Parametric Random Vibrations under Non-Gaussian Delta-Correlated Processes
Publication: Journal of Engineering Mechanics
Volume 121, Issue 12
Abstract
This paper addresses parametric random vibrations subjected to non-Gaussian delta-correlated processes as well as combinations of delta-correlated Gaussian and non-Gaussian processes. The scheme employs a response-moment method, in which response moments are solved through a series of simultaneous equations. This approach requires that a general response moment equation suitable for non-Gaussian/Gaussian, parametric/external excitations be developed. Two problems related to second-order linear systems are explored and their closed-form solutions for response moments up to fourth order are obtained. The first problem considers systems subjected to “physical” Gaussian white-noise parametric excitations together with non-Gaussian delta-correlated external excitations. The second problem considers both parametric and external excitations that are non-Gaussian and delta-correlated.
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References
1.
Bolotin, V. V. (1984). Random vibrations of elastic systems. Martinus Nijhoff Publishers, The Hague, The Netherlands.
2.
Cai, G. Q., and Lin, Y. K.(1992). “Response distribution of non-linear systems excited by non-Gaussian impulsive noise.”Int. J. Non-Linear Mech., 27(6), 955–967.
3.
Di Paola, M., and Falsone, G.(1993a). “Itô and Stratonovich integrals for delta-correlated processes.”Prob. Engrg. Mech., 8, 197–208.
4.
Di Paola, M., and Falsone, G. (1993b). “Stochastic dynamics of nonlinear systems driven by non-normal delta-correlated processes.”J. Appl. Mech., 600, 141—148.
5.
Gray, A. H. Jr., and Caughey, T. K.(1965). “A controversy in problems involving random parametric excitation.”J. Math. Phys., 44(3), 288–296.
6.
Grigoriu, M.(1987). “White noise processes.”J. Engrg. Mech., ASCE, 113(5), 757–765.
7.
Grigoriu, M.(1990). “Simulation of diffusion processes.”J. Engrg. Mech., ASCE, 116(7), 1524–1542.
8.
Hu, S.-L. J.(1993). “Responses of dynamic systems excited by non-Gaussian pulse processes.”J. Engrg. Mech., ASCE, 119(9), 1818–1827.
9.
Ibrahim, R. A. (1985). Parametric random vibration. Research Studies Press Ltd., Letchworth, England.
10.
Lin, Y. K. (1976). Probabilistic theory of structural dynamics. Robert E. Krieger Publishing Co., Inc., Malabar, Fla.
11.
Lutes, L. D., and Hu, S. J.(1986). “Non-normal stochastic response of linear systems.”J. Engrg. Mech., ASCE, 112(2), 127–141.
12.
Mortensen, R. E.(1969). “Mathematical problems of modeling stochastic nonlinear dynamic systems.”J. Stat. Phys., 1(2), 271–296.
13.
Parzen, E. (1962). Stochastic processes. Holden-Day, San Francisco, Calif.
14.
Stratonovich, R. L. (1963). Topics in the theory of random noise. Vol. 1, Gordon and Breach Science Publishers, New York, N.Y.
15.
Wong, E., and Zakai, M.(1965). “On the relationship between ordinary and stochastic differential equations.”Int. J. Engrg. Sci., 3, 213–229.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 121 • Issue 12 • December 1995
Pages: 1366 - 1371
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Dec 1, 1995
Published in print: Dec 1995
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