참고문헌
- Abdelghany, S.M., Ewis, K.M., Mahmoud, A.A. and Nassar, M.M. (2015), "Dynamic response of nonuniform beam under moving load and resting on non-linear viscoelastic foundation", Beni-Suef Univ. J. Basic Appl. Sci., 4, 192-199. https://doi.org/10.1016/j.bjbas.2015.05.007.
- Ahmad, F., Jang, T.S., Carrasco, J.A., Rehman, S.U., Ali, Z. and Ali, N. (2018), "An efficient iterative method for computing deflections of Bernoulli-Euler-von Karman beams on a nonlinear elastic foundation", Appl. Math. Comput., 334, 269-287. https://doi.org/10.1016/j.amc.2018.03.038.
- Awodola, T.O. and Adeoye, A.S. (2021), "Vibration of orthotropic rectangular plates under the action of moving distributed masses and resting on a variable elastic Pasternak foundation with clamped end conditions", Int. J. Adv. Eng. Res. Sci., 8, 26-43. https://doi.org/10.22161/ijaers.86.4
- Bazeley, G.P., Cheung, Y.K., Irons, B.M. and Zienkiewicz, O.C. (1965), "Triangular elements in plate bending-conforming and nonconforming solutions", Proceedings of the Conference on Matrix Methods in Structural Mechanics, Dayton, Ohio.
- Belytschko, T., Liu, W.K. and Moran, B. (2000), Nonlinear Finite Elements for Continua and Structures, Wiley.
- Beskou, N.D. and Muho, E.V. (2018), "Dynamic response of a finite beam resting on a Winkler foundation to a load moving on its surface with variable speed", Soil Dyn. Earthq. Eng., 109, 222-226. https://doi.org/10.1016/j.soildyn.2018.02.033.
- Chien, R.D. and Chen, C.S. (2005), "Nonlinear vibration of laminated plates on a nonlinear elastic foundation", Compos. Struct., 70, 90-99. https://doi.org/10.1016/j.compstruct.2004.08.015.
- Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2002), Concepts and Applications of Finite Element Analysis, 4th Edition, Wiley, New York.
- Daryl, L.M. (2017), A First Course in the Finite Element Method, 6th Edition, Cengage Learning.
- Ding, H., Chen, L.Q. and Yang, S.P. (2012), "Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundations under a moving load', J. Sound Vib., 331, 2426-2442. https://doi.org/10.1016/j.jsv.2011.12.036.
- Ferreira, A.J.M., Roque, C.M.C., Neves, A.M.A., Jorge, A.M.N. and Soares, C.M.M. (2010), "Analysis of plates on Pasternak foundations by radial basis functions", Comput. Mech., 46, 791-803. https://doi.org/10.1007/s00466-010-0518-9.
- Froio, D. and Rizzi, E. (2017), "Analytical solution for the elastic bending of beams lying on a linearly variable Winkler support", Int. J. Mech. Sci., 128, 680-694. https://doi.org/10.1016/j.ijmecsci.2017.04.021.
- Froio, D., Rizzi, E., Simoes, F.M.F. and Costa, A.P. (2017), "Critical velocities of a beam on nonlinear elastic foundation under harmonic moving load", Procedia Eng., 199, 2585-2590. https://doi.org/10.1016/j.proeng.2017.09.348.
- Froio, D., Rizzi, E., Simoes, F.M.F. and Costa, A.P. (2018), "Dynamics of a beam on a bilinear elastic foundation under harmonic moving load", Acta Mechanica, 229(10), 4141-4165. https://doi.org/10.1007/s00707-018-2213-4.
- Ghannadiasl, A. and Mofid, M. (2015), "An analytical solution for free vibration of elastically restrained Timoshenko beam on an arbitrary variable Winkler foundation and under axial load", Lat. Am. J. Solid. Struct., 12, 2417-2438. https://doi.org/10.1590/1679-78251504.
- Huang, M.H. and Thambiratnam, D.P. (2001), "Deflection response of plate on Winkler foundation to moving accelerated loads", Eng. Struct., 23, 1134-1141. https://doi.org/10.1016/S0141-0296(01)00004-9.
- Huang, M.H. and Thambiratnam, D.P. (2002), "Dynamic response of pates on elastic foundation to moving loads", J. Eng. Mech., 128, 1016-1022. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:9(1016).
- Hughes, T.J.R. (1987), The Finite Element Method-Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Inc.
