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A computational procedure for interaction of high-speed vehicles on flexible structures without assuming known vehicle nominal motion. (English) Zbl 0687.73073
Summary: An efficient and reliable computational procedure is proposed for the analysis of interaction between high-speed vehicles and flexible structures. In contrast to traditional approaches, the vehicle nominal motion is considered here as an unknown of the problem. The equations encountered, for vehicle motion (after elimination of algebraic constraints) and for structural motion, form a set of nonlinear, coupled differential equations. In spatially-discrete form, these equations do not have the form of explicit ODEs. Predictor/corrector algorithms, which combine Runge-Kutta methods and linear multistep methods with an unconditionally stable algorithm for structural dynamics, are proposed to solve the partitioned DAEs of the interaction problem. The proposed algorithms carry special features pertaining to our formulation of vehicle/structure interaction, and yield accurate results which satisfy the essential system energy balance. The present approach effectively resolves the Timoshenko paradox in moving load problems. Several illustrative examples are presented.
Reviewer: Reviewer (Berlin)

74S30 Other numerical methods in solid mechanics (MSC2010)
65F30 Other matrix algorithms (MSC2010)
Full Text: DOI
[1] Alscher, H.; Iguchi, M.; Eastham, A.R.; Boldea, I., Noncontact suspension and propulsion technology, Vehicle system dynamics, 12, 259-289, (1983)
[2] Eastham, A.R.; Hayes, W.F., The status of development of maglev systems, (), 231-239
[3] Dalgleish, E.H.; Riches, E.E., A review of Birmingham maglev after one year of public service, (), 1-5
[4] Cortes-Comerer, N., Will maglev ever get off the ground in the U.S.?, Mech. engrg., 58-63, (October, 1988)
[5] See also the letter to the editor of the same journal, Maglev, by A.L. Spivak, p. 64, December 1988.
[6] Lawton, A., Implementation of a maglev vehicle suspension for flexible guideways, (), 293-306
[7] Zicha, J.H., Civil aspects of maglev design, (), 69-87
[8] Vu-Quoc, L.; Olsson, M., Interaction between high-speed moving vehicles and flexible structures: an analysis without assumption of known vehicle nominal motion. structural engineering, mechanics and materials, () · Zbl 0687.73073
[9] Vu-Quoc, L.; Olsson, M., Formulation of a basic building-block model for interaction of high-speed vehicles on flexible structures, ASME J. appl. mech., 56, 451-458, (June 1989)
[10] Blejwas, T.E.; Feng, C.C.; Ayre, R.S., Dynamic interaction of moving vehicles and structures, J. sound vibration, 67, 4, 513-521, (1979)
[11] Hairer, E., Order conditions for numerical methods for partitioned ordinary differential equations, Numer. math., 36, 431-445, (1981) · Zbl 0462.65049
[12] Park, K.C.; Felippa, C.A., Partitioned analysis of coupled systems, () · Zbl 0546.73063
[13] Wood, W.L., Some transient and coupled problems—A state-of-the-art review, (), 149-177
[14] Petzold, L.R., A description of DASSL: A differential/algebraic system solver, () · Zbl 0635.65084
[15] Führer, C., Numerical integration methods in vehicle dynamics simulation, (), 329-345
[16] Führer, C.; Wallrapp, O., A computer-oriented method for reducing linearized multibody system equations by incorporating constraints, Comput. methods appl. mech. engrg., 46, 169-175, (1984) · Zbl 0569.70003
[17] Nikravesh, P.E., Some methods for dynamics analysis of constrained mechanical systems: A survey, (), 351-368
[18] Gupta, G.K.; Sacks-Davis, R.; Tischer, P.E., A review of recent developments in solving odes, ACM computing surveys, 17, 1, 5-47, (1985) · Zbl 0576.65071
[19] Kortüm, W., Introduction to system-dynamics of ground vehicles, (), 1-36
[20] Wallrapp, O., Elastic vehicle guideway structures, (), 215-232
[21] Dekker, K.; Verwer, J.G., Stability of Runge-Kutta methods for stiff nonlinear differential equations, () · Zbl 0571.65057
[22] Maunder, L., On the work of a force crossing a beam, Quart. appl. math., 17, 437-440, (1960) · Zbl 0104.19601
[23] Kalker, J.J., Survey of wheel-rail rolling contact theory, Vehicle system dynamics, 5, 317-358, (1979)
[24] L. Vu-Quoc and M. Olsson, Dynamic Interaction of High-Speed Vehicles on Multiple-Span Elevated Guideways: Lumped-Parameters Vehicle Model and New Algorithmic Treatment, Aerospace Engineering, Mechanics, and Engineering Science Report No. AeMES-TR-70 (in preparation).
