Abstract
In this study, the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated. The boundary conditions and properties of each beam vary, and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations. By examining a high-speed railway (HSR) with mixed boundary conditions, the rationality for the newly proposed method is verified, the difference in simulated multiple-beam models with different beam numbers is explored, and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined. Results suggest that the number of beams in the model should be as close to the actual beam number as possible. Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure. Neglecting the track-structure can overestimate the resonant speed of a high-speed railway, simply-supported beam bridge. The effective interval of foundation stiffness (EIFS) can provide a reference for future engineering designs.
Similar content being viewed by others
References
Abu-Hilal M (2006), “Dynamic Response of a Double Euler-Bernoulli Beam Due to a Moving Constant Load,” Journal of Sound and Vibration, 297(3–5): 477–491.
Ariaei A, Ziaei-Rad S and Ghayour M (2011), “Transverse Vibration of a Multiple-Timoshenko Beam System with Intermediate Elastic Connections Due to a Moving Load,” Archive of Applied Mechanics, 81(3): 263–281.
Chen YH and Sheu JT (1995), “Beam On Viscoelastic Foundation and Layered Beam,” Journal of Engineering Mechanics, 121(2): 340–344.
Feng Y, Jiang L and Zhou W (2020), “Dynamic Response of a Three-Beam System with Intermediate Elastic Connections Under a Moving Load/Mass-Spring,” Earthquake Engineering and Engineering Vibration, 19(2): 377–395.
Guo W, Xia H and Xu Y (2010), “Running Safety Analysis of a Train on the Tsing Ma Bridge Under Turbulent Winds,” Earthquake Engineering and Engineering Vibration, 9(3): 307–318.
Jiang L, Feng Y, Zhou W and He B (2019a), “Vibration Characteristic Analysis of High-Speed Railway Simply Supported Beam Bridge-Track Structure System,” Steel and Composite Structures, 31(6): 591–600.
Jiang L, Zhang Y, Feng Y, Zhou W and Tan Z (2019b), “Dynamic Response Analysis of a Simply Supported Double-Beam System under Successive Moving Loads,” Applied Sciences, 9(10): 2162.
Jiang L, Zhang Y, Feng Y, Zhou W and Tan Z (2020), “Simplified Calculation Modeling Method of Multi-Span Bridges on High-Speed Railways Under Earthquake Condition,” Bulletin of Earthquake Engineering.
Karličić D, Cajić M, Murmu T, Kozić P and Adhikari S (2015), “Nonlocal Effects On the Longitudinal Vibration of a Complex Multi-Nanorod System Subjected to the Transverse Magnetic Field,” Meccanica, 50(6): 1605–1621.
Kelly SG and Srinivas S (2009), “Free Vibrations of Elastically Connected Stretched Beams,” Journal of Sound and Vibration, 326(3–5): 883–893.
Koroma SG, Hussein MFM and Owen JS (2014), “Vibration of a Beam On Continuous Elastic Foundation with Nonhomogeneous Stiffness and Damping Under a Harmonically Excited Mass,” Journal of Sound and Vibration, 333(9): 2571–2587.
Li J, Chen Y and Hua H (2008), “Exact Dynamic Stiffness Matrix of a Timoshenko Three-Beam System,” International Journal of Mechanical Sciences, 50(6): 1023–1034.
Li Y, Chen N, Zhao K and Liao H (2012), “Seismic Response Analysis of Road Vehicle-Bridge System for Continuous Rigid Frame Bridges with High Piers,” Earthquake Engineering and Engineering Vibration, 11(4): 593–602.
Li YX, Hu ZJ and Sun LZ (2016a), “Dynamical Behavior of a Double-Beam System Interconnected by a Viscoelastic Layer,” International Journal of Mechanical Sciences, 105: 291–303.
Li YX and Sun LZ (2016b), “Transverse Vibration of an Undamped Elastically Connected Double-Beam System with Arbitrary Boundary Conditions,” Journal of Engineering Mechanics, 142(2): 4015070.
Lou P, Yu Z and Au FTK (2012), “Rail-Bridge Coupling Element of Unequal Lengths for Analysing Train-Track-Bridge Interaction Systems,” Applied Mathematical Modelling, 36(4): 1395–1414.
Mao Q (2012), “Free Vibration Analysis of Elastically Connected Multiple-Beams by Using the Adomian Modified Decomposition Method,” Journal of Sound and Vibration, 331(11): 2532–2542.
Murmu T and Adhikari S (2011), “Axial Instability of Double-Nanobeam-Systems,” Physics Letters A, 375(3): 601–608.
Museros P, Moliner E and Martínez-Rodrigo MD (2013), “Free Vibrations of Simply-Supported Beam Bridges Under Moving Loads: Maximum Resonance, Cancellation and Resonant Vertical Acceleration,” Journal of Sound and Vibration, 332(2): 326–345.
Oniszczuk Z (2000), “Free Transverse Vibrations of Elastically Connected Simply Supported Double-Beams Complex System,” Journal of Sound and Vibration, 232(2): 387–403.