- Irons, B.M. and Razzaque, A. (1972), "Experience with the patch test for convergence of finite element methods", The Mathematical Foundations of Finite Element Method with Applications to Partial Differential Equations, Academic Press, New York.
- Jafari, P. and Kiani, Y. (2022), "A four-variable shear and normal deformable quasi-3D beam model to analyze the free and forced vibrations of FG-GPLRC beams under moving load", Acta Mechanica, 233(7), 2797-2814. https://doi.org/10.1007/s00707-022-03256-w.
- Jafari, P. and Kiani, Y. (2022), "Analysis of arbitrary thick graphene platelet reinforced composite plates subjected to moving load using a shear and normal deformable plate model", Mater. Today Commun., 31, 103745. https://doi.org/10.1016/j.mtcomm.2022.103745.
- Jahromi, H.N., Aghdam, M.M. and Fallah, A. (2013), "Free vibration analysis of Mindlin plates partially resting on Pasternak foundation", Int. J. Mech. Sci., 75, 1-7. https://doi.org/10.1016/j.ijmecsci.2013.06.001.
- Jiya, M. and Shaba, A. (2018), "Analysis of a uniform Bernoulli-Euler beam on Winkler foundation subjected to harmonic moving load", J. Appl. Sci. Environ. Manage., 22(3), 368. https://doi.org/10.4314/jasem.v22i3.13.
- Jorge, P.C., Simoes, F.M.F. and Costa, A.P. (2015a), "Dynamics of beams on non-uniform nonlinear foundations subjected", Comput. Struct., 148, 26-34. https://doi.org/10.1016/j.compstruc.2014.11.002.
- Jorge, P.C., Simoes, F.M.F. and Costa, A.P. (2015b), "Finite element dynamic analysis of finite beams on a bilinear foundation under a moving load", J. Sound Vib., 346, 328-344. https://doi.org/10.1016/j.jsv.2014.12.044.
- Karahan, M.M.F. and Pakdemirli, M. (2017), "Vibration analysis of a beam on a nonlinear elastic foundation", Struct. Eng. Mech., 62(2), 171-178. https://doi.org/10.12989/sem.2017.62.2.171.
- Kiani, Y. (2017), "Analysis of FG-CNT reinforced composite conical panel subjected to moving load using Ritz method", Thin Wall. Struct., 119, 47-57. https://doi.org/10.1016/j.tws.2017.05.031.
- Kiani, Y. (2017), "Dynamics of FG-CNT reinforced composite cylindrical panel subjected to moving load", Thin Wall. Struct., 111, 48-57. https://doi.org/10.1016/j.tws.2016.11.011.
- Kiani, Y. (2020), "Influence of graphene platelets on the response of composite plates subjected to a moving load", Mech. Bas. Des. Struct. Mach., 50(4), 1123-1136. https://doi.org/10.1080/15397734.2020.1744006.
- Kiani, Y. (2022), "Free and forced vibrations of graphene platelets reinforced composite laminated arches subjected to moving load", Meccanica, 57(5), 1105-1124. https://doi.org/10.1007/s11012-022-01476-x.
- Kim, S.M. and McCullough, B.F. (2003), "Dynamic response of plate on vicous Winkler foundation moving loads of varying amplitude", Eng. Struct., 25, 1179-1188. https://doi.org/10.1016/S0141-0296(03)00066-X.
- Li, M.L., Qian, T., Zhong, Y. and Zhong, H. (2013), "Dynamic response of the rectangular plate under moving loads with variable velocity", J. Eng. Mech., 140(4), 06014001. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000687.
- Liu, H., Liu, F., Jing, X., Wang, Z. and Xia, L. (2017), "Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions", Shock Vib., 2017, Article ID 3425298. https://doi.org/10.1155/2017/3425298.
- MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Finite Elem. Anal. Des., 1(1), 3-20. https://doi.org/10.1016/0168-874X(85)90003-4.
- Mohebpour, S.R. and Ahmadzadeh, P.M.A.A. (2011), "Dynamic analysis of laminated composite plates subjected to a moving oscillator by FEM", Compos. Struct., 93, 1574-1583. https://doi.org/10.1016/j.compstruct.2011.01.003.
- Nguyen, T.P. and Pham, D.T. (2016), "The influence of mass of two-parameter elastic foundation on dynamic response of beams subjected to a moving mass", KSCE J. Civil Eng., 20(7), 2842-2848. https://doi.org/10.1007/s12205-016-0167-4.
