考虑比例阻尼影响的梁式结构损伤识别方法
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摘要
为了研究阻尼对梁式结构损伤识别结果的影响、提高损伤诊断和安全评估的精度,将梁式结构简化为比例阻尼系统,推导出基于单元模态应变能一阶灵敏度的解析表达式,建立了考虑比例阻尼影响的梁式结构损伤方程组及其损伤识别方法.采用混凝土简支梁数值算例模拟了6种小损伤工况,损伤识别结果表明:基于单元模态应变能一阶灵敏度的损伤指标能够识别出小损伤位置和损伤程度,最大相对误差不超过10%.分别采用包含不同位置损伤的实验室简支钢梁模型组和一座有实测损伤的梁桥验证所提方法的可行性.研究结果表明:考虑比例阻尼影响时,基于单元模态应变能的损伤识别方法可以识别出梁式结构小损伤和多损伤.
To study the effect of damping on damage identification and improve the accuracy of damage diagnosis and safety evaluation of beam type structures,the beam structure was simplified as a proportional damping system. The analytic expression of the proportional damping system was derived based on the first-order sensitivity of elemental modal strain energy. The damage equations of the beam type structures considering proportional damping were established,and the corresponding damage identification method was proposed. A concrete beam numerical model was used to simulate six cases of minor damages. The damage identification results show that the damage index based on the first-order sensitivity of elemental modal strain energy can identify micro damage locations and damage degrees,and the maximum relative error is less than 10%. The simply-supported steel beams with different damage locations in the laboratory and a real girder bridge with actual damages were used to verify the feasibility of the proposed method. The results indicate that the damage identification method based on elemental modal strain energy can identify micro-damages and multiple damages of beam type structures considering proportional damping.
To study the effect of damping on damage identification and improve the accuracy of damage diagnosis and safety evaluation of beam type structures,the beam structure was simplified as a proportional damping system. The analytic expression of the proportional damping system was derived based on the first-order sensitivity of elemental modal strain energy. The damage equations of the beam type structures considering proportional damping were established,and the corresponding damage identification method was proposed. A concrete beam numerical model was used to simulate six cases of minor damages. The damage identification results show that the damage index based on the first-order sensitivity of elemental modal strain energy can identify micro damage locations and damage degrees,and the maximum relative error is less than 10%. The simply-supported steel beams with different damage locations in the laboratory and a real girder bridge with actual damages were used to verify the feasibility of the proposed method. The results indicate that the damage identification method based on elemental modal strain energy can identify micro-damages and multiple damages of beam type structures considering proportional damping.
引文
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[11]史治宇,罗绍湘,张令弥.结构破损定位的单元模态应变能变化率法[J].振动工程学报,1998,11(3):356-360.Shi Zhiyu,Luo Shaoxiang,Zhang Lingmi.Determination of structural damage location based on elemental modal strain energy change[J].Journal of Vibration Engineering,1998,11(3):356-360.(in Chinese)
[12]王根会,胡良红.基于单元模态应变能法的桥梁结构损伤识别研究[J].铁道学报,2006,28(3):83-86.DOI:10.3321/j.issn:1001-8360.2006.03.017.Wang Genhui,Hu Lianghong.Study on damage identification of bridge structure based on the method of element modal strain energy[J].Journal of the China Railway Society,2006,28(3):83-86.DOI:10.3321/j.issn:1001-8360.2006.03.017.(in Chinese).
[13]Ren W X.A Singular value decomposition based truncation algorithm in solving the structural damage equations[J].Acta Mechanica Solida Sinica,2005,18(2):181-188.
[14]宗周红,褚福鹏,牛杰.基于响应面模型修正的桥梁结构损伤识别方法[J],土木工程学报,2013,46(2):115-122.Zong Zhouhong,Chu Fupeng,Niu Jie.Damage identification methods using response surface based finite element model updating of bridge structures[J].China Civil Engineering Journal,2013,46(2):115-122.(in Chinese)
[15]曹晖,张新亮,曹永红,等.采用改进单元刚度折减系数法识别结构损伤[J].振动与冲击,2008,27(6):132-139.DOI:10.3969/j.issn.1000-3835.2008.06.029.Cao Hui,Zhang Xinliang,Cao Yonghong,et al.Damage identification based on improved elemental stiffness reduction factor[J].Journal of Vibration and Shock,2008,27(6):132-139.DOI:10.3969/j.issn.1000-3835.2008.06.029.(in Chinese)
[2]Das S,Saha P,Patro S K.Vibration-based damage detection techniques used for health monitoring of structures:A review[J].Journal of Civil Structural Health Monitoring,2016,6(3):477-507.DOI:10.1007/s13349-016-0168-5.
