Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Theoretical formulation for vehicle-bridge interaction analysis based on perturbation method

  • Tan, Yongchao (School of Civil Engineering, Central South University) ;
  • Cao, Liang (College of Civil Engineering, Hunan University) ;
  • Li, Jiang (School of Civil Engineering, Chongqing University)
  • Received : 2021.12.10
  • Accepted : 2022.01.13
  • Published : 2022.04.25
⟨ Previous Next ⟩

Abstract

A three-mass vehicle model including one rigid mass and two unsprung masses is adopted to predict the vehicle-bridge interaction (VBI) and to establish the nonlinear coupled governing equations. To overcome the numerical instability and large computation problems concerning the vehicle-bridge system, the perturbation method is used to convert the nonlinear coupled governing equations into a set of linear uncoupled equations. Formulas for bridge's natural frequencies considering both the VBI and the dynamic responses of bridge and vehicle are proposed. Compared with the numerical results obtained by the Newmark-β method, the theoretical solutions for natural frequencies and dynamic responses are validated. The effects of the important factors of unsprung mass, vehicle damping, surface irregularity on the natural frequencies and dynamic responses of bridge and vehicle are discussed, based on the theoretical solutions.

Keywords

Acknowledgement

The authors are grateful for the financial support provided by the National Natural Science Foundation of China (Grant No. 51908084).

