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TECHNICAL PAPERS

The Probabilistic Solutions to Nonlinear Random Vibrations of Multi-Degree-of-Freedom Systems

[+] Author and Article Information
G.-K. Er

Faculty of Science and Technology, University of Macao, P.O. Box 3001, Macao, Chinae-mail: fstgke@umac.mo

J. Appl. Mech 67(2), 355-359 (Nov 01, 1999) (5 pages) doi:10.1115/1.1304842 History: Received May 18, 1998; Revised November 01, 1999
Copyright © 2000 by ASME
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References

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Er,  G. K., 1998, “Multi-Gaussian Closure Method for Randomly Excited Nonlinear Systems,” Int. J. Non-Linear Mech., 33, pp. 201–214.
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Kloeden, P. E., and Platen, E., 1995, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin.
Er,  G. K., 1999, “A Consistent Method for the PDF Solutions of Random Oscillators,” ASCE Journal of Engineering Mechanics, 125, pp. 443–447.
Soong, T. T., 1973, Random Differential Equations in Science and Engineering, Academic Press, New York.
Scheurkogel, A, and Elishakoff, I, 1988, “Non-linear Random Vibration of a Two-Degree-of-Freedom System,” Non-Linear Stochastic Engineering Systems, F. Ziegler and G. I. Schuëller, eds., Springer-Verlag, Berlin, pp. 285–299.

Figures

Grahic Jump Location
The probability density functions of X1, for Example 1
Grahic Jump Location
The probability density functions of X3, for Example 1
Grahic Jump Location
The logarithmic probability density functions of X1, for Example 1
Grahic Jump Location
The logarithmic probability density functions of X3, for Example 1
Grahic Jump Location
The probability density functions of X1, for Example 2
Grahic Jump Location
The probability density functions of X2, for Example 2
Grahic Jump Location
The logarithmic probability density functions of X1, for Example 2
Grahic Jump Location
The logarithmic probability density functions of X2, for Example 2

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