Abstract
This study investigates the numerical simulation of the interaction between a high-speed train and perforated beams. The perforated bridge beam is modeled according to Timoshenko and Euler–Bernoulli beam theories with a uniform cross-section area. The high-speed dynamic model has been considered a 10-DOF multibody system. The equation of motion perforated bridge beam and high-speed train is obtained by Hamilton's principle. Then, some parameters of the perforated beam, such as different aspect ratios, the filling ratio, and the number of holes along the cross-section area, have been investigated. The frequency variation of the Timoshenko perforated beam has been evaluated according to the nondimensional parameter presented in the study, considering different filling and aspect ratios properties. Then, the mass comparison of the perforated beam with a fully solid beam has been conducted as a dynamical and statical comparison. With this method, the dynamic responses of perforated beams will be examined for the first time compared to the fully solid bridges used in previous studies in the literature. Per length mass of the perforated beam is less than the fully solid beam by the ratios of %41.51 and %30.07 in terms of dynamic and static behavior. Consequently, it has been observed that the perforated beam affects both bridge dynamic and high-speed train's dynamic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data supporting this study's findings are available on request from the corresponding author.
Code availability
The code is not applicable due to privacy.
References
Abdelrahman, A.A., Ashry, M., Alshorbagy, A.E., Abdallah, W.S.: On the mechanical behavior of two directional symmetrical functionally graded beams under moving load. Int. J. Mech. Mater. Des. 17, 563–586 (2021a). https://doi.org/10.1007/s10999-021-09547-9
Abdelrahman, A.A., Esen, I., Eltaher, M.A.: Vibration response of Timoshenko perforated microbeams under accelerating load and thermal environment. Appl. Math. Comput. 407, 126307 (2021b). https://doi.org/10.1016/j.amc.2021.126307
Abdelrahman, A.A., Esen, I., Özarpa, C., Eltaher, M.A.: Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory. Appl. Math. Model 96, 215–235 (2021c). https://doi.org/10.1016/j.apm.2021.03.008
Akin, J.E., Mofid, M.: Numerical solution for response of beams with moving mass. Manager 115, 1–2 (1989)
Dynamics Analysis of Timoshenko Perforated Microbeams under Moving Loads n.d.
Assie, A., Akbaş, D., Bashiri, A.H., Abdelrahman, A.A., Eltaher, M.A.: Vibration response of perforated thick beam under moving load. Eur. Phys. J. Plus 13 (2021). https://doi.org/10.1140/epjp/s13360-021-01224-2
Attia, M.A., Mahmoud, F.F.: Analysis of viscoelastic Bernoulli-Euler nanobeams incorporating nonlocal and microstructure effects. Int. J. Mech. Mater. Des. 13, 385–406 (2017). https://doi.org/10.1007/s10999-016-9343-4
Biggs, J.M.: Introduction to structural dynamics (1964)
Chen, Z., Fang, H.: An alternative solution of train-track dynamic ınteraction. Shock Vib. 2019 (2019). https://doi.org/10.1155/2019/1859261
Cicirello, A.: On the response bounds of damaged Euler-Bernoulli beams with switching cracks under moving masses. Int. J. Solids Struct 172–173, 70–83 (2019). https://doi.org/10.1016/j.ijsolstr.2019.05.003
Demirtaş, S., Ozturk, H.: Effects of the crack location on the dynamic response of multi-storey frame subjected to the passage of a high-speed train. J. Braz. Soc. Mech. Sci. Eng. 43, 1–13 (2021). https://doi.org/10.1007/s40430-020-02794-5
Dugush, Y.A., Eisenberger, M.: Vibrations of non-uniform continuous beams under moving loads. J. Os Sound Vib. 254, 911–926 (2002). https://doi.org/10.1006/jsvi.2001.4135
Eltaher, M.A., Kabeel, A.M., Almitani, K.H., Abdraboh, A.M.: Static bending and buckling of perforated nonlocal size-dependent nanobeams. Microsyst. Technol. 24, 4881–4893 (2018a). https://doi.org/10.1007/s00542-018-3905-3
Eltaher, M.A., Abdraboh, A.M., Almitani, K.H.: Resonance frequencies of size dependent perforated nonlocal nanobeam. Microsyst. Technol. 24, 3925–3937 (2018b). https://doi.org/10.1007/s00542-018-3910-6
Esen, I.: Response of a micro-capillary system exposed to a moving mass in magnetic field using nonlocal strain gradient theory. Int. J. Mech. Sci. 188, 105937 (2020). https://doi.org/10.1016/j.ijmecsci.2020.105937
