Engineering Transactions, 45, 2, pp. 199-213, 1997

Application of Floquet's Method to High-Speed Train/Track Dynamics

T. Krzyżyński
Institute of Fundamental Technological Research, Warsaw
Poland

The paper deals with the vertical dynamics of a railway track and a guideway for the mag­netic high-speed system with contact-free levitation technology (Maglev). The conventional railway track is composed of rails mounted on the equally spaced sleepers which rest on the ballast, with a pad between the rail and sleeper. The guideway for Maglev system is composed of simply supported girders which are mounted on piers. Usually, the span of adjacent girders is equal and the guideway is composed of repetitive elements mounted with high positional accu­racy. The track as well as the guideway form typical periodic systems which consist of a number of identical flexible elements coupled in an identical way. In the paper the free wave propaga­tion problems and the steady-state system dynamic responses to a moving harmonic force are considered. In both cases the solution method proposed consists in the direct application of Floquet's theorem to the differentia! equations of motion of the periodic systems.

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References

KL. HEINRICH and L. KRETZSCHMAR (Eds.], Magnetbahn Transrapid; Die neue Dimen­sion des Reisens, Hestra-Verlag, Darmstadt 1989.

J.R. HALL, F.E. RICHART and R.D. WOODS, Vibrations of soils and foundations, Prentice-Hall, 1970.

R. BOGACZ, T. KRZYŻYŃSKI and K. POPP, On the vertical and lateral dynamics of periodic guideways for Maglev vehicle, (in:] Dynamical Problems in Mechanical Systems, Proc. 3rd German-Polish Workshop, pp. 219-232, Wierzba, Poland, July 1993.

Y.K. LIN and T.J. McDANIEL, Dynamics of beam-type periodic structures, ASME J. Engng. Industry, 91, 1133-1141, 1969.

D.J. MEAD, Free wave propagation in periodically supported infinite beams, J. Sound Vibr., 11, 2, 181-197, 1970.

D.J. MEAD and K.K. PUJARA, Space-harmonic analysis of periodically supported beams: Response to convected random loading, J. Sound Vib., 14, 4, 525-541, 1971.

D.J. MEAD and S.PARTHAN, Free wave propagation in two-dimensional periodic plates,

J. Sound Vib., 64, 3, 325-348, 1979.

L. JEZEQUEL, Response of periodic systems to a moving load, ASME J. Appl. Mech., 48, 3, 613-618, 1981.

D.J. MEAD, A new method of analyzing wave propagation in periodic structures; Applications to periodic Timoshenko beams and stiffened plates, J. Sound Vibr., 104, l, 9-27, 1986.

L. BRILLOUIN, Wave propagation in periodic structures, Dover Publications, 1953.

C.C. SMITH and D.N. WORMLEY, Response of a periodically supported guideway beam to travelling vehicle loads, ASME J. Dyn. Syst., Measur., Control, 97, 21-29, 1975.

R. BOGACZ, T. KRZYŻYŃSKI and K. POPP, On dynamics of systems modelling contin­uous and periodic guideways, Arch. Mech., 45, 5, 575-593, 1993.

H. ILIAS and KL. KNOTHE, Ein diskret-kontinuierliches Gleismodel unter Einftuß schnell bewegter, harmonisch schwankender Wanderlasten, Technical Report, VDI-Fortschritts­bericht, Reihe 12, Nr. 171, 1992.

T. KRZYŻYŃSKI, On continuous subsystem modelling in the dynamic interaction problem of a train-track-system, Supplement to Vehicle System Dynamics, 24, 311-324, 1995.

R. BOGACZ, T. KRZYŻYŃSKI and K. POPP, On the generalization of Mathews problem of the vibrations of a beam on elastic foundation, Z. Angew. Math. Mech., 69, 8, 243-252, 1989.




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