Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A dynamic finite element method for the estimation of cable tension

  • Huang, Yonghui (Guangzhou University-Tamkang University Joint Research Center for Engineering Structure Disaster Prevention and Control, Guangzhou University) ;
  • Gan, Quan (Network & Educational Technology Center, Jinan University) ;
  • Huang, Shiping (School of Civil Engineering and Transportation, South China University of Technology) ;
  • Wang, Ronghui (School of Civil Engineering and Transportation, South China University of Technology)
  • Received : 2018.03.26
  • Accepted : 2018.09.12
  • Published : 2018.11.25
⟨ Previous Next ⟩

Abstract

Cable supported structures have been widely used in civil engineering. Cable tension estimation has great importance in cable supported structures' analysis, ranging from design to construction and from inspection to maintenance. Even though the Bernoulli-Euler beam element is commonly used in the traditional finite element method for calculation of frequency and cable tension estimation, many elements must be meshed to achieve accurate results, leading to expensive computation. To improve the accuracy and efficiency, a dynamic finite element method for estimation of cable tension is proposed. In this method, following the dynamic stiffness matrix method, frequency-dependent shape functions are adopted to derive the stiffness and mass matrices of an exact beam element that can be used for natural frequency calculation and cable tension estimation. An iterative algorithm is used for the exact beam element to determine both the exact natural frequencies and the cable tension. Illustrative examples show that, compared with the cable tension estimation method using the conventional beam element, the proposed method has a distinct advantage regarding the accuracy and the computational time.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Banerjee J.R. (1989), "Coupled bending-torsional dynamic stiffness matrix for beam elements", Int. J. Numer. Meth. Eng., 28(6), 1283-1289. https://doi.org/10.1002/nme.1620280605
  2. Banerjee J.R. (1997), "Dynamic stiffness formulation for structural elements: a general approach", Comput. Struct., 63(1), 101-103. https://doi.org/10.1016/S0045-7949(96)00326-4
  3. Banerjee, J.R. and Fisher, S.A. (1992), "Coupled bending-torsional dynamic stiffness matrix for axially loaded beam elements", Int. J. Numer. Meth. Eng., 33(4), 739-751. https://doi.org/10.1002/nme.1620330405
  4. Banerjee, J.R. and Williams, F.W. (1985), "Exact Bernoulli-Euler dynamic stiffness matrix for a range of tapered beams", Int. J. Numer. Meth. Eng., 21(12), 2289-2302. https://doi.org/10.1002/nme.1620211212
  5. Banerjee, J.R. and Williams, F.W. (1992), "Coupled bendingtorsional dynamic stiffness matrix for Timoshenko beam elements", Comput. Struct., 42(3), 301-310. https://doi.org/10.1016/0045-7949(92)90026-V
  6. Bao, Y.Q., Shi, Z.Q., Beck, J.L., Li, H. and Hou, T.Y. (2017), "Identification of time-varying cable tension forces based on adaptive sparse time-frequency analysis of cable vibrations", Struct. Contr. Health Monitor., 24(3).
  7. Cheng, F.Y. (1970), "Vibration of Timoshenko beams and frameworks", J. Struct. Div., 96(3), 551-571.
  8. Cheng, F.Y. and Tseng, W.H. (1973), "Dynamic matrix of Timoshenko beam columns", J. Struct. Div., 99(3), 527-549.
  9. Clough, R.W. and Penzien, J. (1995), Dynamics of Structures, 3rd Edition, Computer & Structures, Inc., Berkeley, U.S.A.
  10. Friberg, P.O. (1983), "Coupled vibration of beams-an exact dynamic element stiffness matrix", Int. J. Numer. Meth. Eng., 19(4), 479-493. https://doi.org/10.1002/nme.1620190403
  11. Hallauer, W.L. and Liu, R.Y.L. (1982), "Beam bending-torsion dynamic stiffness method for calculation of exact vibration modes", J. Sound Vibr., 85(1), 105-113. https://doi.org/10.1016/0022-460X(82)90473-4
  12. Hashemi, S.M. and Richard, M.J. (2000), "A dynamic finite element (DFE) method for free vibrations of bending-torsion coupled beam", Aerosp. Sci. Technol., 4(1), 41-55. https://doi.org/10.1016/S1270-9638(00)00114-0
  13. Howson, W.P. and Williams, F.W. (1973), "Natural frequencies of frames with axially loaded Timoshenko members", J. Sound Vibr., 26(4), 503-515. https://doi.org/10.1016/S0022-460X(73)80216-0
  14. Huang, Y.H., Fu, J.Y., Gan, Q., Wang, R.H., Pi, Y.L. and Liu, A.R. (2017), "New method for identifying internal forces of hangers based on form-finding theory of suspension cable", J. Brid. Eng., 22(11), 96-105.
  15. Huang, Y.H., Fu, J.Y., Wang, R.H., Gan, Q. and Liu, A.R. (2015), "Unified practical formulas for vibration-based method of cable tension estimation", Adv. Struct. Eng., 18(3), 405-422. https://doi.org/10.1260/1369-4332.18.3.405
  16. Huang, Y.H., Fu, J.Y., Wang, R.H., Gan, Q., Rao, R. and Liu, A.R. (2015), "Practical formula to calculate tension of vertical cable with hinged-fixed conditions based on vibration method", J. Vibroeng., 16(2), 997-1009.
