Abstract
The objective of this research is to study the dynamic response characteristics of a three-beam system with intermediate elastic connections under a moving load/mass-spring. In this study, the finite Sine-Fourier transform was performed for the dynamic partial differential equations of a simply supported three-beam system (SSTBS) under a moving load and a moving mass-spring, respectively. The dynamic partial differential equations were transformed into dynamic ordinary differential equations relative to the time coordinates, and the equations were solved and the displacement Fourier amplitude spectral expressions were obtained. Finally, based on finite Sine-Fourier inverse transform, the expressions for dynamic response of SSTBS under the moving load and moving mass-spring were obtained. The proposed method, along with ANSYS, was used to calculate the dynamic response of the SSTBS under a moving load/mass-spring at different speeds. The results obtained herein were consistent with the ANSYS numerical calculation results, verifying the accuracy of the proposed method. The influence of the load/mass-spring’s moving speed on the dynamic deflections of SSTBS were analyzed. SSTBS has several critical speeds under a moving load/mass-spring. The vertical acceleration incurred by a change in the vertical speed of SSTBS due to the movement of mass-spring and the centrifugal acceleration produced by the movement of massspring on the vertical curve generated by SSTBS vibration could not be neglected.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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): 477–491.
Abu-Hilal M (2007), “Free Transverse Vibrations of a Triple-Beam System,” Journal of Sound and Vibration, 241(4): 635–642.
Ba Zhenning, Kang Zeqing and Liang Jianwen (2018), “In-plane Dynamic Green’s Functions for Inclined and Uniformly Distributed Loads in a Multi-Layered Transversely Isotropic Half-Space,” Earthquake Engineering and Engineering Vibration, 17(2): 293–309.
Bendine K, Boukhoulda FB, Nouari M and Satla Z (2016), “Active Vibration Control of Functionally Graded Beams with Piezoelectric Layers Based on Higher Order Shear Deformation Theory,” Earthquake Engineering and Engineering Vibration, 15(4): 611–620.
Dimitrovová Z (2017), “New Semi-Analytical Solution for a Uniformly Moving Mass on a Beam on a Two-Parameter Visco-Elastic Foundation,” International Journal of Mechanical Sciences, 127: 142–162.
Jia HY, Zhang DY, Zheng SX, Xie WC and Pandey MD (2013), “Local Site Effects on a High-Pier Railway Bridge under Tridirectional Spatial Excitations: Nonstationary Stochastic Analysis,” Soil Dynamics and Earthquake Engineering, 52(6): 55–69.
Jiang LZ, Feng YL, Zhou WB and He BB (2018), “Analysis on Natural Vibration Characteristics of Steel-concrete Composite Truss Beam,” Steel and Composite Structures, 26(1): 79–87.
Kumar CPS, Sujatha C and Shankar K (2015), “Vibration of Simply Supported Beams Under a Single Moving Load: A Detailed Study of Cancellation Phenomenon,” International Journal of Mechanical Sciences, 99: 40–47.
Lei X and Wang J (2014), “Dynamic Analysis of the Train and Slab Track Coupling System with Finite Elements in a Moving Frame of Reference,” Journal of Vibration and Control, 20(9): 1301–1317.
Li C, Li T, Ban D and Ge X (2018), “Equivalent Damping of SDOF Structure with Maxwell Damper,” Earthquake Engineering and Engineering Vibration, 17(3): 627–639.
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 J and Hua H (2008), “Dynamic Stiffness Vibration Analysis of an Elastically Connected Three-Beam System,” Applied Acoustics, 69(7): 591–600.
Li YX, Hu ZJ and Sun LZ (2016), “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 (2016), “Transverse Vibration of an Undamped Elastically Connected Double-Beam System with Arbitrary Boundary Conditions,” Journal of Engineering Mechanics, 142(2): 04015070.
Li YX and Sun LZ (2017), “Active Vibration Control of Elastically Connected Double-Beam Systems,” Journal of Engineering Mechanics, 143(9): 04017112.
Liu B, Wang YZ and Peng H (2015), “Impact Coefficient and Reliability of Mid-Span Continuous Beam Bridge Under Action of Extra Heavy Vehicle with Low Speed,” Journal of Central South University, 22(4): 1510–1520.
Luo N, Jia H and Liao H (2017), “Coupled Wind-Induced Responses and Equivalent Static Wind Loads on Long-Span Roof Structures with the Consistent Load-Response-Correlation Method,” Advances in Structural Engineering, (3): 136943321770678.
Mao Q (2011), “Free Vibration Analysis of Multiple-Stepped Beams by Using Adomian Decomposition Method,” Mathematical and Computer Modelling, 54(1–2): 756–764.
Mao Q and Wattanasakulpong N (2015), “Vibration and Stability of a Double-Beam System Interconnected by an Elastic Foundation under Conservative and Nonconservative Axial Forces,” International Journal of Mechanical Sciences, 93: 1–7.
Mathworks (2016), Matlab Version R2016a.
Muscolino G and Palmeri A (2007), “Response of Beams Resting on Visco-elastically Damped Foundation to Moving Oscillators,” International Journal of Solids and Structures, 44: 1317–1336.
Ni YC and Zhang FL (2018), “Fast Bayesian Approach for Modal Identification Using Forced Vibration Data Considering the Ambient Effect,” Mechanical Systems and Signal Processing, 105: 113–128.
