Swaying of Pedestrian Bridges
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Bridge Engineering
Volume 10, Issue 2
Abstract
The paper considers nonlinear (autoparametric) resonance in footbridges as a reason for excessive lateral vibrations induced by walking pedestrians. To describe the above-mentioned phenomenon, a physical model (an elastic pendulum) is proposed. Under the special frequency conditions (the ratio between frequencies of vertical and lateral beam modes is about 2, or 2:1), nonlinear resonance becomes possible if a vertically excited mode is near a primary resonance and a load parameter (a static displacement caused by pedestrians) is equal or more than its critical value. When the increasing load parameter passes through the critical value, a jump phenomenon is observed for the lateral mode and the vertical mode is saturated. Swaying of pedestrian bridges can be treated as a two-step process. The first step (achievement of the jump phenomenon), described in the paper, is the condition for the beginning of the second step—the process of interaction between applied forces and the lateral mode of vibration.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bachman, H. (1992). “Vibration upgrading of gymnasia, dance halls and footbridges.” Struct. Eng. Int. (IABSE, Zurich, Switzerland), 2, 118–124.
Dallard, P., et al. (2001a). “The London Millennium Footbridge.” Struct. Eng., 79(22), 17–33.
Dallard, P., et al. (2001b). “London Millennium Bridge: Pedestrian-induced lateral vibration.” J. Bridge Eng., 6(6), 412–417.
ENR. (2000), July 10, 14–15.
Fujino, Y., Warnitchai, P., and Pacheco, B. M. (1993a). “An experimental and analytical study of autoparametric resonance in 3 dof model of a cable-stayed beam.” Nonlinear Dyn. 4, 111–138.
Fujino, Y., Pacheco, B. M., Nakamura, S., and Warnitchai, P. (1993b). “Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge.” Earthquake Eng. Struct. Dyn., 22, 741–758.
Gol’denblat, I. I. (1947). Contemporary problems of vibrations and stability of engineering structures, Stroiiizdat, Moscow.
Gorelik, G., and Witt, A. (1933). “Swing of an elastic pendulum as an example of two parametrically bound linear vibration systems.” J. Tech. Phys., 3, 244–307.
Heinbockel, J. H., and Struble, R. A. (1963). “Resonant oscillations of an extensible pendulum.” Z. Angew. Math. Phys., 14, 262–269.
Kane, T. R., and Kahn, M. E. (1968). “On a class of two-degree-of-freedom oscillations.” J. Appl. Mech., 35, 547–552.
Minorsky, N. (1962). Nonlinear oscillations, Van Nostrand, Princeton, N.J.
Nayfeh, A. H. (1973). Perturbation methods, Wiley, New York.
Nayfeh, A. H., and Mook, D. T. (1995). Nonlinear oscillations, Wiley, New York.
Nayfeh, A. H., Mook, D. T., and Marshall, L. R. (1973). “Nonlinear coupling of pitch and roll in ship motions.” J. Hydronaut., 7, 143–152.
Olsson, M. G. (1976). “Why does a mass on a spring sometimes misbehave?” Am. J. Phys., 44, 1211–1212.
Peterson, C. (1972). “Theory of random vibrations and applications.”IT Work Rep. No. 2/72, Structural Engineering Laboratory, Technical Univ. of Munich, Munich, Germany.
Ryland, G., and Meirovitch, L. (1977). “Stability boundaries of a swinging spring with oscillating support.” J. Sound Vib., 51(4), 547–560.
van der Burgh, A. H. (1968). “On the asymptotic solutions of the differential equations for the elastic pendulum.” J. Mec., 7, 507–520.
Information & Authors
Information
Published In
Copyright
© 2005 ASCE.
History
Received: Jan 23, 2002
Accepted: Mar 23, 2004
Published online: Mar 1, 2005
Published in print: Mar 2005
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.