참고문헌
- Arpaci, A. and Bozdag, S.E. (2002), "On free vibration analysis of thin-walled beams with nonsymmetrical open cross-sections", Comput. Struct., 80(7-8), 691-695. https://doi.org/10.1016/S0045-7949(02)00025-1
- Arpaci, A., Bozdag, S.E. and Sunbuloglu, E. (2003), "Triply coupled vibrations of thin-walled open crosssection beams including rotary inertia effects", J. Sound Vib., 260, 889-900. https://doi.org/10.1016/S0022-460X(02)00935-5
- Attard, N.A. (1987), "A direct method of evaluating the warping properties of thin-walled open and closed profiles", Thin Wall. Struct., 5(5), 351-364. https://doi.org/10.1016/0263-8231(87)90026-7
- Banerjee, J.R. (1989), "Coupled bending-torsional dynamic stiffness matrix for beam elements", Int. J. Numer. Method. Eng., 28, 1283-1298. https://doi.org/10.1002/nme.1620280605
- Banerjee, J.R. and Williams, F.W. (1992), "Coupled bending-torsional dynamic stiffness matrix for Timoshenko beam elements", Comput. Struct., 42, 301-310. https://doi.org/10.1016/0045-7949(92)90026-V
- Banerjee, J.R. and Guo S. and Howson, W.P. (1996), "Exact dynamic stiffness matrix of a bending torsion coupled beam including warping", Comput. Struct., 59, 613-621. https://doi.org/10.1016/0045-7949(95)00307-X
- Banerjee, J.R. (1997), "Dynamic stiffness formulation for structural elements: A general approach", Comput. Struct., 63, 101-103. https://doi.org/10.1016/S0045-7949(96)00326-4
- Bishop, R.E.D., Cannon, S.M. and Miao, S. (1989), "On coupled bending and torsional vibration of uniform beams", J. Sound Vib., 131(3), 457-464. https://doi.org/10.1016/0022-460X(89)91005-5
- Cedolin, L. (1996), Torsione e taglio di travi a parete sottile, Milano, Edizioni Cusl.
- Dokumaci, E. (1987), "An exact solution for coupled bending and torsion vibrations of uniform beams having single cross-sectional symmetry", J. Sound Vib., 119(3), 443-449. https://doi.org/10.1016/0022-460X(87)90408-1
- Friberg, P.O. (1983), "Coupled vibration of beams - an exact dynamic element stiffness matrix", Int. J. Numer. Method. Eng., 19, 479-493. https://doi.org/10.1002/nme.1620190403
- Friberg, P.O. (1985), "Beam Element Matrices Derived from Vlasov's theory of open thin-walled elastic beams", Int. J. Numer. Method. Eng., 21, 1205-1228. https://doi.org/10.1002/nme.1620210704
- Fryba, L. (1999), Vibrations of solids and structures under to moving loads, Thomas Telford.
- Fryba, L. (2001), "A rough assessment of railway bridges for high speed trains", Eng. Struct., 23, 548-556. https://doi.org/10.1016/S0141-0296(00)00057-2
- Garinei, A. and Risitano, G. (2008), "Vibrations of railway bridges for high speed trains under moving loads varying in time", Eng. Struct., 30(3), 724-732. https://doi.org/10.1016/j.engstruct.2007.05.009
- Gere, J.M. (1954), "Torsional vibrations of beams of thin-walled open cross section", J. Appl. Mech., 25, 373-378.
- Gere, J.M. and Lin, Y.K. (1958), "Coupled vibration of thin-walled beams of open cross section", J. Appl. Mech., 25, 373-378.
- Gunnlaugsson, G.A. and Pedersen, P.T. (1982), "A finite element formulation for beams with thin walled cross-sections", Comput. Struct., 15(6), 691-699. https://doi.org/10.1016/S0045-7949(82)80011-4
- Hallauer, W.L. and Liu, R.Y.L. (1982), "Beam bending-torsion dynamic stiffness method for calculation of exact", J. Sound Vib., 85,105-113. https://doi.org/10.1016/0022-460X(82)90473-4
- Chen, H. and Hsiao, K.M. (2008), "Quadruply coupled linear free vibrations of thin-walled beams with a generic open section", Eng. Struct., 30(5), 1319-1334. https://doi.org/10.1016/j.engstruct.2007.07.004
- Ichikawa, M., Miyakawa, Y. and Matsuda, A. (2000), "Vibrations analysis of the continuous beam subjected to a moving load", J. Sound Vib., 230(3), 493-506. https://doi.org/10.1006/jsvi.1999.2625
- Ju, S.H. and Lin, H.T. (2003), "Resonance characteristics of high-speed trains passing simply supported bridges", J. Sound Vib., 267, 1127-1141. https://doi.org/10.1016/S0022-460X(02)01463-3
- Kim, M.Y., Yun, H.T. and Kim, N. (2003), "Exact dynamic and static element stiffness matrices of nonsymmetric thin-walled beam-columns", Comput. Struct., 81, 1425-1448. https://doi.org/10.1016/S0045-7949(03)00082-8
- Kim, N. and Kim, M.Y. (2005), "Exact dynamic/static stiffness matrices of non-symmetric thin-walled beams considering coupled shear deformation effects", Thin Wall. Struct., 43, 701-734. https://doi.org/10.1016/j.tws.2005.01.004
- Lee, S.Y. and Yhim, S.S. (2005), "Dynamic behavior of long-span box girder bridges subjected to moving loads: Numerical analysis and experimental verification", Int. J. Solid. Struct., 42, 5021-5035. https://doi.org/10.1016/j.ijsolstr.2005.02.020
- Li, J. and Su, M. (1999), "The Resonant vibration for a simply supported girder bridge under high-speed trains", J. Sound Vib., 224(5), 897-915. https://doi.org/10.1006/jsvi.1999.2226
- Lisi, D. (2012), "A beam finite element including warping", Thesis for Master degree in Structural Engineering, (https://www.politesi.polimi.it/handle/10589/66762?mode=simple).