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.
Peng LP, Ai-Min JI, Zhao YM and Liu CS (2017), “Natural Frequencies Analysis of a Composite Beam Consisting of Euler-Bernoulli and Timoshenko Beam Segments Alternately,” Journal of Central South University, 24(3): 625–636.
Rezaiee-Pajand M and Hozhabrossadati SM (2014), “Free Vibration Analysis of a Double-Beam System Joined by a Mass-Spring Device,” Journal of Vibration and Control, 22(13).
Rusin J, Śniady P and Śniady P (2011), “Vibrations of Double-String Complex System Under Moving Forces. Closed Solutions,” Journal of Sound and vibration, 330(3): 404–415.
Shamalta M and Metrikine AV (2003), “Analytical Study of the Dynamic Response of an Embedded Railway Track to a Moving Load,” Archive of Applied Mechanics, 73(1–2): 131–146.
Şimşek M (2010), “Vibration Analysis of a Functionally Graded Beam Under a Moving Mass by Using Different Beam Theories,” Composite Structures, 92(4): 904–917.
Şimşek M (2011), “Nonlocal Effects in the Forced Vibration of an Elastically Connected Double-Carbon Nanotube System under a Moving Nanoparticle,” Computational Materials Science, 50(7): 2112–2123.
Şimşek M (2015), “Bi-Directional Functionally Graded Materials (Bdfgms) for Free and Forced Vibration of Timoshenko Beams with Various Boundary Conditions,” Composite Structures, 133: 968–978.
Şimşek M and Cansız S (2012), “Dynamics of Elastically Connected Double-Functionally Graded Beam Systems with Different Boundary Conditions under Action of a Moving Harmonic Load,” Composite Structures, 94(9): 2861–2878.
Sun LM, Xie WP, He XW 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.
Sun L, Hayashikawa T, He X and Xie W (2015), “Influential Parameter Analysis on Vibration Responses of Rigid-Frame Viaducts Induced by Running High-Speed Trains,” International Journal of Steel Structures, 15(4): 809–826.
Sun L, He X, Hayashikawa T and Xie W (2015), “Characteristic Analysis on Train-Induced Vibration Responses of Rigid-Frame Rc Viaducts,” Structural Engineering and Mechanics, 55(5): 1015–1035.
Wang Z and Ren W (2013), “Crack Detection Using Integrated Signals from Dynamic Responses of Girder Bridges,” Journal of Central South University, 20(6): 1759–1766.
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): 04015004.
Wu Y and Gao Y (2016), “Dynamic Response of a Simply Supported Viscously Damped Double-Beam System under the Moving Oscillator,” Journal of Sound and Vibration, 384: 194–209.
Yan WJ and Ren WX (2013), “Use of Continuous-Wavelet Transmissibility for Structural Operational Modal Analysis,” Journal of Structural Engineering, 139(9): 1444–1456.
Yan WJ and Ren WX (2015), “An Enhanced Power Spectral Density Transmissibility Approach for Operational Modal Analysis: Theoretical and Experimental Investigation,” Engineering Structures, 102: 108–119.
Yang YB and Lin CW (2005), Vehicle-Bridge Interaction Dynamics and Potential Applications, Directory of documentation, libraries and archives services in Africa, Unesco.
Zhai WM and Cai CB (2011), Train-Track-Bridge Dynamic Interaction: Theory and Engineering Application, Science Press, Beijing.
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 DY, Jia HY, Zheng SX, Xie WC and Pandey MD (2014), “A Highly Efficient and Accurate Stochastic Seismic Analysis Approach for Structures under Tridirectional Nonstationary Multiple Excitations,” Computers and Structures, 145(C): 23–35.
Zhang FL, Ni YC, Au SK and Lam HF (2016), “Fast Bayesian Approach for Modal Identification Using Free Vibration Data, Part I-Most Probable Value,” Mechanical Systems and Signal Processing, s70-71: 209–220.
Zhang YQ, Lu Y and Ma GW (2008), “Effect of Compressive Axial Load on Forced Transverse Vibrations of a Double-Beam System,” International Journal of Mechanical Sciences, 50(2): 299–305.
Zheng DY (2000), “Vibration of Vehicle on Compressed Rail on Viscoelastic Foundation,” Journal of Engineering Mechanics, 126(11): 1141–1147.
Acknowledgement
The research describedrherein was financially supported by the Fundamental Research Funds for the Central Universities of Central South University No. 2018zzts189, the National Natural Science Foundations of China (Nos. 51408449, 51778630), and the Innovation-driven Plan in Central South University under Grant No. 2015CX006.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by: The Fundamental Research Funds for the Central Universities of Central South University under Grant No. 2018zzts189, the National Natural Science Foundations of China under Grant Nos. 51408449 and 51778630, and the Innovation-driven Plan in Central South University under Grant No. 2015CX006
Rights and permissions
About this article
Cite this article
Yulin, F., Lizhong, J. & Wangbao, Z. Dynamic response of a three-beam system with intermediate elastic connections under a moving load/mass-spring. Earthq. Eng. Eng. Vib. 19, 377–395 (2020). https://doi.org/10.1007/s11803-020-0568-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11803-020-0568-8