Froio, D., Rizzi, E., Simões, F.M.F., Pinto Da Costa, A.: Dynamics of a beam on a bilinear elastic foundation under harmonic moving load. Acta Mech. 229, 4141–4165 (2018). https://doi.org/10.1007/s00707-018-2213-4
Frýba, L.: Vibration of solids and structures under moving loads. Vib. Solids Struct. Mov. Loads (1999). https://doi.org/10.1680/vosasuml.35393
He, S., Fang, Z., Mosallam, A.S.: Push-out tests for perfobond strip connectors with UHPC grout in the joints of steel-concrete hybrid bridge girders. Eng. Struct. 135, 177–190 (2017). https://doi.org/10.1016/j.engstruct.2017.01.008
Hirzinger, B., Adam, C., Salcher, P.: Dynamic response of a non-classically damped beam with general boundary conditions subjected to a moving mass-spring-damper system. Int. J. Mech. Sci. 185 (2020). https://doi.org/10.1016/j.ijmecsci.2020.105877
Hoang, T., Duhamel, D., Foret, G.: Dynamical response of a Timoshenko beams on periodical nonlinear supports subjected to moving forces. Eng. Struct 176, 673–680 (2018). https://doi.org/10.1016/j.engstruct.2018.09.028
Karkon, M.: An efficient finite element formulation for bending, free vibration and stability analysis of Timoshenko beams. J. Braz. Soc. Mech. Sci. Eng. 40, 1–16 (2018). https://doi.org/10.1007/s40430-018-1413-0
Khasawneh, F.A., Segalman, D.: Exact and numerically stable expressions for Euler-Bernoulli and Timoshenko beam modes. Appl. Acoust. 151, 215–228 (2019). https://doi.org/10.1016/j.apacoust.2019.03.015
Koç, M.A., Esen, İ, Eroğlu, M., Çay, Y.: A new numerical method for analysing the interaction of a bridge structure and travelling cars due to multiple high-speed trains Mehmet Akif Koç Mustafa Ero ğ lu Yusuf Çay. Int. J. Heavy Veh. Syst. 28, 79–109 (2021)
Koç, M.A.: Finite element and numerical vibration analysis of a Timoshenko and Euler-Bernoulli beams traversed by a moving high-speed train. J. Braz. Soc. Mech. Sci. Eng. 7 (2021). https://doi.org/10.1007/s40430-021-02835-7
Koç, M.A, Esen, İ.: Modelling and analysis of vehicle-structure-road coupled interaction considering structural flexibility, vehicle parameters and road roughness. J. Mech. Sci. Technol. 31 (2017). https://doi.org/10.1007/s12206-017-0403-y
König, P., Salcher, P., Adam, C., Hirzinger, B.: Dynamic analysis of railway bridges exposed to high-speed trains considering the vehicle–track–bridge–soil interaction. Acta Mech (2021). https://doi.org/10.1007/s00707-021-03079-1
Li, H., Yin, X.W., Wu, W.W.: Dynamic stiffness approach to vibration transmission within a beam structure carrying spring–mass systems. Int. J. Mech. Mater. Des. 16, 279–288 (2020). https://doi.org/10.1007/s10999-019-09474-w
Liang, C., Liu, Y., Yang, F.: Flexural strengths of steel girder-concrete abutment connections incorporating the effect of perfobond connectors. Eng. Struct. 214, 110611 (2020). https://doi.org/10.1016/j.engstruct.2020.110611
Liu, C., Wu, D., Li, Y., Du, Y.: Large-scale pavement roughness measurements with vehicle crowdsourced data using semi-supervised learning. Transp. Res. Part C Emerg. Technol. 125, 103048 (2021). https://doi.org/10.1016/j.trc.2021.103048
Liu, C., Wu, D., Li, Y., Jiang, S., Du, Y.: Mathematical insights into the relationship between pavement roughness and vehicle vibration. Int. J. Pavement Eng. 23, 1935–1947 (2022). https://doi.org/10.1080/10298436.2020.1830092
Lu, N., Wang, H., Wang, K., Liu, Y.: Maximum probabilistic and dynamic traffic load effects on short-to-medium span bridges. C Comput. Model Eng. Sci. 127, 345–60 (2021). https://doi.org/10.32604/cmes.2021.013792
Luschi, L., Pieri, F.: An analytical model for the determination of resonance frequencies of perforated beams. J. Micromech. Microeng. 24 (2014). https://doi.org/10.1088/0960-1317/24/5/055004
Martínez-Rodrigo, M.D., Andersson, A., Pacoste, C., Karoumi, R.: Resonance and cancellation phenomena in two-span continuous beams and its application to railway bridges. Eng. Struct. 222, 111103 (2020). https://doi.org/10.1016/j.engstruct.2020.111103
Misaghi, S., Tirado, C., Nazarian, S., Carrasco, C.: Impact of pavement roughness and suspension systems on vehicle dynamic loads on flexible pavements. Transp. Eng. 3, 100045 (2021). https://doi.org/10.1016/j.treng.2021.100045
