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TECHNICAL PAPERS

Methods for Calculating Bending Moment and Shear Force in the Moving Mass Problem

[+] Author and Article Information
Bruno Biondi

University of Catania, Dipartimento di Ingegneria Civile e Ambientale, V.le A. Doria 6, I-95100, Catania, Italy

Giuseppe Muscolino

University of Messina, Dipartimento di Ingegnezia Civile, Salita Sperone 31, I-98166, Messina, Italy

Anna Sidoti

University of Palermo, Dipartimento di Ingegneria Strutturale e Geotecnica, Viale delle Scienze, I-90123, Palermo, Italy

J. Vib. Acoust 126(4), 542-552 (Dec 21, 2004) (11 pages) doi:10.1115/1.1804992 History: Received July 01, 2002; Revised March 01, 2004; Online December 21, 2004
Copyright © 2004 by ASME
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References

Frýba, L., 1996, Dynamics of Railway Bridges, Thomas Telford, London.
Tzou, H. S., and Bergman, L. A., (eds), 1998, Dynamics and Control of Distributed Systems, Cambridge University Press, Cambridge, England.
Stanisic,  M. M., Euler,  J. A., and Montgomery,  S. T., 1974, “On a Theory Concerning the Dynamical Behavior of Structures Considering Moving Mass,” Ing. Arch., 43, pp. 295–305.
Sadiku,  S., and Leipholz,  H. H. E., 1987, “On the Dynamic Effects of Elastic Systems With Moving Concentrated Masses,” Ing. Arch., 57, pp. 223–242.
Frýba, L., 1999, Vibration of Solids and Structures Under Moving Loads, Thomas Telford, London.
Pesterev,  A. V., and Bergman,  L. A., 2000, “An Improved Series Expansion of the Solution to the Moving Oscillator Problem,” ASME J. Vibr. Acoust., 122, pp. 54–61.
Pesterev,  A. V., Tan,  C. A., and Bergman,  L. A., 2001, “A New Method for Calculating Bending Moment and Shear Force in Moving Load Problems,” ASME J. Appl. Mech., 68, pp. 252–259.
Stanisic,  M. M., and Lafayette,  W., 1985, “On a New Theory of the Dynamic Behavior of the Structures Carrying Moving Masses,” Ing. Arch., 55, pp. 176–185.
Foster,  J., and Richards,  F. B., 1991, “The Gibbs Phenomenon for Piecewise-Linear Approximation,” Am. Math. Monthly, 98, pp. 47–49.
Bathe, K. J., 1996, Finite Element Procedures in Engineering Analysis, Prentice Hall, Englewood Cliffs, NJ.
Muscolino,  G., 1996, “Dynamically Modified Linear Structures: Deterministic and Stochastic Response,” J. Eng. Mech. Div., 122, pp. 1044–1051.
Maddox,  N. R., 1975, “On the Number of Modes Necessary for Accurate Response and Resulting Forces in Dynamic Analysis,” ASME J. Appl. Mech., 42, pp. 516–517.
Hansteen,  O. E., and Bell,  K., 1979, “On the Accuracy of Mode Superposition Analysis in Structural Dynamics,” Earthquake Eng. Struct. Dyn., 7, pp. 405–411.
Borino,  G., and Muscolino,  G., 1986, “Mode-Superposition Methods in Dynamics Analysis of Classically and Non-Classically Damped Linear Systems,” Earthquake Eng. Struct. Dyn., 14, pp. 705–717.
Clough, R. W., and Penzien, J., 1993, Dynamics of Structures, McGraw-Hill, New York.
Meirovitch, L., 1997, Principles and Techniques of Vibrations, Prentice Hall Englewood Cliffs, NJ.

Figures

Grahic Jump Location
Structural system: beam crossed by N moving masses mi
Grahic Jump Location
Bending moment time history at the midspan of the beam evaluated by applying the described series expansions with two eigenfunctions (— — CSE– ⋅ – ⋅ MAM - - - IMAM – ⋅ ⋅ – DCM — PSE)
Grahic Jump Location
Shear force time history at the midspan of the beam evaluated by applying the described series expansion, with two eigenfunctions (— — CSE – ⋅ – ⋅ MAM - - - IMAM – ⋅ ⋅ – DCM — PSE)
Grahic Jump Location
Bending moment distributions at the instant t=0.5 s evaluated by applying the described series expansion, with two eigenfunctions (— — CSE – ⋅ – ⋅ MAM - - - IMAM – ⋅ ⋅ – DCM — PSE)
Grahic Jump Location
Shear force distributions at the instant t=0.5 s evaluated by applying the described series expansion, with two eigenfunctions (— — CSE – ⋅ – ⋅ MAM - - - IMAM – ⋅ ⋅ – DCM — PSE)
Grahic Jump Location
Percentage errors of the lateral displacement maximum values at the midspan of the beam varying the number n of eigenfunctions (— — CSE – ⋅ – ⋅ MAM - - - IMAM – ⋅ ⋅ – DCM — PSE)
Grahic Jump Location
Percentage errors of the bending moment maximum values at the midspan of the beam varying the number n of eigenfunctions (— — CSE – ⋅ – ⋅ MAM - - - IMAM – ⋅ ⋅ – DCM — PSE)
Grahic Jump Location
Percentage errors of the shear force discontinuity at the midspan of the beam varying the number n of eigenfunctions (– ⋅ – ⋅MAM – – –IMAM – ⋅⋅ –DCMPSE)
Grahic Jump Location
Bending moment maximum value and the shear force at x=0 at the instant t=0.5 s versus the parameter γ (— — CSE – ⋅ – ⋅ MAM - - - IMAM – ⋅ ⋅ – DCM–PSE)

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