  17. Issa, M.S. (1988), "Natural frequencies of continuous curved beams on Winkler-type foundation", J. Sound Vibr., 127(2), 291-301. https://doi.org/10.1016/0022-460X(88)90304-5
  18. Kalousek, V. (1973), Dynamics in Engineering Structures, Butterworths, London, U.K.
  19. Kim, B.H. and Park, T. (2007), "Estimation of cable tension force using the frequency-based system identification method", J. Sound Vibr., 304(3-5), 660-676. https://doi.org/10.1016/j.jsv.2007.03.012
  20. Kim, J.M., Lee, J. and Sohn, H. (2018), "Detection of tension force reduction in a post-tensioning tendon using pulsed-eddycurrent measurement", Struct. Eng. Mech., 62(2), 129-139.
  21. Kolousek, V. (1941), "Anwendung des Gesetzes der virtuellen Verschiebungen und des Reziprozitatssatzes in der Stabwerksdynamic", Arch. Appl. Mech., 12(6), 363-370.
  22. Leung, A.Y.T. (1992), "Dynamic stiffness for lateral buckling", Comput. Struct., 42(3), 321-325. https://doi.org/10.1016/0045-7949(92)90028-X
  23. Liao, W.Y., Ni, Y.Q. and Zheng, G. (2012), "Tension force and structural parameter identification of bridge cables", Adv. Struct. Eng., 15(6), 983-995. https://doi.org/10.1260/1369-4332.15.6.983
  24. Lunden, R. and Akesson, B.A. (1983), "Damped second-order Rayleigh-Timoshenko beam vibration in spacean exact complex dynamic member stiffness matrix", Int. J. Numer. Meth. Eng., 19(3), 431-449. https://doi.org/10.1002/nme.1620190310
  25. Ma, H.T. (2008), "Exact solutions of axial vibration problems of elastic bars", Int. J. Numer. Meth. Eng., 16(5), 241-252.
  26. Ma, H.T. (2010), "Exact solution of vibration problems of frame structures", Commun. Numer. Meth. Eng., 26(5), 587-596.
  27. Ma, L. (2017), "A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions", J. Sound Vibr., 409, 65-80. https://doi.org/10.1016/j.jsv.2017.07.043
  28. Maes, K., Peeters, J., Reynders, E., Lombaert, G. and Roeck, G.D. (2017), "Identification of axial forces in beam members by local vibration measurements", J. Sound Vibr., 332(21), 5417-5432. https://doi.org/10.1016/j.jsv.2013.05.017
  29. Mohammadnejad, M. and Kazemi, H.H. (2018), "A new and simple analytical approach to determining the natural frequencies of framed tube structures", Struct. Eng. Mech., 56(6), 939-957. https://doi.org/10.12989/sem.2015.56.6.939
  30. Mohsin, M.E. and Sadek, E.A. (1968), "The distributed massstiffness technique for the dynamical analysis of complex frameworks", Struct. Eng., 46(11), 345-351.
  31. Park, D.U. and Kim, N.S. (2014), "Back analysis technique for tensile force on hanger cables of a suspension bridge", J. Vibr. Contr., 20(5), 761-772. https://doi.org/10.1177/1077546312464679
  32. Wang, J., Liu, W.Q., Lu, W. and Han, X.J. (2015), "Estimation of main cable tension force of suspension bridges based on ambient vibration frequency measurements", Struct. Eng. Mech., 56(6), 939-957. https://doi.org/10.12989/sem.2015.56.6.939
  33. Wang, R.H., Gan, Q., Huang, Y.H. and Ma, H.T. (2011), "Estimation of tension in cables with intermediate elastic supports using finite-element method", J. Brid. Eng., 16(5), 675-678. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000192
  34. Wang, T.M. and Kinsman, T.A. (1970), "Vibration of frame structures according to the Timoshenko theory", J. Sound Vibr., 14(2), 215-227. https://doi.org/10.1016/0022-460X(71)90385-3
  35. Williams, F.W. and Kennedy, D. (1987), "Exact dynamic member stiffnesses for a beam on an elastic foundation", Earthq. Eng. Struct. Dyn., 15(1), 133-136. https://doi.org/10.1002/eqe.4290150110
  36. Wittrick, W.H. and Williams, F.W. (1971), "A general algorithm for computing natural frequencies of elastic structures", Quarter. J. Mech. Appl. Math., 24(3), 263-284. https://doi.org/10.1093/qjmam/24.3.263
  37. Yan, B.F., Yu, J.Y. and Soliman, M. (2015), "Estimation of cable tension force independent of complex boundary conditions", J. Eng. Mech., 141(1), 15-22.
  38. Yuan, S., Ye, K.S., Xiao, C., Williams, F.W. and Kennedy, D. (2007), "Exact dynamic stiffness method for non-uniform Timoshenko beam vibrations and Bernoulli-Euler column buckling", J. Sound Vibr., 303(1), 526-537. https://doi.org/10.1016/j.jsv.2007.01.036
  39. Yucel, A., Arpaci, A. and Tufekci, E. (2014), "Coupled axialflexural-torsional vibration of Timoshenko frames", J. Sound Vibr., 20(15), 2366-2377.
  40. Zarhaf, S.E.H.A.M., Norouzi, M., Allemang, R.L., Hunt, V.J., Helmicki, A. and Nims, D.K. (2017), "Stay force estimation in cable-stayed bridges using stochastic subspace identification methods", J. Brid. Eng., 22(9), 04017055. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001091
  41. Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method for Solid and Structural Mechanics, 2nd Eition, Butterworth-Heinemann, Oxford.

Cited by

  1. Numerical assessment of the damage-tolerance properties of polyester ropes and metallic strands vol.79, pp.1, 2018, https://doi.org/10.12989/sem.2021.79.1.083