On the basis of the cubic Hermitian polynomials being used as the shape functions of a rail element and the conditions of equilibrium of forces acting in the vertical direction and of bending moment, this article presents a method for calculating the sectional force (i.e. shear force and bending moment) of discretely supported rail subjected to multiple moving concentrated forces. The correctness of the present method is illustrated by a comparison with the analytical solution. Two numerical examples are chosen to investigate the effects of the length of rail element, the stiffness and damping coefficients of railpad, and the speed of moving force on the responses of rail. The numerical results show that the length of a rail element may be adopted as two times sleeper space; the effect of the stiffness and damping coefficients of railpad on the responses of rail is significant; however, the effect of the speed of moving force on the responses of rail with smooth surface is not significant.
TimoshenkoS. Method of analysis of statical and dynamical stresses in rail. Proceedings of the Second International Congress for Applied Mechanics, Zurich, Swiss, 1926, pp. 407–418.
2.
SatoY.Study on high frequency vibration in track operated with high-speed trainsQ. Rep. Railw. Tech. Res. Inst., 1977, 24 (2), 109–114.
3.
GrassieS. L.GregoryR. W.HarrisonD.JohnsonK. L.The dynamic response of railway track to high frequency vertical excitationJ. Mech. Eng. Sci., 1982, 24 (2), 77–90.
4.
PatilS. P.Response of infinite railway track to vibrating massJ. Eng. Mech. ASCE, 1988, 114 (4), 688–703.
5.
DuffyD. G.The response of an infinite railroad track to a moving vibrating massJ. Appl. Mech. ASME, 1990, 57 (1), 66–73.
6.
ClarkR. A.DeanP. A.ElkinsJ. A.NewtonS. G.An investigation into the dynamic effects of railway vehicles running on corrugated railsJ. Mech. Eng. Sci., 1982, 24 (2), 65–76.
7.
CaiZ.RaymondG. P. Theoretical model for dynamic wheel/rail and track interaction. Proceedings of the 10th International Wheelset Congress, Sydney, Australia, 1992, pp. 127–131.
8.
DongR. G.SankarS.DukkipatiR. V.A finite element model of railway track and its application to wheel flat problemProc. Instn Mech. Engrs, Part F: J. Rail and Rapid Transit, 1994, 208 (F1), 61–72.
9.
ZhaiW.SunX.A detailed model for investigating vertical interaction between railway vehicle and trackVeh. Sys. Dyn., 1994, 23 (suppl.), 603–615.
10.
NielsenJ. C.O.IgelandA.Vertical dynamic interaction between train and track - influence of wheel and track imperfectionsJ. Sound Vib., 1995, 187 (5), 825–839.
11.
ZhaiW.CaiZ.Dynamic interaction between a lumped mass vehicle and a discretely supported continuous rail trackComput. Struct., 1997, 63 (5), 987–997.
12.
EsveldC.KokA. W. M.Interaction between moving vehicles and railway track at high speedRail Eng. Int., 1998, 27 (3), 14–16.
DukkipattiR. V.DongR.Idealized steady state interaction between railway vehicle and trackProc. Instn Mech. Engrs, Part F: J. Rail and Rapid Transit, 1999, 213 (F1), 15–29.
15.
SunY. Q.DhanasekarM. A.Dynamic model for the vertical interaction of the rail track and wagon systemInt. J. Solids Struct., 2002, 39 (5), 1337–1359.
16.
LeiX.NodaN. A.Analyses of dynamic response of vehicle-track coupling system with random irregularity of track vertical profileJ. Sound Vib., 2002, 258 (1), 147–165.
17.
LeiX.MaoL.Dynamic responses analyses of vehicle and track coupling system on track transition of conventional high speed railwayJ. Sound Vib., 2004, 271 (3–4), 1133–1146.
18.
KohC. G.OngJ. S. Y.ChuaD. K. H.FengJ.Moving element method for train-track dynamicsInt. J. Numer. Methods Eng., 2003, 56 (11), 1549–1567.
19.
HouK.KalousekJ.DongR.A dynamic model for an asymmetrical vehicle/track systemJ. Sound Vib., 2003, 267 (3), 591–604.
NielsenJ. C.O.OscarssonJ.Simulation of dynamic train-track interaction with state-dependent track propertiesJ. Sound Vib., 2004, 275 (3–5), 515–532.
22.
BaezaL.RodaA.NielsenJ. C. O.Railway vehicle/track interaction analysis using a modal sub-structuring approachJ. Sound Vib., 2006, 293 (1–2), 112–124.
23.
LouP.ZengQ. Y.Vertical vehicle-track coupling elementProc. IMechE, Part F: J. Rail and Rapid Transit, 2006, 220 (F3), 293–304.
24.
CookR. D.Concepts and applications of finite element analysis, 2nd edition, 1981 (Wiley, New York).
25.
CloughR. W.PenzienJ.Dynamics of structures, 2nd edition, 1993 (McGraw-Hill, New York).
26.
ZengQ. Y.The principle of a stationary value of total potential energy of dynamic system (in Chinese)J. Huazhong Univ. Sci. Technol., 2000, 28 (1), 1–3.
27.
ZengQ. Y.GuoX. R.Theory and application of vibration analysis of train-bridge time-dependent system (in Chinese), 1999 (China Railway Publishing House, Beijing).
28.
LouP.ZengQ. Y.Formulation of equations of motion of finite element form for vehicle-track-bridge interaction system with two types of vehicle modelsInt. J. Numer. Methods Eng., 2005, 62 (3), 435–474.
29.
BatheK. J.WilsonE. L.Numerical methods in finite element analysis, 1976 (Prentice-Hall, Englewood Cliffs, NJ).
30.
SackR. L.Structural analysis, 1984 (McGraw-Hill Book Company, New York).
31.
YangY. B.YauJ. D.HsuL. C.Vibration of simple beams due to trains moving at high speedsEng. Struct., 1997, 19 (11), 936–944.
32.
TimoshenkoS.YoungD. H.WeaverW. J. R.Vibration problems in engineering, 4th edition, 1974 (John Wiley & Sons, New York).