Oniszczuk Z (2003), “Forced Transverse Vibrations of an Elastically Connected Complex Simply Supported Double-Beam System,” Journal of Sound and Vibration, 264(2): 273–286.
Palmeri A and Adhikari S (2011), “A Galerkin-Type State-Space Approach for Transverse Vibrations of Slender Double-Beam Systems with Viscoelastic Inner Layer,” Journal of Sound and Vibration, 330(26): 6372–6386.
Stojanović V, Kozić P and Janevski G (2013), “Exact Closed-Form Solutions for the Natural Frequencies and Stability of Elastically Connected Multiple Beam System Using Timoshenko and High-Order Shear Deformation Theory,” Journal of Sound and Vibration, 332(3): 563–576.
Sun L, Xie W, He X and Hayashikawa T (2016), “Prediction and Mitigation Analysis of Ground Vibration Caused by Running High-Speed Trains on Rigid-Frame Viaducts,” Earthquake Engineering and Engineering Vibration, 15(1): 31–47.
Thambiratnam D and Zhuge Y (1996), “Dynamic Analysis of Beams on an Elastic Foundation Subjected to Moving Loads,” Journal of Sound and Vibration, 198(2): 149–169.
Vu HV, Ordonez AM and Kaenopp BH (2000), “Vibration of a Double-Beam System,” Journal of Sound and Vibration, 229(4): 807–822.
Wang L, Zhu Z, Bai Y, Li Q, Costa PA and Yu Z (2018), “A Fast Random Method for Three-Dimensional Analysis of Train-Track-Soil Dynamic Interaction,” Soil Dynamics and Earthquake Engineering, 115: 252–262.
Wu Y and Gao Y (2015), “Analytical Solutions for Simply Supported Viscously Damped Double-Beam System Under Moving Harmonic Loads,” Journal of Engineering Mechanics, 141(7): 4015004.
Wu Y and Gao Y (2016), “Dynamic Response of a Simply Supported Viscously Damped Double-Beam System Under the Moving Oscillator,” Journal of Sound & Vibration, 384: 194–209.
Xia H, Chen JG, Wei PB, Xia CY, DeRoeck G and Degrande G (2009), “Experimental Investigation of Railway Train-Induced Vibrations of Surrounding Ground and a Nearby Multi-Story Building,” Earthquake Engineering and Engineering Vibration, 8(1): 137–148.
Yan W, Zhao M, Sun Q and Ren W (2019), “Transmissibility-Based System Identification for Structural Health Monitoring: Fundamentals, Approaches, and Applications,” Mechanical Systems and Signal Processing, 117: 453–482.
Yang Y, Yau J and Hsu L (1997), “Vibration of Simple Beams Due to Trains Moving at High Speeds,” Engineering Structures, 19(11): 936–944.
Yang YB and Yau JD (2015), “Vertical and Pitching Resonance of Train Cars Moving Over a Series of Simple Beams,” Journal of Sound and Vibration, 337: 135–149.
Yang YB and Yau JD (2017), “Resonance of High-Speed Trains Moving Over a Series of Simple Or Continuous Beams with Non-Ballasted Tracks,” Engineering Structures, 143: 295–305.
Zhai W, He Z and Song X (2010), “Prediction of High-Speed Train Induced Ground Vibration Based on Train-Track-Ground System Model,” Earthquake Engineering and Engineering Vibration, 9(4): 545–554.
Zhan Y, Yao H, Lu Z and Yu D (2014), “Dynamic Analysis of Slab Track on Multi-Layered Transversely Isotropic Saturated Soils Subjected to Train Loads,” Earthquake Engineering and Engineering Vibration, 13(4): 731–740.
Zhang Y, Jiang L, Zhou W, Feng Y, Tan Z and Chai X (2020), “Study of Bridge-Subgrade Longitudinal Constraint Range for High-Speed Railway Simply-Supported Beam Bridge with CRTSII Ballastless Track Under Earthquake Excitation,” Construction and Building Materials, 241: 118026.
Acknowledgement
The work was financially supported by the National Natural Science Foundations of China (U1934207 and 51778630), the Hunan Innovative Provincial Construction Project (2019RS3009), the Innovation-driven Plan in Central South University (2020zzts159), and the Fundamental Research Funds for the Central Universities of Central South University (2018zzts189).
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by: National Natural Science Foundations of China under Grant Nos. U1934207 and 51778630, the Hunan Innovative Provincial Construction Project under Grant No. 2019RS3009, the Innovation-driven Plan in Central South University under Grant No. 2020zzts159, and the Fundamental Research Funds for the Central Universities of Central South University under Grant No. 2018zzts189
Rights and permissions
About this article
Cite this article
Zhang, Y., Jiang, L., Zhou, W. et al. Dynamic response analysis of a multiple-beam structure subjected to a moving load. Earthq. Eng. Eng. Vib. 21, 769–784 (2022). https://doi.org/10.1007/s11803-022-2106-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11803-022-2106-3