structural health monitoring; cable tension; end restraints; flexural rigidity; identification; mode shape; natural frequency
Abstract :
[en] This paper aims at presenting the guidelines to follow in order to set up an identification procedure which is able to determine the axial force, the flexural rigidity and the rotational end stiffnesses of slender and tensioned structural elements, based on measurements of their natural frequencies and mode shapes. First of all, when such an element is slightly affected by bending stiffness effects, perturbation methods can be applied to get a composite approximation for its natural frequencies and an asymptotic expression for its mode shapes. These simple analytical formulas allow to understand the role played by each model parameter in the modal response and show that the axial force, the flexural rigidity and the rotational end stiffnesses can be correctly identified under some conditions, which are established and provided in this document. Among others, it is necessary that the identification procedure relies on the first few natural frequencies and mode shapes, which are measured near each extremity of the element, as well as some natural frequencies associated with higher modes.
Disciplines :
Civil engineering
Author, co-author :
Geuzaine, Margaux ; Université de Liège - ULiège > Département ArGEnCo > Analyse sous actions aléatoires en génie civil
Foti, Francesco
Denoël, Vincent ; Université de Liège - ULiège > Département ArGEnCo > Analyse sous actions aléatoires en génie civil
Language :
English
Title :
Minimal requirements for the vibration-based identification of the axial force, the bending stiffness and the flexural boundary conditions in cables
Publication date :
October 2021
Journal title :
Journal of Sound and Vibration
ISSN :
0022-460X
eISSN :
1095-8568
Publisher :
Elsevier, United States
Volume :
511
Pages :
116326
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture SPW DGO2 - Service Public de Wallonie. Mobilité et des Voies hydrauliques
Ko, J.M., Ni, Y.Q., Zhou, H.F., Wang, J.Y., Zhou, X.T., Investigation concerning structural health monitoring of an instrumented cable-stayed bridge. Struct. Infrastruct. Eng., 2009.
Santos, João P., Crémona, Christian, Calado, Luís, Silveira, Paulo, Orcesi, André D., On-line unsupervised detection of early damage. Struct. Control Health Monit., 2016.
de Sá Caetano, Elsa, International Association for Bridge, and Structural Engineering. Cable Vibrations in Cable-Stayed Bridges Structural Engineering Documents, 2007, IABSE.
Kangas, S., Helmicki, A., Hunt, V., Sexton, R., Swanson, J., Cable-stayed bridges: Case study for ambient vibration-based cable tension estimation. J. Bridge Eng. 17:6 (2012), 839–846.
Gourmelon, Jean Paul, Fatigue des câbles de haubanage: Organisation et principaux résultats du programme de recherche dirigé par le LCPC. Bull. Lab. Ponts Chaussees(244–245), 2003, 53–71.
Siegert, D., Brevet, P., Fatigue of stay cables inside end fittings: high frequencies of wind induced vibrations. Bull.-Int. Org. Study Endur. Ropes, 89, 2005, 43.
Mehrabi, Armin B., In-service evaluation of cable-stayed bridges, overview of available methods and findings. J. Bridge Eng. 11:6 (2006), 716–724.
Kernicky, Timothy, Whelan, Matthew, Al-Shaer, Ehab, Dynamic identification of axial force and boundary restraints in tie rods and cables with uncertainty quantification using set inversion via interval analysis. J. Sound Vib. 423 (2018), 401–420.
Tabatabai, Habib, Inspection and Maintenance of Bridge Stay Cable Systems. 2005, Transportation Research Board of the National Academies, Washington.
Hua, X.G., Ni, Y.Q., Chen, Z.Q., Ko, J.M., Structural damage detection of cable-stayed bridges using changes in cable forces and model updating. J. Struct. Eng. 135:9 (2009), 1093–1106.
Clemente, Paolo, Bongiovanni, Giovanni, Buffarini, Giacomo, Saitta, Fernando, Structural health status assessment of a cable-stayed bridge by means of experimental vibration analysis. J. Civ. Struct. Health Monit., 2019.
Kim, Byeong Hwa, Park, Taehyo, Estimation of cable tension force using the frequency-based system identification method. J. Sound Vib. 304:3–5 (2007), 660–676.
