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浙江大学学报(工学版)
浙江大学学报(工学版)  2019, Vol. 53 Issue (5): 899-909    DOI: 10.3785/j.issn.1008-973X.2019.05.010
土木与水利工程     
梁结构疲劳刚度退化对模态频率的影响
卫军(),杜永潇,梁曼舒
中南大学 土木工程学院，湖南 长沙 410075
Influence of fatigue stiffness degradation for beam structure on modal frequency
Jun WEI(),Yong-xiao DU,Man-shu LIANG
School of Civil Engineering, Central South University, Changsha 410075, China
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摘要：

为了研究梁结构疲劳刚度退化对模态频率的影响，对预应力混凝土梁进行疲劳试验和动力测试，得到疲劳历程中疲劳刚度和模态频率的演化规律. 建立疲劳全过程变刚度有限元修正模型，并对其进行模态分析. 比较分析试验和模拟结果，讨论模态频率退化规律及疲劳刚度退化对其影响机制. 研究结果表明，梁结构模态频率具有类似抗弯刚度退化的三阶段衰减规律，表明疲劳刚度与模态频率退化存在映射关系；在疲劳作用下，第1阶频率的下降幅度最大，第2阶频率次之，第3阶频率的下降幅度最小；提出的变刚度假设在有限元模拟中运用良好，模拟结果显示第1阶频率模拟值的偏差基本在10%以内. 提出的疲劳全过程动力特性分析方法为梁结构疲劳分析研究提供了新思路.
关键词： 疲劳试验;  疲劳刚度退化;  有限元模拟;  模型修正;  模态频率;  动力特性    
Abstract:

The fatigue experiment and dynamic test were carried out on the prestressed concrete beam, and the evolution laws of fatigue stiffness and modal frequency during the whole fatigue process were obtained, in order to study the influence of fatigue stiffness degradation for beam structure on the modal frequency. A variable stiffness finite element correction model for the whole fatigue process was established and its modal analysis was carried out. The modal frequency degradation law and the influence mechanism on modal frequency by the fatigue stiffness degradation were discussed, by comparing and analyzing the experiment and simulation results. Results showed that the modal frequency of beam structure had a three-stage attenuation law which was similar to the degradation of bending stiffness, and it indicated that there was a mapping relationship between fatigue stiffness and modal frequency degradation. The first-order frequency had the largest decrease, the second-order frequency was the second, and the third-order frequency had the smallest decrease under the action of fatigue. The proposed variable stiffness assumption was well used in the finite element simulation and the simulation results showed that the deviation of the first-order frequency simulation value was basically within 10%. The proposed full-process dynamic characteristics analysis method provides a new idea for the fatigue analysis of beam structure.
Key words: fatigue experiment    fatigue stiffness degradation    finite element simulation    model modification    modal frequency    dynamic characteristics
收稿日期: 2018-10-22 出版日期: 2019-05-17
CLC:  TU 317  
作者简介: 卫军（1957—），男，教授，博士，从事混凝土结构耐久性等研究. orcid.org/0000-0001-5473-5959. E-mail： juneweii@126.com
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引用本文:

卫军,杜永潇,梁曼舒. 梁结构疲劳刚度退化对模态频率的影响[J]. 浙江大学学报(工学版), 2019, 53(5): 899-909.

Jun WEI,Yong-xiao DU,Man-shu LIANG. Influence of fatigue stiffness degradation for beam structure on modal frequency. Journal of ZheJiang University (Engineering Science), 2019, 53(5): 899-909.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2019.05.010    或    http://www.zjujournals.com/eng/CN/Y2019/V53/I5/899

