Calculation of Power Spectra from Response Spectra
Publication: Journal of Engineering Mechanics
Volume 109, Issue 1
Abstract
A method is presented to determine the power spectral density functions from given smooth response spectra. It is assumed that the underlying excitations constitute a stationary Gaussian random process. The relationship between the response spectrum and the power spectral density function is established by the probability distribution of the extreme values. The power spectral density function is discretized by parameters and piecewise polynomials and the free parameters are determined iteratively by a least square fit. Due to this discretization all required integrations can be carried out analytically. It is also possible to obtain a least square fit value of the duration of the stationary output process. The numerical examples include the calculation of the power spectral density functions for selected response spectra.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ang, A., “Probability Concepts in Earthquake Engineering,” Applied Mechanics in Earthquake Engineering, W. D. Iwan, ed., AMD‐Vol. 8, American Society of Mechanical Engineers, New York, N.Y., 1974, pp. 225–259.
2.
Clough, R. W., “Earthquake Analysis by Response Spectrum Superposition,” Bulletin of the Seismological Society of America, Vol. 52, No. 3, July, 1962, pp. 647–660.
3.
Clough, R. W., and Penzien, J., Dynamics of Structures, McGraw‐Hill Book Co., Inc., New York, N.Y., 1975.
4.
Damrath, R., “Ein stochastisches Verfahren der seismischen Analyse von Bauwerken mit Anwendung auf Kernkraftwerke,” thesis presented to Technische Universität Berlin, at Berlin, West Germany, in 1974, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
5.
Davenport, A. G., “Note on the Distribution of the Largest Value of a Random Function with Application to Gust Loading,” Proceedings of the Institution of Civil Engineers, Vol. 28, Paper No. 6739, 1964, pp. 187–196.
6.
Der Kiureghian, A., “On Response of Structures to Stationary Excitation,” Report No. EERC 79‐32, Earthquake Engineering Research Center, University of California, Berkeley, Calif., Dec., 1979.
7.
Housner, G. W., “Behavior of Structures during Earthquakes,” Journal of the Engineering Mechanics Division, ASCE, Vol. 85, No. EM4, Oct., 1959, pp. 109–129.
8.
Newmark, N. M., Blume, J. A., and Kapur, K. K., “Seismic Design Spectra for Nuclear Power Plants,” Journal of the Power Division, ASCE, Vol. 99, No. PO2, Nov., 1973, pp. 287–303.
9.
Newmark, N. M., and Rosenblueth, E., Fundamentals of Earthquake Engineering, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1971.
10.
Pfaffinger, D. D., “Comparative Seismic Analysis,” Proceedings of the European NASTRAN User's Conference, The MacNeal‐Schwendler Corp., Munich, West Germany, 1976.
11.
Pfaffinger, D. D., “Analytical Evaluation of Modal Covariance Matrices,” Computer Methods in Applied Mechanics and Engineering, Vol. 24, No. 3, Dec., 1980, pp. 269–286.
12.
Pfaffinger, D. D., “Dynamische Probleme unter Anwendung Finiter Elemente,” Finite Berechnungsmethoden im konstruktiven Ingenieurbau, Mitteilung Nr. 76‐8, Institut für konstruktiven Ingenieurbau, Ruhr‐Universität Bochum, Bochum, 1976.
13.
Pfaffinger, D. D., “Die Methods der Antwortspektren aus der Sicht der probabilistischen Tragwerksdynamik,” Report Nr. 90, Institute of Structural Engineering, Swiss Federal Institute of Technology, Zurich, Switzerland, 1979.
14.
Ruiz, P., and Penzien, J., “Probabilistic Study of the Behaviour of Structures during Earthquakes,” Report No. EERC 69‐3, Earthquake Engineering Research Center, University of California, Berkeley, Calif., 1969.
15.
Vanmarcke, E. H., “On the Distribution of the First‐Passage Time for Normal Stationary Random Processes,” Journal of Applied Mechanics, Vol. 42, Mar. 1975, pp. 215–220.
16.
Vanmarcke, E. H., and Gasparini, D. A., “Simulated Earthquake Ground Motions,” Transactions of the 4th International Conference on Structural Mechanics in Reactor Technology, San Francisco, Aug. 15–19, 1977, Vol. K. (a), Paper K 1/9, North‐Holland Publishing Company, Amsterdam, the Netherlands, 1977.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 109 • Issue 1 • February 1983
Pages: 357 - 372
Copyright
Copyright © 1983 ASCE.
History
Published online: Feb 1, 1983
Published in print: Feb 1983
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.