Cho, Soojin, Yim, Jinsuk, Shin, Sung Woo, Jung, Hyung Jo, Yun, Chung Bang, Wang, Ming L., Comparative field study of cable tension measurement for a cable-stayed bridge. J. Bridge Eng. 18:8 (2013), 748–757.
Bedon, Chiara, Dilena, Michele, Morassi, Antonino, Ambient vibration testing and structural identification of a cable-stayed bridge. Meccanica 51:11 (2016), 2777–2796.
Benedettini, Francesco, Gentile, Carmelo, Operational modal testing and FE model tuning of a cable-stayed bridge. Eng. Struct., 2011.
Zhao, Xuefeng, Ri, Kwang, Wang, Niannian, Experimental verification for cable force estimation using handheld shooting of smartphones. J. Sens., 2017, 2017.
Yan, Banfu, Chen, Wenbing, Yu, Jiayong, Jiang, Xiaomo, Mode shape-aided tension force estimation of cable with arbitrary boundary conditions. J. Sound Vib. 440 (2019), 315–331.
De Mars, Ph., Hardy, D., Mesure des efforts dans les structures à câbles. Ann. Travaux Publics Belg. 6 (1985), 515–531.
Preumont, A., Twelve Lectures on Structural Dynamics, Vol. 198. 2013.
Irvine, H.M., Caughey, T.K., The linear theory of free vibrations of a suspended cable. Proc. R. Soc. Lond. 341:1626 (1974), 299–315.
Ceballos, Marcelo A., Prato, Carlos A., Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests. J. Sound Vib. 317:1–2 (2008), 127–141.
Geier, R., De Roeck, G., Flesch, R., Accurate cable force determination using ambient vibration measurements. Struct. Infrastruct. Eng. 2:1 (2006), 43–52.
Lagomarsino, Sergio, Calderini, Chiara, The dynamical identification of the tensile force in ancient tie-rods. Eng. Struct. 27:6 (2005), 846–856.
Huang, Yong Hui, Fu, Ji Yang, Wang, Rong Hui, Gan, Quan, Liu, Ai Rong, Unified practical formulas for vibration-based method of cable tension estimation. Adv. Struct. Eng. 18:3 (2015), 405–422.
Tang, Sheng Hua, Fang, Zhi, Yang, Suo, Practical formula for the estimation of cable tension in frequency method considering the effects of boundary conditions. Hunan Daxue Xuebao/J. Hunan Univ. Nat. Sci., 2012.
Géradin, M., Rixen, D., Mechanical Vibrations: Theory and Application to Structural Dynamics. 1997, Wiley.
Foti, Francesco, Geuzaine, Margaux, Denoël, Vincent, On the identification of the axial force and bending stiffness of stay cables anchored to flexible supports. Appl. Math. Model., 2020.
Li, Suzhen, Reynders, Edwin, Maes, Kristof, De Roeck, Guido, Vibration-based estimation of axial force for a beam member with uncertain boundary conditions. J. Sound Vib. 332:4 (2013), 795–806.
Rebecchi, Giovanni, Tullini, Nerio, Laudiero, Ferdinando, Estimate of the axial force in slender beams with unknown boundary conditions using one flexural mode shape. J. Sound Vib. 332:18 (2013), 4122–4135.
Chen, Chien Chou, Wu, Wen Hwa, Chen, Shin Yi, Lai, Gwolong, A novel tension estimation approach for elastic cables by elimination of complex boundary condition effects employing mode shape functions. Eng. Struct. 166:March (2018), 152–166.
Zhang, Songhan, Shen, Ruili, Wang, Yuan, Roeck, Guido De, Lombaert, Geert, A two-step methodology for cable force identification. J. Sound Vib., 472, 2020, 115201.
Timoshenko, S.P., Gere, J.M., Prager, W., Theory of elastic stability, second edition. J. Appl. Mech., 1962.
Natsiavas, S., Mode localization and frequency veering in a non-conservative mechanical system with dissimilar components. J. Sound Vib. 165:1 (1993), 137–147.
Gattulli, Vincenzo, Lepidi, Marco, Localization and veering in the dynamics of cable-stayed bridges. Comput. Struct. 85:21–22 (2007), 1661–1678.
