Please wait a minute...
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
 全文: PDF(1271 KB)   HTML
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
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
作者相关文章  
卫军
杜永潇
梁曼舒

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        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=0.20PuPmax=0.50Pu 45
No.5 50 120 70 Pmin=0.20PuPmax=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 wfn wen δ/% γfn γen
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
Apσconn)/
kN
B/
(1013 N·mm2
Apσconn)/
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
1 吴晓莉, 顾彬 识别钢筋混凝土桥面板疲劳损伤的剩余刚度法[J]. 特种结构, 2008, 25 (3): 69- 71
WU Xiao-li, GU Bin The residual stiffness (RS) method for indentifying fatigue damage of reinforced concrete bridge slabs[J]. Special Structures, 2008, 25 (3): 69- 71
doi: 10.3969/j.issn.1001-3598.2008.03.019
2 陈才生. 重载及腐蚀损伤下钢筋混凝土梁疲劳性能试验研究[D]. 杭州: 浙江大学, 2015: 3–12.
CHEN Cai-sheng. Experimental research on fatigue performance of reinforced concrete beams under overload and corrosion damage [D]. Hangzhou: Zhejiang University, 2015: 3–12.
3 NATáRIO F, FERNáNDEZ R M, MUTTONI A Experimental investigation on fatigue of concrete cantilever bridge deck slabs subjected to concentrated loads[J]. Engineering Structures, 2015, 89: 191- 203
doi: 10.1016/j.engstruct.2015.02.010
4 PATHAK P, ZHANG Y X Nonlinear finite element analyses of fiber-reinforced polymer-strengthened steel-reinforced concrete beams under cyclic loading[J]. Structural Concrete, 2017, 18 (6): 929- 937
doi: 10.1002/suco.2017.18.issue-6
5 朱红兵. 公路钢筋混凝土简支梁桥疲劳试验与剩余寿命预测方法研究[D]. 长沙: 中南大学, 2011: 11?12.
ZHU Hong-bing. Research on fatigue test and residual life prediction method of highway reinforced-concrete simply-supported beam bridge [D]. Changsha: Central South University, 2011: 11?12.
6 VAN PAEPEGEM W, DEGRIECK J A new coupled approach of residual stiffness and strength for fatigue of fiber-reinforced composites[J]. International Journal of Fatigue, 2002, 24 (7): 747
doi: 10.1016/S0142-1123(01)00194-3
7 MA Y, XIANG Y, WANG L, et al Fatigue life prediction for aging RC beams considering corrosive environments[J]. Engineering Structures, 2014, (79): 211- 221
8 刘芳平, 周建庭 基于疲劳应变演化的混凝土弯曲强度退化分析[J]. 中国公路学报, 2017, 30 (4): 97- 105
LIU Fang-ping, ZHOU Jian-ting Concrete bending strength degradation analysis based on fatigue strain evolution[J]. China Journal of Highway and Transport, 2017, 30 (4): 97- 105
doi: 10.3969/j.issn.1001-7372.2017.04.012
9 CHOPRA A K. Dynamics of structures theory and applications to earthquake engineering [M]. 3rd ed. London: Prentice Hall, 2006.
10 HAMED E, FROSTIG Y Free vibrations of cracked prestressed concrete beams[J]. Engineering Structures, 2004, 26 (11): 1611- 1621
doi: 10.1016/j.engstruct.2004.06.004
11 曹晖, 郑星, 华建民, 等 基于非线性振动特性的预应力混凝土梁损伤识别[J]. 工程力学, 2014, 32 (2): 190- 194
CAO Hui, ZHENG Xing, HUA Jian-min, et al Damage detection of prestressed concrete beams based on nonlinear dynamic characteristics[J]. Engineering Mechanics, 2014, 32 (2): 190- 194
12 SANGKEUN A, EUN-BEOM J, HYO-IN K, et al Identification of stiffness distribution of fatigue loaded polymer concrete through vibration measurements[J]. Composite Structures, 2016, 136: 11- 15
doi: 10.1016/j.compstruct.2015.09.026
13 ELYAS G, GARY S P, EMMANUEL M Finite element analysis for fatigue damage reduction in metallic riveted bridges using pre-stressed cfrp plates[J]. Polymers, 2014, 6 (4): 1096- 1118
doi: 10.3390/polym6041096
14 余志武, 李进洲, 宋力 重载铁路桥梁疲劳试验研究[J]. 土木工程学报, 2012, 45 (12): 115- 126
YU Zhi-wu, LI Jin-zhou, SONG Li Experimental study on fatigue behaviors of heavy-haul railway bridges[J]. China Civil Engineering Journal, 2012, 45 (12): 115- 126
15 中华人民共和国住房与城乡建设部, 中华人民共和国国家质量监督检验检疫总局. 混凝土结构试验方法标准: GB/T 50152−2012 [S]. 北京: 中国建筑工业出版社, 2012: 35–41.
