[1] Trochanis, A. Chelliah R. Bielak J. (1987). Unified approach for beams on elastic foundations under moving loads. Journal of Geotechnical engineering. 13(8) 879-895.
[2] Timoshenko, S. and Young, DH. and Weaver, Jr.W. (1955). Vibration Problems in Engineering (4th ed). New York: John Wiley.
[3] Koh, C. Ong, J.S.Y. Chua, D.K.H. Feng, J. (2003) Moving element method for train-track dynamics. International Journal for Numerical Methods in Engineering 56(11)1549-1567.
[4] Tran, T.M. Ang, K.K. Loung, V.H. (2014) Vertical dynamic response of non-uniform motion of high-speed rails. Journal of Sound and Vibration. (333)5427–5442.
[5] Nguyen, V. Duhamel, D. (2006). “Finite Element Procedures for Nonlinear Structures in Moving Coordinates. Part I: Infinite Bar under Moving Axial Loads”, Journal of Computers and Structures, (84)1368–1380
[6] Nguyen, V. Duhamel, D. (2006). Finite element procedures for nonlinear structures in moving coordinates. Part II: Infinite beam under moving harmonic loads. Journal of Computers and Structures. (84)2056–2063.
[7] Biot, M.A. (1937) Bending of an Infinite Beam on an Elastic Foundation. Reprinted from Journal of Applied Mechanics. No 203
[8] Mathews, P.M. (1958). Vibration of a beam on elastic foundation. ZAMM-Journal of Applied Mathematics and Mechanics. 38(3-4)105-115.
[9] Florence, A. (1965). Traveling Force on Timoshenko beam, Journal of Applied Mechanics, 32(2)351-358.
[10] Ferreira, P.A. Lopez, P. (2015). Numerical modelling of high-speed train/track system for the reduction of vibration levels and maintenance needs of railway tracks. Contents lists available at ScienceDirect Construction and Building Materials. 79 14-21.
[11] Metrikine, A.V. Dieterman, H.A. (1997). Instability of vibrations of a mass moving uniformly along an axially compressed beam on a viscoelastic foundation. Journal of Sound and Vibration. 201(5)567-576.
[12] Arbabi, F. Looi, E. (1987). Stability and dynamic response of railroad tracks under stochastic loads, Vol. II, Dynamic response. M.S. Thesis, Department of Civil Engineering Michigan Technological University.
[13] Arbabi, F. Li, F. (1987) Stability and dynamic response of railroad tracks under stochastic loads, Vol. I, nonlinear formulation and stability. M.s. Thesis, Department of Civil Engineering Michigan Technological University.
[14] Arbabi, F. Loh, C.U. (1991) Reliability analysis of railroad tracks. ASCE Journal of the Structural Division.
[15] Khalighi, M. Arbabi, F. (2010) Stability of Railroad Tracks under the Effects of Temperature Change and Earthquake. JSEE’ International Journal of Earthquake Engineering. Vol. 12, No. 3
[16] Arbabi, F. (1977) Variational Formulation of Rail Overturning, Part 4, Structural dynamics, systems identification. computer amplifications. Shock and Vibration Bulletin. 149-154
[17] Arbabi, F. Ghazaly, E.L. Sherbourne, H.A. (1991) Strength and deflection of railway tracks -I: probabilistic finite element analysis. Journal of Computers and Structures. (39):9–21.
[18] Zhang, S. Cheng, G. Sheng, X. Thompson, DJ. (2020) Dynamic wheel-rail interaction at high speed based on time-domain moving Green’s functions. J Sound Vib (488):115632.
[19]Faragau, AB. Keijdener, C. de Oliveira Barbosa, JM. Metrikine, A.V. van Dalenm, KN.(2021) Transitionradiation in a nonlinear and infinite one-dimensional structure: a comparison of solutionmethods. Nonlinear Dyn.
[20] Shan, Y. Zhou, S., Wang, B. Ho, CL. Differential Settlement Prediction of Ballasted Tracks in Bridge–Embankment Transition Zones. J Geotech Geoenvironmental. (146):04020075
[21]Connolly, DP. Galvín, P. Olivier, B. Romero, A. Kouroussis, G. A.(2019) 2.5D time-frequency domainmodel for railway induced soil-building vibration due to railway defects. Soil Dyn Earthq Eng(120):332–44
[22] Lopez-Mendoza, D. Connolly, DP. Romero, A. Kouroussis, G. Galvín, P. (2020)A transfer functionmethod to predict building vibration and its application to railway defects. Constr Build Mater (232):1–16.
[23]Auersch, L. (2021)Train-induced ground vibration due to the irregularities of the soil. Soil Dyn Earthq Eng (140):106438.
[24] Younesian, D. Hosseinkhani, A. Askari, H. Esmailzadeh, E. (2019)Elastic and viscoelastic foundations:a review on linear and nonlinear vibration modeling and applications. Nonlinear Dyn (97):853–95.
[25] McGuire, W. Gallagher, R. Ziemian, R. (2000). Matrix structural Analysis. John Wiley & Sons. Inc. New York.
[26] Chopra, A.K. (1995). Dynamics of Structures Theory and Applications to Earthquake Engineering, (4th ed) San Francisco.
[27] Banimahd, A. Arbabi, F. (2013)
Seismic Vulnerability Assessment and Development of Analytical Fragility Curves for Railroads, Journal of Seismology and Earthquake Engineering. (14):251–262.