[25] Venancio-Filho, F., Finite element analysis of structures under moving loads, Shock and vibration digest, 10, 8, 27-35, (1978)
[26] Deuflhard, P., Recent progress in extrapolation methods for ordinary differential equations, SIAM rev., 27, 4, 505-535, (1985) · Zbl 0602.65047
[27] Olsson, M., Finite element, modal coordinate analysis of structures subjected to moving loads, J. sound vibration, 99, 1, 1-12, (1985)
[28] Olsson, M., Analysis of structures subjected to moving loads, ()
[29] Dormand, J.R.; Prince, P.J., New Runge-Kutta algorithms for numerical simulation in dynamical astronomy, Celestial mech., 18, 223-232, (1978) · Zbl 0386.70006
[30] Butcher, J.C., The numerical analysis of ordinary differential equations, (1987), Wiley New York · Zbl 0616.65072
[31] Fine, J.M., Low-order practical Runge-Kutta-nystrom methods, Computing, 38, 281-297, (1987) · Zbl 0602.65044
[32] Hoff, C., Dissipative step-by-step integration methods for nonlinear structures under earthquake loading (in German), ()
[33] Hoff, C.; Pahl, P.J., Development of an implicit method with numerical dissipation from a generalized single step algorithm for structural dynamics, Comput. methods appl. mech. engrg., 67, 367-385, (1988) · Zbl 0619.73002
[34] Hughes, T.J.R., Analysis of transient algorithms with particular reference to stability behavior, () · Zbl 0547.73070
[35] Hilber, H.M.; Hughes, T.J.R.; Taylor, R.L., Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake engrg. structural dynamics, 5, 283-292, (1977)
[36] Katona, M.G.; Zienkiewicz, O.C., A unified set of single step algorithms. part 3: the beta-m method, a generalization of the newmark scheme, Internat. J. numer. methods engrg., 21, 1345-1359, (1985) · Zbl 0584.65044
[37] Trujillo, D.H., An unconditionally stable explicit algorithm for structural dynamics, Internat. J. numer. methods engrg., 11, 1579-1592, (1972) · Zbl 0365.65053
[38] Belytschko, T., Overview of semidiscretization, () · Zbl 0542.73106
[39] Gellert, M., A new algorithm for integration of dynamic systems, Comput & structures, 9, 401-408, (1978) · Zbl 0405.65047
[40] Gear, C.W., The stability of numerical methods of 2nd order odes, SIAM J. numer. anal., 15, 188-197, (1978) · Zbl 0388.65030
[41] Gupta, G.K., A note about overhead costs in ODE solvers, ACM trans. math. software, 6, 3, 319-326, (1980)
[42] Lambert, J.D., Computational methods in ordinary differential equations, (1973), Wiley London · Zbl 0258.65069
[43] Gear, C.W., Numerical initial value problems in ordinary differential equations, (1971), Prentice-Hall Englewood Cliffs, N.Y · Zbl 0217.21701
[44] Gear, C.W., Runge-Kutta starters for multistep methods, ACM trans. math. software, 6, 263-279, (1980) · Zbl 0455.65051
[45] Vu-Quoc, L., Dynamics of flexible structures performing large overall motions: A geometrically-nonlinear approach, ()
[46] Vu-Quoc, L.; Simo, J.C., Dynamics of Earth-orbiting satellites with flexible multibody components, AIAA J. guidance, control and dynamics, 10, 6, 549-558, (1987) · Zbl 0657.70028
[47] Zienkiewicz, O.C.; Taylor, R.L., ()
[48] Frýba, L., Vibration of solids and structures under moving loads, (1972), Noordhoff Groningen · Zbl 0301.73015
[49] Smith, C.C.; Gilchrist, A.J.; Wormley, D.N., Multiple and continuous span elevated guideway-vehicle dynamic performance, ASME J. dynamic systems, measurements and control, 97, 1, 30-40, (1975)
[50] Gupta, R.K.; Traill-Nash, R.W., Bridge dynamic loading due to road surface irregularities and braking of vehicle, Earthquake engrg. structural dynamics, 8, 83-96, (1980)
[51] Lex-Mulcahy, N., Bridge response with tractor-trailer vehicle loading, Earthquake engrg. structural dynamics, 11, 649-665, (1983)
[52] Vu-Quoc, L.; Olsson, M., A computational procedure for interaction of high-speed vehicles on flexible structures without assuming known vehicle motion, structural engineering, mechanics and materials, () · Zbl 0687.73073
[53] Vu-Quoc, L.; Olsson, M., Computational methods for high-speed vehicles on flexible guideways, () · Zbl 0687.73073
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