Nonstationary Response Analysis of Long Span Bridges under Spatially Varying Differential Support Motions Using Continuous Wavelet Transform
Publication: Journal of Engineering Mechanics
Volume 134, Issue 2
Abstract
An input-output relation for the nonstationary response of long-span bridges subjected to random differential support motions is proposed in the present study. The proposed methodology is more general than the existing ones, in the sense that it can evaluate nonstationarity in both the intensity and frequency content of the response statistics for spatially correlated multipoint random excitations. Furthermore, because the input-output relation is established through the transfer functions of dynamic systems, the proposed wavelet-based methodology can easily be used to predict the stochastic response of any structural systems in conjunction with available finite-element software. The input-output formulation is also not restricted to a particular wavelet basis function, since it has been derived by following a general wavelet-based description of input nonstationary processes. The bridge has been modeled as a simply supported beam with multispans in a finite-element framework to obtain the dynamic properties. With a modified form of the Littlewood-Paley (real part of harmonic) wavelet basis function, the support motion has been modeled as a summation of independent random processes in different nonoverlapping frequency bands. At each frequency band, the random process is expressed as a product of a stationary orthogonal process and a deterministic envelope function that depends on the scale. An exponential coherence function is used to model the spatial variation of the ground motion. The response statistics are obtained by using a random vibration formulation in the wavelet domain. The results demonstrate the effects of frequency nonstationarity on the response of a multispan bridge with closely spaced modes and excitation of higher modes locally in time.
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References
Abrahamson, N. A. (1993). “Spatial variation of multiple support inputs.” Proc., 1st U.S. Seminar on Seismic Evaluation and Retrofit of Steel Bridges, Caltrans and Univ. of Berkeley, San Francisco.
Basu, B., and Gupta, V. K. (1998). “Seismic response of SDOF system by wavelet modeling of nonstationary processes.” J. Eng. Mech., 124(10), 1142–1150.
Basu, B., and Gupta, V. K. (2000). “Stochastic seismic response of SDOF systems through wavelets.” Eng. Struct., 22(12), 1714–1722.
Berrah, M., and Kausel, E. (1992). “Response spectrum analysis of structures subjected to spatially varying motions.” Earthquake Eng. Struct. Dyn., 21(6), 461–470.
Chan, Y. T. (1995). Wavelet basics, Kluwer Academic Publishers, Boston.
Chen, M. T., and Harichandran, R. S. (2001). “Response of an earth dam to spatially varying earthquake ground motion.” J. Eng. Mech., 127(9), 932–939.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures, McGraw-Hill, New York.
Conte, J. P., and Peng, B. F. (1996). “An explicit closed-form solution for linear systems subjected to nonstationary random excitation.” Probab. Eng. Mech., 11(1), 37–50.
DerKiureghian, A., and Crempien, J. (1989). “An evolutionary model for earthquake ground motion.” Struct. Safety, 6(2–4), 235–246.
DerKiureghian, A., and Neuenhofer, A. N. (1990). “Response spectrum method for multisupport seismic excitation.” Earthquake Eng. Struct. Dyn., 21(8), 713–740.
Hao, H., Olivera, C. S., and Penzien, J. (1989). “Multiple-station ground motion processing and simulation based on SMART-I array data.” Nucl. Eng. Des., 111(3), 293–310.
Harichandran, R. S., and Vanmarcke, E. (1986). “Stochastic variation of earthquake ground motion in space and time.” J. Eng. Mech., 112(2), 154–174.
Hindy, A., and Novak, M. (1980). “Earthquake response of buried insulated pipes.” J. Engrg. Mech. Div., 106(6), 1135–1149.
Kanai, K. (1957). “Semiempirical formula for the seismic characteristics of the ground.” Bulletin of Earthquake Research Institute, Tokyo, 35, 309–325.
Kijewski-Correa, T., and Kareem, A. (2006). “Efficacy of Hilbert and wavelet transforms for time-frequency analysis.” J. Eng. Mech., 132(10), 1037–1049.
Lin, C. W., and Loceff, F. A. (1980). “A new approach to compute system response with multiple support response spectra input.” Nucl. Eng. Des., 60(3), 347–352.
Loh, C. H., and Ku, B. D. (1995). “An efficient analysis of structural response for multiple-support seismic excitations.” Eng. Struct., 17(1), 15–26.
Newland, D. E. (1993). An introduction to random vibration, spectral and wavelet analysis, Longman Scientific and Technical, Essex, U.K.
Priestley, M. B. (1981). Spectral analysis and time series, Academic Press, New York.
Shinozuka, M., and Sato, Y. (1967). “Simulation of nonstationary random processes.” J. Engrg. Mech. Div., 93(1), 11–40.
Spanos, P. D., and Failla, G. (2004). “Evolutionary spectra estimation using wavelets.” J. Eng. Mech., 130(8), 952–960.
Staszewski, W. J. (1997). “Identification of damping in MDOF systems using time-scale decomposition.” J. Sound Vib., 203(2), 283–305.
Tajimi, T. (1960). “A statistical method for determining the maximum response of a building structure during an earthquake.” Proc., 2nd World Conf. on Earthquake Engineering, Tokyo and Kyoto, Japan, 781–797.
Uscinski, B. J. (1977). The elements of wave propagation in random media, McGraw-Hill, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 2 • February 2008
Pages: 155 - 162
Copyright
© 2008 ASCE.
History
Received: Nov 1, 2006
Accepted: Apr 19, 2007
Published online: Feb 1, 2008
Published in print: Feb 2008
Notes
Note. Associate Editor: Arvid Naess
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