Abstract
Previous research shows that an accurate simulation of vehicle–bridge systems is not feasible using beam models because they cannot adequately represent the torsional and transverse behavior of a bridge. Three-dimensional dynamic vehicle–bridge analytical solutions and FE models can also be cumbersome to develop and are prone to errors from idealization and modeling assumptions. To address these limitations, this paper presents a novel analytical vehicle–bridge simulation method that utilizes the experimentally estimated modal parameters of a bridge structure. The estimated modes from ambient vibration tests inherently enable the simulation to be valid for any generalized structural system and boundary condition because they truly represent the actual structure. In this paper, the mathematical derivation of the analytical model using plate vibration is presented in detail, the framework for the application of the model is outlined, and the proposed model is validated using a full-scale case study arterial highway bridge in the Canadian Province of New Brunswick. The proposed model offers a valuable solution applicable to real-time structural health monitoring and diagnostics, bridge weight in motion, and drive-by vehicle monitoring fields.
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Data Availability Statement
All data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (ALLRP558332-20) and the New Brunswick Department of Transportation and Infrastructure (2020-87-1) for supporting this research.
References
Akima, H. 1970. “A new method of interpolation and smooth curve fitting based on local procedures.” J. ACM 17 (4): 589–602. https://doi.org/10.1145/321607.321609.
Akin, J. E., and M. Mofid. 1989. “Numerical solution for response of beams with moving mass.” J. Struct. Eng. 115 (1): 120–131. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:1(120).
An, L., D. Li, P. Yu, and P. Yuan. 2016. “Numerical analysis of dynamic response of vehicle–bridge coupled system on long-span continuous girder bridge.” Theor. Appl. Mech. Lett. 6 (4): 186–194. https://doi.org/10.1016/j.taml.2016.05.006.
Arjomandi, K., and Y. Araki. 2019. “Monitoring time in operational modal tests with broad and narrow band excitations.” Structures 22: 245–251. https://doi.org/10.1016/j.istruc.2019.08.009.
Brincker, R., A. Skafte, M. López-Aenlle, A. Sestieri, W. D’Ambrogio, and A. Canteli. 2014. “A local correspondence principle for mode shapes in structural dynamics.” Mech. Syst. Sig. Process. 45 (1): 91–104. https://doi.org/10.1016/j.ymssp.2013.10.025.
Colmenares, D., A. Andersson, and R. Karoumi. 2022. “Closed-form solution for mode superposition analysis of continuous beams on flexible supports under moving harmonic loads.” J. Sound Vib. 520: 116587. https://doi.org/10.1016/j.jsv.2021.116587.
Deng, L., and C. S. Cai. 2009. “Identification of parameters of vehicles moving on bridges.” Eng. Struct. 31 (10): 2474–2485. https://doi.org/10.1016/j.engstruct.2009.06.005.
Ding, L., H. Hao, and X. Zhu. 2009. “Evaluation of dynamic vehicle axle loads on bridges with different surface conditions.” J. Sound Vib. 323 (3–5): 826–848. https://doi.org/10.1016/j.jsv.2009.01.051.
Dmitriev, A. S. 1974. “Transverse vibrations of a three-span beam under a moving load.” Sov. Appl. Mech. 10 (11): 1263–1266. https://doi.org/10.1007/BF00882128.
Dmitriev, A. S. 1982. “Dynamics of continuous multispan beams under a moving force.” Sov. Appl. Mech. 18 (2): 179–186. https://doi.org/10.1007/BF00883326.
Dormand, J. R., and P. J. Prince. 1986. “A reconsideration of some embedded Runge—Kutta formulae.” J. Comput. Appl. Math. 15 (2): 203–211. https://doi.org/10.1016/0377-0427(86)90027-0.
Elkasem, N. Z. A., M. A. Abdel-Mooty, and S. A. Mourad. 2009. “Dynamic response of highway bridges to moving vehicles considering higher modes.” J. Eng. Appl. Sci. 56 (1): 21–38.
Fitzgerald, P. C., E. Sevillano, E. J. OBrien, and A. Malekjafarian. 2017. “Bridge weigh-in-motion using a moving force identification algorithm.” In Proc., 10th Int. Conf. on Structural Dynamics, EURODYN 2017, 2955–2960. Amsterdam, Netherlands: Elsevier.
Foda, M. A., and Z. Abduljabbar. 1998. “A dynamic green function formulation for the response of a beam structure to a moving mass.” J. Sound Vib. 210 (3): 295–306. https://doi.org/10.1006/jsvi.1997.1334.
