Non‐Normal Stochastic Response of Linear Systems
Publication: Journal of Engineering Mechanics
Volume 112, Issue 2
Abstract
Conventional analysis of mean squared values is extended to calculation of the fourth moment of the response of a linear system. This provides a way to investigate the non‐normality of structural response, due to a non‐normal excitation. Studies are made for a linear SDF structure subjected to fairly simple non‐normal forces, which include a “white noise” process and filtered processes. Each filtered non‐normal process is generated by passing a “white noise” non‐normal process through a linear second‐order filter. The non‐normality of the structural response is investigated by integration in both the time domain and the frequency domain and by a more efficient technique that is an extension of the Lyapunov equation. This latter method reduces the calculation of the fourth moment of the response to solving a set of simultaneous linear algebraic equations.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Benjamin, J. K., and Cornell, C. A., Probability, Statistics and Decision for Civil Engineers, McGraw‐Hill Book Company, New York, NY, 1970.
2.
Grigoriu, M., “Crossings of Non‐Gaussian Translation Processes,” Journal of Engineering Mechanics, ASCE, Vol. 110, No. EM4, Proc. Paper 18732, Apr., 1984, pp. 610–620.
3.
Hu, S.‐L. J., Effects of Nonnormality on Stochastic Structural Dynamics and Fatigue, thesis submitted, to Rice Univ., at Houston, TX, in 1984, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
4.
Kuznetsov, P. I., Stratonovich, R. L., and Tikhonov, V. I., “The Transmission of Certain Random Functions Through Linear Systems,” Non‐Linear Transformations of Stochastic Processes, translated by O. M. Blunn, Pergamon Press, Ltd., 1965, pp. 3–28.
5.
Lin, Y. K., Probabilistic Theory of Structural Dynamics, McGraw‐Hill Book Company, New York, NY, 1976, reprinted by Krieger Publishing Co., Melbourne, FL.
6.
Lutes, L. D., Corazao, M., Hu, S.‐L. J., and Zimmerman, J. J., “Stochastic Fatigue Damage Accumulation,” Journal of Structural Engineering, ASCE, Vol. 110, No. ST11, Proc. Paper 19823, Nov., 1984, pp. 2585–2601.
7.
Spanos, P. D., “Spectral Moments Calculation of Linear System Output,” Journal of Applied Mechanics, ASME, Vol. 50, Dec., 1983, pp. 901–903.
8.
Spanos, P. D., “A Useful Integral for Random Vibration Analyses,” Proceedings, 4th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, Jan., 1984, pp. 151–154.
9.
Stratonovich, R. L., Topics in the Theory of Random Noise, Gordon and Breach, Science Publishers, Inc., 1963.
Information & Authors
Information
Published In
Copyright
Copyright © 1986 ASCE.
History
Published online: Feb 1, 1986
Published in print: Feb 1986
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.