[3]宗周红,钟儒勉,郑沛娟,等.基于健康监测的桥梁结构损伤预后和安全预后研究进展及挑战[J].中国公路学报,2014,27(12):46-57.Zong Zhouhong,Zhong Rumian,Zheng Peijuan,et al.Damage and safety prognosis of bridge structures based on structural health monitoring:Progress and challenges[J].China Journal of Highway and Transport,2014,27(12):46-57.(in Chinese)
[4]Yan W J,Ren W X,Huang T L.Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity[J].Mechanical Systems and Signal Processing,2012,28:183-194.DOI:10.1016/j.ymssp.2011.04.011.
[5]颜王吉.单元模态应变能灵敏度及其在结构损伤识别中的应用[D].长沙:中南大学土木建筑学院,2008.
[6]Zimoch Z.Sensitivity analysis of vibrating systems[J].Journal of Sound and Vibration,1987,115(3):447-458.DOI:10.1016/0022-460x(87)90289-6.
[7]Lee I W,Kim D O,Jung G H.Natural frequency and mode shape sensitivities of damped systems:PartⅠ,distinct natural frequencies[J].Journal of Sound and Vibration,1999,223(3):399-412.DOI:10.1006/jsvi.1998.2129.
[8]Niu J,Zong Z,Chu F.Damage identification method of girder bridges based on finite element model updating and modal strain energy[J].Science China Technological Sciences,2015,58(4):701-711.DOI:10.1007/s11431-014-5763-2.
[9]Doebling S W,Hemez F M,Peterson L D,et al.Improved damage location accuracy using strain energy based on mode selection criteria[J].AIAA Journal,1997,35(4):693-699.DOI:10.2514/3.13567.
[10]Guan H,Karbhari V M.Improved damage detection method based on element modal strain damage index using sparse measurement[J].Journal of Sound and Vibration,2008,309(3/4/5):465-494.DOI:10.1016/j.jsv.2007.07.060.
[11]史治宇,罗绍湘,张令弥.结构破损定位的单元模态应变能变化率法[J].振动工程学报,1998,11(3):356-360.Shi Zhiyu,Luo Shaoxiang,Zhang Lingmi.Determination of structural damage location based on elemental modal strain energy change[J].Journal of Vibration Engineering,1998,11(3):356-360.(in Chinese)
[12]王根会,胡良红.基于单元模态应变能法的桥梁结构损伤识别研究[J].铁道学报,2006,28(3):83-86.DOI:10.3321/j.issn:1001-8360.2006.03.017.Wang Genhui,Hu Lianghong.Study on damage identification of bridge structure based on the method of element modal strain energy[J].Journal of the China Railway Society,2006,28(3):83-86.DOI:10.3321/j.issn:1001-8360.2006.03.017.(in Chinese).
[13]Ren W X.A Singular value decomposition based truncation algorithm in solving the structural damage equations[J].Acta Mechanica Solida Sinica,2005,18(2):181-188.
[14]宗周红,褚福鹏,牛杰.基于响应面模型修正的桥梁结构损伤识别方法[J],土木工程学报,2013,46(2):115-122.Zong Zhouhong,Chu Fupeng,Niu Jie.Damage identification methods using response surface based finite element model updating of bridge structures[J].China Civil Engineering Journal,2013,46(2):115-122.(in Chinese)
[15]曹晖,张新亮,曹永红,等.采用改进单元刚度折减系数法识别结构损伤[J].振动与冲击,2008,27(6):132-139.DOI:10.3969/j.issn.1000-3835.2008.06.029.Cao Hui,Zhang Xinliang,Cao Yonghong,et al.Damage identification based on improved elemental stiffness reduction factor[J].Journal of Vibration and Shock,2008,27(6):132-139.DOI:10.3969/j.issn.1000-3835.2008.06.029.(in Chinese)
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