Au, F.T.K., Cheng, Y.S., Cheung, Y.K., Zheng, D.Y., On the determination of natural frequencies and mode shapes of cable-stayed bridges. Appl. Math. Model. 25:12 (2001), 1099–1115.
Liu, Ming-Yi, Zuo, Delong, Jones, Nicholas P., Analytical and numerical study of deck-stay interaction in a cable-stayed bridge in the context of field observations. J. Eng. Mech. 139:11 (2013), 1636–1652.
Abdel-Ghaffar, Ahmed M., Khalifa, Magdi A., Importance of cable vibration in dynamics of cable-stayed bridges. J. Eng. Mech. 117:11 (1991), 2571–2589.
Caetano, E., Cunha, A., Taylor, C.A., Investigation of dynamic cable-deck interaction in a physical model of a cable-stayed bridge. Part I: modal analysis. Earthq. Eng. Struct. Dyn. 29:4 (2000), 481–498.
Anna De Falco, Carlo Resta, Sevieri, Giacomo, Sensitivity analysis of frequency-based tie-rod axial load evaluation methods. Eng. Struct., 229, 2021, 111568.
Maes, K., Peeters, J., Reynders, E., Lombaert, G., De Roeck, G., Identification of axial forces in beam members by local vibration measurements. J. Sound Vib. 332:21 (2013), 5417–5432.
Zui, Hiroshi, Shinke, Tohru, Namita, Yoshio, Practical formulas for estimation of cable tension by vibration method. J. Struct. Eng. 122:6 (1996), 651–656.
Hinch, E.J., Perturbation Methods. 1995, Cambridge University Press, Cambridge.
Denoël, Vincent, Canor, Thomas, Patching asymptotics solution of a cable with a small bending stiffness. J. Struct. Eng. (U. S.), 2013.
Denoël, V., Detournay, E., Multiple scales solution for a beam with a small bending stiffness. J. Eng. Mech. 136:1 (2010), 69–77.
Mehrabi, Armin B., Tabatabai, Habib, Unified finite difference formulation for free vibration of cables. J. Struct. Eng. 124:11 (1998), 1313–1322.
Amabili, M., Carra, S., Collini, L., Garziera, R., Panno, A., Estimation of tensile force in tie-rods using a frequency-based identification method. J. Sound Vib. 329:11 (2010), 2057–2067.
Penzien, Joseph, Clough, Ray W., Dynamics of structures. Earthq. Eng. Handb., 2002, 3–1–3–40.
Shi, Z.Y., Law, S.S., Zhang, L.M., Structural damage detection from modal strain energy change. J. Eng. Mech. 126:12 (2000), 1216–1223.
Shabbir, Faisal, Khan, Muhammad Imran, Ahmad, Naveed, Tahir, Muhammad Fiaz, Ejaz, Naeem, Hussain, Jawad, Structural damage detection with different objective functions in noisy conditions using an evolutionary algorithm. Appl. Sci., 7(12), 2017.
Perera, Ricardo, Torres, Ronald, Structural damage detection via modal data with genetic algorithms. J. Struct. Eng. 132:9 (2006), 1491–1501.
Hou, Rongrong, Xia, Yong, Zhou, Xiaoqing, Structural damage detection based on l1 regularization using natural frequencies and mode shapes. Struct. Control Health Monit., 25(3), 2018, e2107 e2107 STC-17-0060.R1.
Xiang, Jiawei, Liang, Ming, He, Yumin, Experimental investigation of frequency-based multi-damage detection for beams using support vector regression. Eng. Fract. Mech. 131 (2014), 257–268.
Tondreau, Gilles, Deraemaeker, Arnaud, Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method. J. Sound Vib. 333:18 (2014), 4376–4401.
Brincker, Rune, Some elements of operational modal analysis. Shock Vib., 2014, 2014.
Storn, Rainer, Price, Kenneth, Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim., 1997.
Das, Swagatam, Abraham, Ajith, Chakraborty, Uday K., Konar, Amit, Differential evolution using a neighborhood-based mutation operator. IEEE Trans. Evol. Comput., 2009.