Frequency Analysis in Stochastic Linearization
Publication: Journal of Engineering Mechanics
Volume 120, Issue 12
Abstract
This paper presents a frequency domain method to estimate the second‐order statistics of the response of complex hysteretic structures under stationary stochastic excitation. The nonlinear constitutive relations are dealt with by means of a stochastic linearization approach of an iterative nature. Since the first iteration has been accomplished, a criterion is established that allows location of the regions where inelastic deformations progress. Other regions of potential plastic behavior, which actually remain elastic, may thus be removed from the structural equation of motion with a tremendous computational advantage. Hinged frames and shear‐beam models are numerically investigated to illustrate the effectiveness of the proposed scheme.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Atalik, T. S., and Utku, S. (1976). “Stochastic linearization of multidegree of freedom nonlinear systems.” J. Earthq. Engrg. Struct. Dynamics, 4, 411–420.
2.
Bouc, R. (1967). “Forced vibrations of a mechanical system with hysteresis.” Proc., 4th Conf. Nonlinear Oscillations, Prague, Czechoslovakia.
3.
Casciati, F., and Faravelli, L. (1985). “Methods of nonlinear stochastic dynamics for the assessment of structural fragility.” Nuclear Engrg. Des., 90, 341–356.
4.
Casciati, F., and Faravelli, L. (1988). “Stochastic linearization for 3‐D frames.” J. Engr. Mech., ASCE, 114(10), 1760–1771.
5.
Casciati, F., and Faravelli, L. (1989). “Hysteretic 3‐D frames under stochastic excitation.” Res Mechanica, 26, 193–213.
6.
Casciati, F., and Faravelli, L. (1991). Fragility analysis of complex structural systems. Research Studies Press Ltd., Taunton, Mass.
7.
Casciati, F., Faravelli, L., and Hasofer, M. (1993). “A new philosophy for stochastic equivalent linearization.” Prob. Engrg. Mech., 8, 179–185.
8.
Casciati, F., Faravelli, L., and Venini, P. (1991). “Neglecting higher complex modes in nonlinear stochastic vibration.” Proc., 4th Int. Conf. on Recent Advances in Struct. Dynamics, Elsevier, London, England, 865–874.
9.
Faravelli, L., Casciati, F., and Singh, M. P. (1988). “Stochastic equivalent linearization algorithms and their applicability to hysteretic systems.” Meccanica, 23(2), 107–112.
10.
Faravelli, L., and Venini, P. (1992). “Stochastic dynamics of hysteretic systems.” Proc., 6th ASCE Conf. on Prob. Mech. and Struct. and Geotech. Rel., Y. K. Lin, ed., ASCE, New York, N.Y., 53–56.
11.
Meirovitch, L. (1980). Computational methods in structural dynamics. Sijthoff & Noordhoff, The Hague, The Netherlands.
12.
Mochio, T., Samaras, E., and Shinozuka, M. (1985). “Stochastic equivalent linearization for finite‐element based reliability analysis.” Proc., ICOSSAR '85, ASCE, New York, N.Y., 1, 375–384.
13.
Roberts, J. B., and Spanos, P. D. (1990). Random vibration and statistical linearization. John Wiley and Sons, Ltd., Chichester, England.
14.
Singh, M. P., Maldonado, G., Heller, R., and Faravelli, L. (1988). “Modal analysis of nonlinear hysteretic structures for seismic motions.” Nonlinear structural dynamics in engineering systems, F. Ziegler and G. Schueller, eds., Springer‐Verlag, Berlin, Germany, 443–454.
15.
Wen, Y. K. (1980). “Equivalent linearization for hysteretic systems under random excitation.” J. Appl. Mech., 47, 150–154.
Information & Authors
Information
Published In
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jun 8, 1993
Published online: Dec 1, 1994
Published in print: Dec 1994
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.