16 LIU Fang-ping, ZHOU Jian-ting Experimental research on fatigue damage of reinforced concrete rectangular beam[J]. KSCE Journal of Civil Engineering, 2018, 22 (9): 3512- 3523
doi: 10.1007/s12205-018-1767-y
17 汤红卫, 李士彬, 朱慈勉 基于刚度下降的混凝土梁疲劳累积损伤模型的研究[J]. 铁道学报, 2007, 29 (3): 84- 88
TANG Hong-wei, LI Shi-bin, ZHU Ci-mian A fatigue cumulative damage model of RC beam based on stiffness degradation[J]. Journal of the China Railway Society, 2007, 29 (3): 84- 88
doi: 10.3321/j.issn:1001-8360.2007.03.016
18 牛鹏志, 黄培彦, 姚国文, 等 CFL增强RC梁的疲劳累积损伤模型[J]. 华南理工大学学报: 自然科学版, 2007, 35 (2): 23- 26
NIU Peng-zhi, HUANG Pei-yan, YAO Guo-wen, et al Fatigue accumulative damage model of rc beam strengthened with carbon fiber laminate[J]. Journal of South China University of Technology: Natural Science Edition, 2007, 35 (2): 23- 26
19 SAIIDI M, DOUGLAS B, FENG S Prestress force effect on vibration frequency of concrete bridges[J]. Journal of Structural Engineering, 1994, 120 (7): 2233- 2241
doi: 10.1061/(ASCE)0733-9445(1994)120:7(2233)
20 李瑞鸽. 全预应力混凝土梁动力性能研究及有效预应力识别[D]. 武汉: 华中科技大学, 2009: 74–76.
LI Rui-ge. Research on dynamic performance of full prestressed concrete beam and identification of virtual prestressing force [D]. Wuhan: Huazhong University of Science and Technology, 2009: 74–76.
21 杜进生, 刘西拉 基于结构变形的无粘结预应力筋应力变化研究[J]. 土木工程学报, 2003, 36 (8): 12- 19
DU Jin-sheng, LIU Xi-la Research on the variations of unbounded prestressed tendon stresses based upon the structural deformation[J]. China Civil Engineering Journal, 2003, 36 (8): 12- 19
doi: 10.3321/j.issn:1000-131X.2003.08.003
22 WU X H, OTANI S, SHIOHARA H Tendon model for nonlinear analysis of prestressed concrete structures[J]. Journal of Structural Engineering, ASCE, 2001, 127 (4): 398- 405
doi: 10.1061/(ASCE)0733-9445(2001)127:4(398)
23 雷兵. 部分预应力混凝土梁疲劳性能试验研究及数值模拟[D]. 大连: 大连理工大学, 2013: 60–61.
LEI Bing. Experimental research and numerical simulation on mechanical properties of P.P.C beam under fatigue loading [D]. Dalian: Dalian University of Technology, 2013: 60–61.
[1] 刘佩,朱海鑫,杨维国,皇甫楠琦. 机械振动引起的高层建筑共振与减振响应实测[J]. 浙江大学学报(工学版), 2020, 54(1): 102-109.
[2] 黄祖慰,雷俊卿,桂成中,郭殊伦. 斜拉桥正交异性钢桥面板疲劳试验研究[J]. 浙江大学学报(工学版), 2019, 53(6): 1071-1082.
[3] 周瑾,高天宇,陈怡,席鸿皓. 采用动力测试的双转子卧螺离心机模型修正[J]. 浙江大学学报(工学版), 2019, 53(2): 241-249.
[4] 戴美玲, 杨福俊, 何小元, 代祥俊. 新型空心球结构的压缩力学性能[J]. 浙江大学学报(工学版), 2018, 52(11): 2043-2049.
[5] 廖子南, 邵旭东, 乔秋衡, 曹君辉, 刘湘宁. 钢-超高性能混凝土组合板横向受弯静力试验及有限元模拟[J]. 浙江大学学报(工学版), 2018, 52(10): 1954-1963.
[6] 范海贵, 陈志平, 徐烽, 唐小雨, 苏文强. 基于实测沉降的浮顶储罐变形分析[J]. 浙江大学学报(工学版), 2017, 51(9): 1824-1833.
[7] 金伟良, 周峥栋, 张军, 毛江鸿, 崔磊, 潘崇根. 基于动态压磁的锈蚀钢筋疲劳特性的试验研究[J]. 浙江大学学报(工学版), 2017, 51(2): 225-230.
[8] 刘海宾, 王勇, 马鹏磊, 谢玉东. 基于平行式振荡翼系统参数耦合分析[J]. 浙江大学学报(工学版), 2017, 51(1): 153-159.
[9] 赵庆娟, 徐杰, 单德彬, 郭斌. 基于阵列微通道的电磁成形数值模拟及实验研究[J]. 浙江大学学报(工学版), 2017, 51(1): 198-203.
[10] 何奔,王欢,洪义,王立忠,赵长军,秦肖. 竖向荷载对黏土地基中单桩水平受荷性能的影响[J]. 浙江大学学报(工学版), 2016, 50(7): 1221-1229.
[11] 何志明, 张晓晶, 刘天琦, 杨树勋. 300M钢耳片孔挤压强化全过程有限元模拟[J]. 浙江大学学报(工学版), 2016, 50(4): 783-791.
[12] 宋筱轩,冯天恒,黄平捷,侯迪波,张光新. 基于动态数据驱动的突发水污染事故仿真方法[J]. 浙江大学学报(工学版), 2015, 49(1): 63-68.
[13] 楼文娟,杨伦,陈勇,阎东. 覆冰导线静张力对输电塔横担的作用特征[J]. J4, 2013, 47(11): 1917-1925.
[14] 楼文娟, 姜雄, 夏亮, 金晓华, 王振华. 长横担输电塔风致薄弱部位及加强措施[J]. J4, 2013, 47(10): 1798-1784.
[15] 欧阳雯欣, 王清远, 石宵爽, 谭莲飞, 彭泽维. PBL剪力连接件的疲劳试验与分析[J]. J4, 2012, 46(6): 1090-1096.