Transient Response of Supported Beams to Moving Forces with Sinusoidal Time Variation
Publication: Journal of Engineering Mechanics
Volume 137, Issue 6
Abstract
Moving forces are a common loading pattern for flexible beams, found in many applications in both civil and mechanical engineering. These forces give rise to a transient response, the nature of which depends on the time variation of the amplitude of the force and its position along the beam. In addition to the possibility of numerical evaluation, closed form solutions of the beam response are beneficial for their simplicity of use, and because they allow an understanding of the system behavior. On the other hand, these prove to be rather complicated in most cases, and only a limited number of cases are available in the literature. This paper studies the simple but common case of a supported beam loaded by a force with sinusoidal time variation moving at a constant speed. Simple equations are presented for the approximated responses at and away from resonance, and their accuracy is discussed. Transient frequency response functions are also shown. Finally, as an example, the results are applied to an evaluation of the response of a beam footbridge to the action of a walker, and compared to code specifications.
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Acknowledgments
The results presented in this paper have been obtained within the research project AER-BRIDGE, partially funded by the UNSPECIFIEDItalian Ministry for University and by the University of Chieti-Pescara, the University of Florence, the University of Reggio Calabria, the Technical University of Turin, and the University IUAV of Venice.
References
CEN. (1997). “Eurocode 5: Design of timber structures—Part 2: Bridges.” ENV 1995-2, Brussels, Belgium.
Frýba, L. (1973). Vibration of solids and structures under moving loads, Nordhoff, Groningen, Netherlands.
Frýba, L. (2001). “A rough assessment of railway bridges for high speed trains.” Eng. Struct., 23, 548–556.
Garinei, A. (2006). “Vibration of simple beam-like modelled bridge under harmonic moving loads.” Int. J. Eng. Sci., 44, 778–787.
Garinei, A., and Risitano, G. (2008). “Vibration of railway bridges for high speed trains under moving loads varying in time.” Eng. Struct., 30, 724–732.
Henchi, K., Fafard, M., Dhatt, G., and Talbot, M. (1997). “Dynamic behaviour of multi-span beams under moving loads.” J. Sound Vib., 199(1), 33–50.
Inglis, C. E. (1934). A mathematical treatise on vibration in railway bridges. University Press, Cambridge, UK.
Koloušek, V. (1956). Dynamics of civil engineering structures—Part I: General problems, Prague (in Czech).
Koloušek, V. (1961). Dynamics of civil engineering structures—Part II—Continuous beams and frame systems, Prague (in Czech).
Koloušek, V. (1967). Dynamics of civil engineering structures—Part III—Select topics, Prague (in Czech).
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.
Mackertich, S. (1992). “Response of a beam to a moving mass.” J. Acoust. Soc. Am., 92(3), 1766–1769.
Michaltsos, G., Sophianopoulos, D., and Kounadis, A. N. (1996). “The effect of a moving mass and other parameters on the dynamic response of a simply supported beam.” J. Sound Vib., 191(3), 357–362.
Ricciardelli, F., and Pizzimenti, A. D. (2007). “Lateral walking-induced forces on footbridges.” J. Bridge Eng., 12(6), 677–688.
Timoshenko, S. P. (1922). “On the forced vibration of bridges.” Philos. Mag., Ser. 6, 43.
Yang, Y. B., Yau, J. D., and Hsu, L. C. (1997). “Vibration of simple beams due to trains moving at high speeds.” Eng. Struct., 19(11), 936–944.
Yang, Y. B., Yau, J. D., and Wu, Y. S. (2004). Vehicle-bridge interaction dynamics, with applications to high-speed railways. World Scientific, Singapore.
Yau, J. D., Wu, Y. S., and Yang, Y. B. (2001). “Impact response of bridges with elastic bearings to moving loads.” J. Sound Vib., 248(1), 9–30.
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Information
Published In
Journal of Engineering Mechanics
Volume 137 • Issue 6 • June 2011
Pages: 422 - 430
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Dec 21, 2008
Accepted: Nov 29, 2010
Published online: Nov 30, 2010
Published in print: Jun 1, 2011
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