Fritsch, F. N., and R. E. Carlson. 1980. “Monotone piecewise cubic interpolation.” SIAM J. Numer. Anal. 17 (2): 238–246. https://doi.org/10.1137/0717021.
Gong, L., and M. S. Cheung. 2008. “Computer simulation of dynamic interactions between vehicle and long span box girder bridges.” Tsinghua Sci. Technol. 13: 71–77. https://doi.org/10.1016/S1007-0214(08)70129-9.
Green, M. F., and D. Cebon. 1997. “Dynamic interaction between heavy vehicles and highway bridges.” Comput. Struct. 62 (2): 253–264. https://doi.org/10.1016/S0045-7949(96)00198-8.
ISO. 2016. Mechanical vibration—Road surface profiles—Reporting of measured data. ISO 8608. Geneva: ISO.
Jeffcott, H. H. 1929. “VI. On the vibration of beams under the action of moving loads.” London Edinburgh Dublin Philos. Mag. J. Sci. 8 (48): 66–97. https://doi.org/10.1080/14786440708564857.
Johansson, C., C. Pacoste, and R. Karoumi. 2013. “Closed-form solution for the mode superposition analysis of the vibration in multi-span beam bridges caused by concentrated moving loads.” Comput. Struct. 119: 85–94. https://doi.org/10.1016/j.compstruc.2013.01.003.
Li, H., J. Wekezer, and L. Kwasniewski. 2008. “Dynamic response of a highway bridge subjected to moving vehicles.” J. Bridge Eng. 13 (5): 439–448. https://doi.org/10.1061/(ASCE)1084-0702(2008)13:5(439).
MacLeod, E., B. Wyman, J. Matthews, and K. Arjomandi. 2023. “Practical considerations for implementing SHM systems in highway bridges.” In Proc., Canadian Society of Civil Engineering Annual Conf., 2021, edited by S. Walbridge, M. Nik-Bakht, K. T. W. Ng, M. Shome, M. S. Alam, A. El Damatty, and G. Lovegrove. Singapore: Springer. CSCE International Structural Specialty Conference, Lecture Notes in Civil Engineering.
Nassif, H. H., and M. Liu. 2004. “Analytical modeling of bridge–road–vehicle dynamic interaction system.” J. Vib. Control 10 (2): 215–241. https://doi.org/10.1177/1077546304033950.
Nikkhoo, A., M. Ebrahimzadeh Hassanabadi, S. Eftekhar Azam, and J. Vaseghi Amiri. 2014. “Vibration of a thin rectangular plate subjected to series of moving inertial loads.” Mech. Res. Commun. 55: 105–113. https://doi.org/10.1016/j.mechrescom.2013.10.009.
Nikkhoo, A., and F. R. Rofooei. 2012. “Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass.” Acta Mech. 223 (1): 15–27. https://doi.org/10.1007/s00707-011-0547-2.
O’Brien, E., A. González, C. Caprani, Y. Li, and N. Harris. 2006. “Bridge dynamics and loading.” In Proc., Bridge and Infrasturcture Research in Ireland, 347–358. Dublin, Ireland: Trinity College Dublin and University College Dublin.
Overbey, L. A., C. C. Olson, and M. D. Todd. 2007. “A parametric investigation of state-space-based prediction error methods with stochastic excitation for structural health monitoring.” Smart Mater. Struct. 16 (5): 1621–1638. https://doi.org/10.1088/0964-1726/16/5/016.
Paeglite, I., and J. Smirnovs. 2015. “Dynamic effects caused by the bridge–vehicle interaction.” In Proc., 5th Int. Conf. Civil Engineering. Jelgava, Latvia: Latvia University of Agriculture.
Pesterev, A. V., B. Yang, L. A. Bergman, and C.-A. Tan. 2001. “Response of elastic continuum carrying multiple moving oscillators.” J. Eng. Mech. 127 (3): 260–265. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:3(260).
Rao, S. S. 2006. Vibration of continuous systems. Hoboken, NJ: Wiley.
Sadeghi Eshkevari, S., T. J. Matarazzo, and S. N. Pakzad. 2020. “Bridge modal identification using acceleration measurements within moving vehicles.” Mech. Syst. Sig. Process. 141: 106733. https://doi.org/10.1016/j.ymssp.2020.106733.
