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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (5): 899-909    DOI: 10.3785/j.issn.1008-973X.2019.05.010
    
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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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     
Received: 22 October 2018      Published: 17 May 2019
CLC:  TU 317  
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Jun WEI
Yong-xiao DU
Man-shu LIANG
Cite this article:

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.

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


梁结构疲劳刚度退化对模态频率的影响

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 
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
Tab.1 Design parameters of model beam
Fig.1 Dimensions and reinforcement for PC model beam
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
Tab.2 Measured mechanical properties of concrete　MPa
钢筋种类 d/mm fy/MPa fu/MPa
HRB335 10 395 475
HPB300 8 310 452
Tab.3 Measured mechanical properties of steel bar
Fig.2 Physical map of PC model beam
Fig.3 Experiment loading mode
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
Tab.4 Test parameters and fatigue life of model beams
Fig.4 Acceleration sensor distribution
Fig.5 Failure patterns of PC model beams
Fig.6 Fatigue bending stiffness distribution curves
Fig.7 Fatigue bending stiffness degradation curves for mid-span
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
Tab.5 Simulated and measured frequency and deviation summary
Fig.8 Measured frequency degradation curves
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 ?
Tab.6 Basic material parameters of model beam
Fig.9 Finite element model of PC beam
Fig.10 Effective prestressing trend of model beams
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
Tab.7 Main damage feature simulation during fatigue process
Fig.11 Process of fatigue modal analysis
Fig.12 Simulation frequency degradation curves
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