L/mm L0/mm h/mm b/mm 混凝土强度等级 预应力筋（1×7钢绞线） 普通钢筋型号
fptk/MPa 束数 每束根数 纵筋 箍筋
5 500 5 400 428 80 C50 1 860 1 2 HRB335 HPB300
表 1  模型梁设计参数
图 1  预应力混凝土模型梁尺寸及配筋
梁编号 fcu fc Ec
No.4 43.1 26.5 31 725
No.2 46.2 29.0 32 204
No.5 40.8 25.7 30 516
表 2  实测混凝土力学性能参数
钢筋种类 d/mm fy/MPa fu/MPa
HRB335 10 395 475
HPB300 8 310 452
表 3  实测钢筋力学性能参数
图 2  预应力混凝土模型梁实体图
图 3  试验荷载施加方式
编号 Pmin/kN Pmax/kN ΔP/kN 应力幅 Nf/万次
No.4 ? ? ? 静载试验；Pu=265 kN ?
No.2 50 130 80 Pmin=0.20Pu；Pmax=0.50Pu 45
No.5 50 120 70 Pmin=0.20Pu；Pmax=0.45Pu 50
表 4  模型梁试验参数及疲劳寿命
图 4  加速度传感器布置图
图 5  预应力混凝土模型梁破坏形态
图 6  疲劳抗弯刚度分布曲线
图 7  跨中疲劳抗弯刚度退化曲线
梁编号 n n/Nf wf（n） we（n） δ/% γf（n） γe（n）
1阶 2阶 3阶 1阶 2阶 3阶 1阶 2阶 3阶 1阶 2阶 3阶 1阶 2阶 3阶
No.2 初始 0 24.103 86.444 185.898 26.482 68.082 149.745 ?8.98 26.97 24.14 1.000 1.000 1.000 1.000 1.000 1.000
1 0.02 21.180 76.394 165.871 23.759 63.569 146.501 ?10.86 20.17 13.22 0.879 0.884 0.892 0.897 0.934 0.978
5 0.11 20.937 75.534 164.131 22.917 59.535 144.523 ?8.64 26.87 13.57 0.869 0.874 0.883 0.865 0.874 0.965
10 0.22 20.822 75.133 163.319 22.615 59.495 143.659 ?7.93 26.28 13.68 0.864 0.869 0.879 0.854 0.874 0.959
25 0.56 20.574 74.323 161.674 22.706 59.791 144.608 ?9.39 24.30 11.80 0.854 0.860 0.870 0.857 0.878 0.966
45 1.00 18.576 67.256 147.180 21.331 57.353 136.215 ?12.91 17.27 8.05 0.771 0.778 0.792 0.805 0.842 0.910
No.5 初始 0 23.147 83.103 178.905 24.803 60.426 141.294 ?6.68 37.53 26.62 1.000 1.000 1.000 1.000 1.000 1.000
1 0.02 21.760 78.323 169.421 22.495 58.034 139.205 ?3.27 34.96 21.71 0.940 0.942 0.947 0.907 0.960 0.985
5 0.10 21.401 77.113 167.000 21.012 54.957 135.731 1.85 40.32 23.04 0.925 0.928 0.933 0.847 0.909 0.961
9 0.18 21.235 76.500 165.768 21.238 54.827 134.034 ?0.02 39.53 23.68 0.917 0.921 0.927 0.856 0.907 0.949
25 0.50 20.805 75.000 162.749 20.996 54.199 133.445 ?0.91 38.38 21.96 0.899 0.903 0.910 0.847 0.897 0.944
50 1.00 18.427 68.023 148.538 19.982 52.199 130.813 ?7.78 30.32 13.55 0.796 0.819 0.830 0.806 0.864 0.926
表 5  模拟与实测频率及偏差汇总表
图 8  实测频率退化曲线
类别 E/（105 N·mm?2） ν ρ/（103 kg·m?3） fy/MPa
纵筋 2.00 0.3 7.8 395
箍筋 2.00 0.3 7.8 310
预应力筋 1.95 0.3 7.8 1 860
混凝土 ? 0.2 2.6 ?
表 6  模型梁基本材料参数
图 9  预应力混凝土梁有限元模型
图 10  模型梁有效预应力变化趋势
n/Nf 梁No.2 n/Nf 梁No.5
B/
（1013 N·mm2） 		Apσcon（n）/
kN 		B/
（1013 N·mm2） 		Apσcon（n）/
kN
0 3.161 289.00 0 2.916 313.00
0.02 2.435 279.31 0.02 2.571 301.96
0.11 2.378 262.08 0.10 2.488 284.47
0.22 2.350 252.94 0.18 2.449 276.34
0.30 2.336 248.63 0.30 2.407 268.86
0.40 2.320 244.55 0.40 2.377 264.53
0.56 2.297 239.70 0.50 2.348 261.13
0.60 2.291 238.69 0.60 2.318 258.33
0.70 2.275 236.44 0.70 2.283 255.95
0.80 2.254 234.49 0.80 2.238 253.87
0.90 2.223 232.75 0.90 2.164 252.04
1.00 1.869 231.20 1.00 1.626 250.40
表 7  疲劳全过程主要损伤特征模拟
图 11  疲劳模态分析基本流程
图 12  模拟频率退化曲线
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