- Nguyen, T.P., Pham, D.T. and Hoang, P.H. (2016a), "A dynamic foundation model for the analysis of plates on foundation to a moving oscillator", Struct. Eng. Mech., 59(6), 1019-1035. https://doi.org/10.12989/sem.2016.59.6.1019.
- Nguyen, T.P., Pham, D.T. and Hoang, P.H. (2016b), "A new foundation model of dynamic analysis of beams on nonlinear foundation subjected to a moving mass", Procedia Eng., 142, 166-173. https://doi.org/10.1016/j.proeng.2016.02.028.
- Nguyen, T.P., Pham, D.T. and Hoang, P.H. (2020a), "A nonlinear dynamic foundation model for dynamic response of track-train interaction", Shock Vib., 2020, Article ID 5347082. https://doi.org/10.1155/2020/5347082.
- Nguyen, T.P., Pham, D.T. and Hoang, P.H. (2020b), "Effects of foundation mass on dynamic responses of beams subjected to moving oscillators", J. Vibroeng., 22(2), 280-297. https://doi.org/10.21595/jve.2019.20729.
- Phadke, H.D. and Jaiswal, O.R. (2021), "Dynamic analysis of railway track on variable foundation under harmonic moving load", J. Rail Rapid Transit., 223(3), 302-316. https://doi.org/10.1177/09544097211020838.
- Phadke, H.D. and Jaiswal, O.R. (2021), "Dynamic response of railway track resting on variable foundation using finite element method", Arab. J. Sci. Eng., 45, 4823-4841. https://doi.org/10.1007/s13369-020-04360-6.
- Pham, D.T., Hoang, P.H. and Nguyen, T.P. (2018), "Experiments on influence of foundation mass on dynamic characteristic of structures", Struct. Eng. Mech., 65(5), 505-512. https://doi.org/10.12989/sem.2018.65.5.505.
- Praharaj, R.K. and Datta, N. (2020), "Dynamic response of plates resting on a fractional viscoelastic foundation and subjected to a moving load", Mech. Bas. Des. Struct. Mach., 50(7), 1-16. https://doi.org/10.1080/15397734.2020.1776621.
- Rodrigues, C., Simoes, F.M.F., Costa, A.P., Froio, D. and Rizzi, E. (2018), "Finite element dynamic analysis of beams on nonlinear elastic foundations under a moving oscillator", Eur. J. Mech./A Solid., 68, 9-24. https://doi.org/10.1016/j.euromechsol.2017.10.005.
- Taylor, R.L., Simo, J.C., Zienkiewicz, O.C. and Chan, A.C.H. (1986), "The patch test-a condition for assessing FEM convergence", Int. J. Numer. Meth. Eng., 22(1), 39-62. https://doi.org/10.1002/nme.1620220105.
- Teodoru, I.B. and Musat, V. (2010), "The modified Vlasov foundation model an attractive approach for beams resting on elastic supports", Electr. J. Geotech. Eng., 15, 1-13.
- Wang, Y. and Kiani, Y. (2022), "Effects of initial compression/tension, foundation damping and pasternak medium on the dynamics of shear and normal deformable GPLRC beams under moving load", Mater. Today Commun., 33(1), 104938. https://doi.org/10.1016/j.mtcomm.2022.104938.
- Yang, Y., Ding, H. and Chen, L.Q. (2013), "Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation", Acta Mechanica Sinica, 29(5), 718-727. https://doi.org/10.1007/s10409-013-0069-3.
- Yu, H., Yang, Y. and Yuan, Y. (2018), "Analytical solution for a finite Euler-Bernoulli beam with single discontinuity in section under arbitrary dynamic loads", Appl. Math. Model., 60, 571-580. https://doi.org/10.1016/j.apm.2018.03.046.
- Yu, K., Surianinov, M., Petrash, S. and Yezhov, M. (2021), "Development of an analytical method for calculating beams on a variable elastic Winkler foundation", IOP Conf. Ser., Mater. Sci. Eng., 1162(1), 012009. https://doi.org/10.1088/1757-899X/1162/1/012009.
- Zhou, S., Song, G., Wang, R., Ren, Z. and Wen, B. (2017), "Nonlinear dynamic analysis for coupled vehicle-bridge vibration system on nonlinear foundation", Mech. Syst. Signal Pr., 87, 259-278. https://doi.org/10.1016/j.ymssp.2016.10.025.