ε_{j, max}	1+μ_y	1+μ_M
20	0.956	0.836	3.972	3.675	1.14	1.08
30	0.993	0.918	4.393	4.151	1.08	1.06
40	1.369	1.278	5.091	4.895	1.07	1.04
50	1.192	1.010	5.100	4.388	1.18	1.16

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