- Michaltsos, G.T., Sarantithou, E. and Sophianopoulos, D.S. (2005), "Flexural-torsional vibration of simply supported open cross-section steel beams under moving loads", J. Sound Vib., 280, 479-494. https://doi.org/10.1016/j.jsv.2003.12.041
- Mohammad, A. R., Farzad, V. and Atefeh E. (2013), "Dynamic response of railway bridges traversed simultaneously by opposing moving trains", Struct. Eng. Mech., 46(5), 713-734. https://doi.org/10.12989/sem.2013.46.5.713
- Olsson, M. (1985), "Finite Element Modal Coordinate Analysis of structures subjected to moving loads", J. Sound Vib., 99(1), 1-12. https://doi.org/10.1016/0022-460X(85)90440-7
- Olsson, M. (1991), "Finite Element Modal Coordinate Analysis of structures subjected to moving loads", J. Sound Vib., 145(2), 299-307. https://doi.org/10.1016/0022-460X(91)90593-9
- Piccardo, G. and Tubino, F. (2012), "Dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads", Struct. Eng. Mech., 44(5), 681-704. https://doi.org/10.12989/sem.2012.44.5.681
- Podworna, M. (2011), "Dynamics of a bridge beam under a stream of moving elements. Part 1 - modelling and numerical integration", Struct. Eng. Mech., 38(3), 283-300. https://doi.org/10.12989/sem.2011.38.3.283
- Podworna, M. (2011), "Dynamics of a bridge beam under a stream of moving elements. Part 2 - numerical simulations", Struct. Eng. Mech., 38(3), 301-314. https://doi.org/10.12989/sem.2011.38.3.301
- Prokic, A. (2005), "On triply coupled vibrations of thin-walled beams with arbitrary cross-section", J. Sound Vib., 279(3-5), 21, 723-737.
- Prokic, A. (2006), "On fivefold coupled vibrations of Timoshenko thin-walled beams", Eng. Struct., 28(1), 54-62. https://doi.org/10.1016/j.engstruct.2005.07.002
- Tanaka, M and Bercin, A.N. (1997), "Finite element modelling of the coupled bending and torsional free vibration of uniform beams with arbitrary cross-section", Appl. Math. Model., 21, 339-344. https://doi.org/10.1016/S0307-904X(97)00030-9
- Tanaka, M. and Bercin, A.N. (1999), "Free vibration solution for uniform beams of nonsymetrical cross section using Mathematica", Comput. Struct., 71, 1-8. https://doi.org/10.1016/S0045-7949(98)00236-3
- Timoshenko, S.P., Young, D.H. and Weaver, W. (1974), Vibration Problems in Engineering, Wiley, New York.
- Yang, Y.B., Yau, J.D. and Hsu, L.C. (1997), "Vibration of simple beam due to trains moving at highs speeds", Eng. Struct., 19(11), 936-944. https://doi.org/10.1016/S0141-0296(97)00001-1
- Vlasov, V. (1961), Thin-Walled Elastic Beams, Israel program for scientific translations, Jerusalem.
- Zhu, L., Zhao, Y. and Wang, G. (2013), "Exact solution for free vibration of curved beams with variable curvature and torsion", Struct. Eng. Mech., 47(3), 345-359. https://doi.org/10.12989/sem.2013.47.3.345
피인용 문헌
- Condition assessment for high-speed railway bridges based on train-induced strain response vol.54, pp.2, 2015, https://doi.org/10.12989/sem.2015.54.2.199
- Lateral-torsional buckling of functionally graded tapered I-beams considering lateral bracing vol.28, pp.4, 2018, https://doi.org/10.12989/scs.2018.28.4.403