Wave Propagation in a Timoshenko Beam Building Model
Publication: Journal of Engineering Mechanics
Volume 140, Issue 5
Abstract
This study analyzes wave propagation in a Timoshenko beam model of a high-rise building excited by base motion. This model accounts for wave dispersion caused by bending and is more realistic for analysis of wave propagation in high-rise buildings than shear beam and other discrete nondispersive models. The model transfer functions and impulse response functions are obtained from the analytical solution for a forced vibration response of the beam excited by base motion. The impulse response functions represent the model response to a virtual input pulse; a set of such functions at different levels is used to study pulse propagation in the beam. A parametric study of dispersion and its effects on the model transfer functions and impulse response functions is presented in terms of dimensionless parameters and in ranges corresponding to buildings. The model is validated for a 9-story full-scale RC building and smaller earthquake excitation. The results provide insight into dispersive wave propagation in buildings caused by bending, which is useful for the interpretation of impulse responses of buildings obtained from earthquake records and for the development and testing of wave methods for structural health monitoring. The results can also be used for testing numerical models for pulse propagation in buildings.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The strong motion data for Millikan Library were provided by the National Strong Motion Program of the USGS, and are accessible from the Engineering Center for Strong Motion Data (http://www.strongmotioncenter.org). The authors appreciate insightful discussions on the behavior of Millikan Library with F. Udwadia, T. Heaton, and M. Trifunac, and also the constructive comments of two of the anonymous reviewers, which significantly improved the paper.
References
Boutin, C., Hans, S., Ibraim, E., and Roussillon, P. (2005). “In situ experiments and seismic analysis of existing buildings. Part II: Seismic integrity threshold.” Earthquake Eng. Struct. Dynam., 34(12), 1531–1546.
Cowper, G. R. (1966). “The shear coefficient in Timoshenko’s beam theory.” J. Appl. Mech., 33(2), 335–340.
Gičev, V., and Trifunac, M. D. (2009a). “Transient and permanent shear strains in a building excited by strong earthquake pulses.” Soil. Dyn. Earthquake Eng., 29(10), 1358–1366.
Gičev, V., and Trifunac, M. D. (2009b). “Rotations in a shear-beam model of a seven-story building caused by nonlinear waves during earthquake excitation.” Struct. Contr. Health Monit., 16(4), 460–482.
Hutchinson, J. R. (1981). “Transverse vibrations of beams, exact versus approximate solutions.” J. Appl. Mech., 48(4), 923–928.
Kanai, K., and Yoshizawa, S. (1963). “Some new problems of seismic vibrations of a structure. Part 1.” Bull. Earthq. Res. Inst., 41, 825–833.
Kawakami, H., and Oyunchimeg, M. (2004). “Wave propagation modeling analysis of earthquake records for buildings.” J. Asian Archit. Build. Eng., 3(1), 33–40.
Kohler, M. D., Heaton, T., and Bradford, S. C. (2007). “Propagating waves in the steel, moment-frame factor building recorded during earthquakes.” Bull. Seismol. Soc. Am., 97(4), 1334–1345.
Luco, J. E., Trifunac, M. D., and Wong, H. L. (1988). “Isolation of soil-structure interaction effects by full-scale forced vibration tests.” Earthquake Eng. Struct. Dynam., 16(1), 1–21.
Mead, D. J. (1985). “Wave propagation in Timoshenko beams.” Strojnicky Casopis, 36, 556–584.
Park, J. (2005). “Transfer function methods to measure dynamic mechanical properties of complex structures.” J. Sound Vibrat., 288(1–2), 57–79.
Prasad, C. (1965). “Effect of viscous damping on the flexural vibrations of a rod.” Proc. Natl. Inst. Sci. India, 31(2), 152–163.
Rahmani, M., and Todorovska, M. I. (2013). “1D system identification of buildings during earthquakes by seismic interferometry with waveform inversion of impulse responses—Method and application to Millikan library.” Soil. Dyn. Earthquake Eng., 47, 157–174.
Reis, M. A. S. (1978).“Wave propagation in elastic beams and rods.” Ph.D. thesis., Dept. of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA.
Şafak, E. (1999). “Wave-propagation formulation of seismic response of multistory buildings.” J. Struct. Eng., 426–437.
Snieder, R., and Şafak, E. (2006). “Extracting the building response using seismic interferometry: Theory and application to the Millikan Library in Pasadena, California.” Bull. Seismol. Soc. Am., 96(2), 586–598.
Stephen, N.G., and Puchegger, S. (2006). “On the valid frequency range of Timoshenko beam theory.” J. Sound Vibrat., 297(3–5), 1082–1087.
Timoshenko, S. P. (1921). “On the correction for shear of the differential equation for transverse vibrations of prismatic bars.” Philos. Mag., 41(245), 744–746.
Todorovska, M. I. (2009). “Seismic interferometry of a soil-structure interaction model with coupled horizontal and rocking response.” Bull. Seismol. Soc. Am., 99(2A), 611–625.
Todorovska, M. I., and Lee, V. W. (1989). “Seismic waves in buildings with shear walls or central core.” J. Eng. Mech., 2669–2686.
Todorovska, M. I., and Rahmani, M. T. (2013). “System identification of buildings by wave travel time analysis and layered shear beam models—Spatial resolution and accuracy.” Struct. Control Health Monit., 20(5), 686–702.
Todorovska, M. I., and Trifunac, M. D. (1989). “Antiplane earthquake waves in long structures.” J. Eng. Mech., 2687–2708.
Todorovska, M. I., and Trifunac, M. D. (2008a). “Earthquake damage detection in the Imperial County Services Building III: Analysis of wave travel times via impulse response functions.” Soil. Dyn. Earthquake Eng., 28(5), 387–404.
Todorovska, M. I., and Trifunac, M. D. (2008b). “Impulse response analysis of the Van Nuys 7-story hotel during 11 earthquakes and earthquake damage detection.” Struct. Contr. Health Monit., 15(1), 90–116.
Weaver, W., Timoshenko, S., and Young, D. H. (1989). Vibration problems in engineering, 5th Ed., Wiley, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 140 • Issue 5 • May 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jan 19, 2013
Accepted: Sep 29, 2013
Published online: Oct 2, 2013
Published in print: May 1, 2014
Discussion open until: Jun 14, 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.