References

  1. Bucinskas, P. and Andersen, L.V. (2020), "Dynamic response of vehicle-bridge-soil system using lumped-parameter models for structure-soil interaction", Comput. Struct., 238, 106270. https://doi.org/10.1016/j.compstruc.2020.106270.
  2. Cai, C.B., He, Q.L., Zhu, S.Y., Zhai, W.M. and Wang, M.Z. (2019), "Dynamic interaction of suspension-type monorail vehicle and bridge: Numerical simulation and experiment", Mech. Syst. Signal Pr., 118, 388-407. https://doi.org/10.1016/j.ymssp.2018.08.062.
  3. Erdogan, Y.S. and Catbas, N.F. (2020), "Seismic response of a highway bridge in case of vehicle-bridge dynamic interaction", Earthq. Struct., 18(1), 1-14. https://doi.org/10.12989/eas.2020.18.1.014.
  4. Fryba, L. (1972), Vibration of Solids and Structures under Moving Loads, Noordhoff International Publishing, Groningen.
  5. Gonzalez, A. and Mohammed, O. (2019), "Damage detection in bridges based on patterns of dynamic amplification", Struct. Control Hlth., 26 (7), e2361. https://doi.org/10.1002/stc.2361.
  6. Greco, F. and Lonetti, P. (2018), "Numerical formulation based on moving mesh method for vehicle-bridge interaction", Adv. Eng. Softw., 121, 75-83. https://doi.org/10.1016/j.advengsoft.2018.03.013.
  7. Greco, F., Lonetti, P. and Pascuzzo, A. (2020), "A moving mesh FE methodology for vehicle-bridge interaction modeling", Mech. Adv. Mater. Struct., 27(14), 1256-1268. https://doi.org/10.1080/15376494.2018.1506955.
  8. ISO 8608: 2016 (2016), Mechanical Vibration-Road Surface Profiles-Reporting of Measured Data, International Organization for Standardization, Geneva.
  9. Liu, H.Y., Yu, Z.W., Guo, W. and Han, Y. (2021), "A model for investigating vehicle-bridge interaction under high moving speed", Struct. Eng. Mech., 77(5), 627-635. https://doi.org/10.12989/sem.2021.77.5.627.
  10. Liu, J.P., Cao, L. and Chen, Y.F. (2019a), "Analytical solution for free vibration of multi-span continuous anisotropic plates by the perturbation method", Struct. Eng. Mech., 69(3), 283-291. https://doi.org/10.12989/sem.2019.69.3.283.
  11. Liu, L.Y., Qin, J.L., Zhou, Y.L., Xi, R. and Peng, S.Y. (2019b), "Structural noise mitigation for viaduct box girder using acoustic modal contribution analysis", Struct. Eng. Mech., 72(4), 421-432. https://doi.org/10.12989/sem.2019.72.4.421.
  12. Liu, X.W., Xie, J., Wu, C. and Huang, X.C. (2008), "Semi-analytical solution of vehicle-bridge interaction on transient jump of wheel", Eng. Struct., 30(9), 2401-2412. https://doi.org/10.1016/j.engstruct.2008.01.007.
  13. Montenegro, P.A., Castro, J.M., Calcada, R., Soares, J.M., Coelho, H. and Pacheco, P. (2021), "Probabilistic numerical evaluation of dynamic load allowance factors in steel modular bridges using a vehicle-bridge interaction model", Eng. Struct., 226, 111316. https://doi.org/10.1016/j.engstruct.2020.111316.
  14. Mousavi, M., Holloway, D., Olivier, J.C. and Gandomi, A.H. (2021), "Beam damage detection using synchronisation of peaks in instantaneous frequency and amplitude of vibration data", Measure., 168, 108297. https://doi.org/10.1016/j.measurement.2020.108297.
  15. Rieker, J.R., Lin, Y.H. and Trethewey, M.W. (1996), "Discretization considerations in moving load finite element beam models", Finite Elem. Anal. Des., 21(3), 129-144. https://doi.org/10.1016/0168-874X(95)00029-S.
  16. Shafigh, A., Ahmadi, H.R. and Bayat, M. (2021), "Seismic investigation of cyclic pushover method for regular reinforced concrete bridge", Struct. Eng. Mech., 78(1), 41-52. https://doi.org/10.12989/sem.2021.78.1.041.
  17. Shi, Z.H. and Uddin, N. (2021), "Extracting multiple bridge frequencies from test vehicle-A theoretical study", J. Sound Vib., 490, 115735. https://doi.org/10.1016/j.jsv.2020.115735.
  18. Wu, C.P. and Lin, C.C. (2020) "Static analysis of multiple graphene sheet systems in cylindrical bending and resting on an elastic medium", Struct. Eng. Mech., 75(1), 109-122. https://doi.org/10.12989/sem.2020.75.1.109.
  19. Yang, J. and Cao, C.Y. (2020), "Wheel size embedded two-mass vehicle model for scanning bridge frequencies", Acta Mechanica, 231(4), 1461-1475. https://doi.org/10.1007/s00707-019-02595-5.
  20. Yang, J.P. (2021), "Theoretical formulation of three-mass vehicle model for vehicle-bridge interaction", Int. J. Struct. Stab. Dyn., 21(07), 2171004. https://doi.org/10.1142/S0219455421710048.
  21. Yang, J.P. and Chen, B.H. (2018), "Two-mass vehicle model for extracting bridge frequencies", Int. J. Struct. Stab. Dyn., 18(4), 1850056. https://doi.org/10.1142/S0219455418500566.
  22. Yang, J.P. and Sun, J.Y. (2020), "Pitching effect of a three-mass vehicle model for analyzing vehicle-bridge interaction", Eng. Struct., 224, 11248. https://doi.org/10.1016/j.engstruct.2020.111248.
  23. Yang, Y.B. and Lin, B.H. (1995), "Vehicle-bridge interaction analysis by dynamic condensation method", J. Struct. Eng., 121(11), 1636-1643. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:11(1636).
  24. Yang, Y.B. and Yang, J.P. (2018), "State-of-the-art review on modal identification and damage detection of bridges by moving test vehicles", Int. J. Struct. Stab. Dy., 18(2), 1850025. https://doi.org/10.1142/S0219455418500256.
  25. Yang, Y.B. and Yau, J.D. (1997), "Vehicle-bridge interaction element for dynamic analysis", J. Struct. Eng., ASCE, 123(11), 1512-1518. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:11(1512).
  26. Yang, Y.B. Li, Y.C. and Chang, K.C. (2012), "Effect of road surface roughness on the response of a moving vehicle for identification of bridge frequencies", Interact. Multisc. Mech., 5(4), 347-368. https://doi.org/10.12989/imm.2012.5.4.347.
  27. Yang, Y.B., Chang, C.H. and Yau, J.D. (1999), "An element for analysing vehicle-bridge systems considering vehicle's pitching effect", Int. J. Numer. Meth. Eng., 46(7), 1031-1047. https://doi.org/10.1002/(SICI)1097-0207(19991110)46:7<1031::AID-NME738>3.0.CO;2-V.
  28. Yang, Y.B., Lin, C.W. and Yau, J.D. (2004), "Extracting bridge frequencies from the dynamic response of a passing vehicle", J. Sound Vib., 272(3-5), 471-493. https://doi.org/10.1016/S0022-460X(03)00378-X.
  29. Yang, Y.B., Wang, Z.L., Shi, K., Xu, H. and Wu, Y.T. (2020), "State-of-the-art of vehicle-based methods for detecting various properties of highway bridges and railway tracks", Int. J. Struct. Stab. Dyn., 20(13), 2041004. https://doi.org/10.1142/S0219455420410047.
  30. Yang, Y.B., Zhang, B., Wang, T.Y., Xu, H. and Wu, Y.T. (2019), "Two-axle test vehicle for bridges: Theory and applications", Int. J. Mech. Sci., 152, 51-62. https://doi.org/10.1016/j.ijmecsci.2018.12.043.
  31. Yigit, C.O., El-Mowafy, A., Bezcioglu, M. and Dindar, A.A. (2020), "Investigating the effects of ultra-rapid, rapid vs. final precise orbit and clock products on high-rate GNSS-PPP for capturing dynamic displacements", Struct. Eng. Mech., 73(4), 427-436. https://doi.org/10.12989/sem.2020.73.4.427.
  32. Zhan, Y. and Au, F.T.K. (2019), "Bridge surface roughness identification based on vehicle-bridge interaction", Int. J. Struct. Stab. Dyn., 19(7), 1950069. https://doi.org/10.1142/S021945541950069X.