Montenegro, P.A., Carvalho, H., Ribeiro, D., Calçada, R., Tokunaga, M., Tanabe, M., et al.: Assessment of train running safety on bridges: a literature review. Eng. Struct. 241, 112425 (2021). https://doi.org/10.1016/j.engstruct.2021.112425
Nguyen, M.H., Hirano, Y., Nakajima, A., Fujikura, S., Niimura, R.: Experimental evaluation of the shear capacity of perfobond strips with steel fiber-reinforced mortar in narrow joint structures. Structures 28, 1173–1186 (2020). https://doi.org/10.1016/j.istruc.2020.09.059
Pala, Y., Beycimen, S., Kahya, C.: Damped vibration analysis of cracked Timoshenko beams with restrained end conditions. J. Braz. Soc. Mech. Sci. Eng. 42, 1–16 (2020). https://doi.org/10.1007/s40430-020-02558-1
Stanišić, M.M., Hardin, J.C.: On the response of beams to an arbitrary number of concentrated moving masses. J. Franklin Inst. 287, 115–123 (1969). https://doi.org/10.1016/0016-0032(69)90120-3
Suzuki, A., Suzuki, K., Kimura, Y.: Ultimate shear strength of perfobond shear connectors subjected to fully reversed cyclic loading. Eng. Struct. 248, 113240 (2021). https://doi.org/10.1016/j.engstruct.2021.113240
Timoshenko S.: On the forced vibration of bridges. Philos. Mag. Ser. 80 (1921)
Ting, E.C., Genin, J., Ginsberg, J.H.: A general algorithm for moving mass problems. J. Sound Vib. 33, 49–58 (1974). https://doi.org/10.1016/S0022-460X(74)80072-6
Van Do, V.N., Ong, T.H., Thai, C.H.: Dynamic responses of Euler-Bernoulli beam subjected to moving vehicles using isogeometric approach. Appl. Math Model 51, 405–428 (2017). https://doi.org/10.1016/j.apm.2017.06.037
Wen, R.K.: Dynamic response of beams traversed by two-axle loads. J. Eng. Mech. Div. (1960) 86
Wu, J., Dai, C.: dynamic responses of multispan nonuniform beam due to moving loads. J. Struct. Eng. 113, 458–474 (1987). https://doi.org/10.1061/(asce)0733-9445(1987)113:3(458)
Xu, L., Zhai, W.: A three-dimensional dynamic model for train-track interactions. Appl. Math Model 76, 443–465 (2019). https://doi.org/10.1016/j.apm.2019.04.037
Yang, J.P., Sun, J.Y.: Pitching effect of a three-mass vehicle model for analyzing vehicle-bridge interaction. Eng. Struct. 224, 111248 (2020). https://doi.org/10.1016/j.engstruct.2020.111248
Yang, Y.B., Yau, J.D., Wu, Y.S.: Vehicle-Bridge Interaction Dynamics with Applications to High-Speed Railways. World Scientific Publishing Co., Pte. Ltd., Danvers (2004)
Yu, H., Yang, Y., Yuan, Y.: Analytical solution for a finite Euler – Bernoulli beam with single discontinuity in section under arbitrary dynamic loads. Appl. Math. Model 60, 571–580 (2018). https://doi.org/10.1016/j.apm.2018.03.046
Zhai, W., Han, Z., Chen, Z., Ling, L., Zhu, S.: Train–track–bridge dynamic interaction: a state-of-the-art review. Veh. Syst. Dyn. 57, 984–1027 (2019). https://doi.org/10.1080/00423114.2019.1605085
Zhang, H., Liu, Y., Deng, Y.: Temperature gradient modeling of a steel box-girder suspension bridge using Copulas probabilistic method and field monitoring. Adv. Struct. Eng. 24, 947–961 (2021). https://doi.org/10.1177/1369433220971779
Zheng, S., Liu, Y., Yoda, T., Lin, W.: Parametric study on shear capacity of circular-hole and long-hole perfobond shear connector. J. Constr. Steel Res. 117, 64–80 (2016). https://doi.org/10.1016/j.jcsr.2015.09.012
Zhu, Q., Li, L., Chen, C.J., Liu, C.Z., Di, Hu.G.: A low-cost lateral active suspension system of the high-speed train for ride quality based on the resonant control method. IEEE Trans. Ind. Electron. 65, 4187–4196 (2018). https://doi.org/10.1109/TIE.2017.2767547
Zou, Y., Zheng, K., Zhou, J., Zhang, Z., Li, X.: Mechanical behavior of perfobond connector group in steel–concrete joint of hybrid bridge. Structures 30, 925–936 (2021). https://doi.org/10.1016/j.istruc.2021.01.046
Zuo, Y., Mosallam, A., Xin, H., Liu, Y., He, J.: Flexural performance of a hybrid GFRP-concrete bridge deck with composite T-shaped perforated rib connectors. Compos. Struct. 194, 263–278 (2018). https://doi.org/10.1016/j.compstruct.2018.03.105
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Koç, M.A., Eroğlu, M. & Esen, İ. Dynamic analysis of high-speed train moving on perforated Timoshenko and Euler–Bernoulli beams. Int J Mech Mater Des 18, 893–917 (2022). https://doi.org/10.1007/s10999-022-09610-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10999-022-09610-z