Presence of Resonance Frequencies in a Heavily Damped Two-Degree-of-Freedom System
Publication: Journal of Engineering Mechanics
Volume 140, Issue 2
Abstract
It has been experimentally identified that a stationary crowd or an individual acts like a mass-spring-damper in structural vibration. However, experiments have shown that only one resonance frequency or damped natural frequency of human–structure systems are observed on structures, such as grandstands or floors with crowds. This paper studies the presence of the two resonance frequencies in a heavily damped, two-degree-of-freedom (TDOF) system in theory and in experiment. The invisibility, or nonpresence, of a resonance frequency is defined by investigating a heavily damped single-degree-of-freedom (SDOF) system subjected to a harmonic load. By using frequency response functions (FRFs) for acceleration, it is demonstrated that the observable presence of the two resonance frequencies of the TDOF system depends on the mass ratio and frequency ratio of the upper SDOF model to the lower SDOF model and the damping ratio of the upper SDOF model. The conditions for the presence of the two resonance frequencies are presented graphically based on a study of over 5,000 cases that covered reasonable ranges for these three parameters. Two sets of human–structure interaction experiments, whose design was based on the conditions for observing the resonance frequencies, demonstrated qualitatively the effect of the mass ratio of the system and damping ratio of the human body on the presence of the resonance frequencies, thus verifying the theoretical results. These limiting conditions are discussed and the observation of only one resonance frequency in experiments on some human–structure systems is explained.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work reported in this paper has been supported by the Leverhulme Trust for the Human-Structure Interaction—Applying Body Biodynamics into Structural Dynamics project, which is gratefully acknowledged. The authors thank the reviewers for providing critical but constructive comments that improved the quality and presentation of the paper, and Dr. Brian Ellis for commenting on the paper. The first test rig [Fig. 8(a)] was designed and made by Prof. Jon Wright.
References
Brownjohn, J. M. W. (2001). “Energy dissipation from vibrating floor slabs due to human-structure interaction.” J. Shock Vib., 8(6), 315–323.
Den Hartog, J. P. (1947). Mechanical vibrations, 3rd Ed., McGraw-Hill, New York.
De Silva, C. W. (2007). Vibration: Fundamentals and practice, 2nd Ed., CRC Press, Boca Raton, FL.
Duarte, E. (2008). “Human body actions on structures: Bouncing, standing and walking on the spot.” Ph.D. thesis, Univ. of Manchester, Manchester, U.K.
Ellis, B. R., and Ji, T. (1997). “Human-structure interaction in vertical vibrations.” Proc., Institution of Civil Engineers—Structures and Buildings, 122(February), 1–9.
Ellis, B. R., and Ji, T. (2004). The response of structures to dynamic crowd loads, Building Research Establishment (BRE), Watford, U.K.
Fairley, T. E., and Griffin, M. J. (1989). “The apparent mass of the seated human body: Vertical vibration.” J. Biomech., 22(2), 81–94.
Griffin, M. J. (1990). Handbook of human vibration, 1st Ed., Academic Press, London.
Institution of Structural Engineers. (2008). Dynamic performance requirements for permanent grandstands subject to crowd action: Recommendations for management, design and assessment, London.
Ji, T. (2003). “Understanding the interactions between people and structures.” The Structural Engineer, 81(14), 12–13.
Li, H., Wang, S.-Y., Song, G., and Liu, G. (2004). “Reduction of seismic forces on existing building with newly constructed additional stories including friction layer and dampers.” J. Sound Vib., 269(3–5), 653–667.
Matsumoto, Y., and Griffin, M. J. (1998). “Dynamic response of the standing human body exposed to vertical vibration: Influence of posture and vibration magnitude.” J. Sound Vib., 212(1), 85–107.
Meriam, J. L., and Kraige, L. G. (1998). Engineering mechanics, Vol. 2: Dynamics, 4th Ed., Wiley, New York.
Murray, M. M., Allen, D. E., and Ungar, E. E. (1997). “Floor vibrations due to human activity.” AISC/CISC Steel Design Guide Series 11, AISC, Chicago, IL.
National Research Council of Canada. (2006). User’s guide—NBC 2005: Structural commentaries (part 4 of division B), Canadian Commission on Buildings and Fire Codes, Ottawa.
Sachse, R., Pavic, A., and Reynolds, P. (2003). “Human-structure dynamic interaction in civil engineering dynamics: A literature review.” Shock Vib. Digest, 35(1), 3–18.
Sachse, R., Pavic, A., and Reynolds, P. (2004). “Parametric study of modal properties of damped two-degree-of-freedom crowd-structure dynamic systems.” J. Sound Vib., 274(3–5), 461–480.
Sim, J., Blakeborough, A., and Williams, M. (2006). “Modelling effects of passive crowds on grandstand vibration.” Proc., Institution of Civil Engineers—Structures and Buildings, 159(5), 261–272.
Spike 2 [Computer software]. Cambridge, U.K., Cambridge Electronic Design.
Tiernan, S., and Fahy, M. (2002). “Dynamic FEA modelling of ISO tank containers.” J. Mater. Process. Technol., 124(1–2), 126–132.
Yao, S., Wright, J. R., Pavic, A., and Reynolds, P. (2006). “Experimental study of human-induced dynamic forces due to jumping on a perceptibly moving structure.” J. Sound Vib., 296(1–2), 150–165.
Zhang, Q., and Ji, T. (2010). “Representation of a standing body in the vertical vibration.” Proc., 45th U.K. Conf. on Human Response to Vibration, Institute of Naval Medicine, Gosport, U.K.
Zhou, D., and Ji, T. (2006). “Dynamic characteristics of a beam and distributed spring-mass system.” Int. J. Solids Struct., 43(18–19), 5555–5569.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Sep 1, 2010
Accepted: May 13, 2013
Published online: May 15, 2013
Published in print: Feb 1, 2014
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.