Shao, Y., C. Miao, J. M. W. Brownjohn, and Y. Ding. 2022. “Vehicle–bridge interaction system for long-span suspension bridge under random traffic distribution.” Structures 44: 1070–1080. https://doi.org/10.1016/j.istruc.2022.08.074.
Shi, Z., and N. Uddin. 2021. “Theoretical vehicle bridge interaction model for bridges with non-simply supported boundary conditions.” Eng. Struct. 232: 111839. https://doi.org/10.1016/j.engstruct.2020.111839.
Shokravi, H., H. Shokravi, N. Bakhary, M. Heidarrezaei, S. S. Rahimian Koloor, and M. Petrů. 2020. “Vehicle-assisted techniques for health monitoring of bridges.” Sensors 20 (12): 3460. https://doi.org/10.3390/s20123460.
Stancioiu, D., S. James, H. Ouyang, and J. E. Mottershead. 2009. “Vibration of a continuous beam excited by a moving mass and experimental validation.” J. Phys. Conf. Ser. 181 (1): 012084. https://doi.org/10.1088/1742-6596/181/1/012084.
Structural Vibrations Solutions. 2021. ARTeMIS modal 7.1.0.0. Aalborg East, Denmark: Structural Vibrations Solutions.
Tan, C., N. Uddin, E. J. OBrien, P. J. McGetrick, and C.-W. Kim. 2019. “Extraction of bridge modal parameters using passing vehicle response.” J. Bridge Eng. 24 (9): 1–15.
Tan, C., H. Zhao, E. J. OBrien, N. Uddin, P. C. Fitzgerald, P. J. McGetrick, and C.-W. Kim. 2021. “Extracting mode shapes from drive-by measurements to detect global and local damage in bridges.” Struct. Infrastruct. Eng. 17 (11): 1582–1596. https://doi.org/10.1080/15732479.2020.1817105.
The MathWorks. 2021. MATLAB 2021a release. Natick, MA: The MathWorks.
Timoshenko, S. P. 1922. “CV. On the forced vibrations of bridges.” London Edinburgh Dublin Philos. Mag. J. Sci. 43 (257): 1018–1019. https://doi.org/10.1080/14786442208633953.
Wang, S., D. Mccrum, and E. J. O. Brien. 2020. “Acceleration based bridge weigh-in-motion using moving force identification.” In Proc., Civil Engineering Research in Ireland 2020, 6–9. Cork, Ireland: Civil Engineering Research Association of Ireland.
Wang, S., E. J. OBrien, and D. P. McCrum. 2021. “A novel acceleration-based moving force identification algorithm to detect global bridge damage.” Appl. Sci. 11 (16): 7271. https://doi.org/10.3390/app11167271.
Xu, H., and W. L. Li. 2008. “Dynamic behavior of multi-span bridges under moving loads with focusing on the effect of the coupling conditions between spans.” J. Sound Vib. 312 (4–5): 736–753. https://doi.org/10.1016/j.jsv.2007.11.011.
Yang, Y. B., and C. W. Lin. 2005. “Vehicle–bridge interaction dynamics and potential applications.” J. Sound Vib. 284 (1–2): 205–226. https://doi.org/10.1016/j.jsv.2004.06.032.
Yang, Y.-B., C. W. Lin, and J. D. Yau. 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.
Yang, Y.-B., and J.-D. Yau. 1997. “Vehicle–bridge interaction element for dynamic analysis.” J. Struct. Eng. 123 (11): 1512–1518. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:11(1512).
Yang, Y.-B., J.-D. Yau, and L.-C. Hsu. 1997. “Vibration of simple beams due to trains moving at high speeds.” Eng. Struct. 19 (11): 936–944. https://doi.org/10.1016/S0141-0296(97)00001-1.
Yang, Y. B., B. Zhang, Y. Chen, Y. Qian, and Y. Wu. 2019. “Bridge damping identification by vehicle scanning method.” Eng. Struct. 183: 637–645. https://doi.org/10.1016/j.engstruct.2019.01.041.
Yoshizawa, M., T. Takizawa, and Y. Tsujioka. 1985. “Vibration of a beam and a moving load with sprung and unsprung masses.” Bull. JSME 28 (239): 911–918. https://doi.org/10.1299/jsme1958.28.911.
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© 2023 American Society of Civil Engineers.
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Received: Oct 26, 2022
Accepted: Jun 2, 2023
Published online: Jul 13, 2023
Published in print: Sep 1, 2023
Discussion open until: Dec 13, 2023
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