The problem of approximating the probability distribution of peaks, associated with a special class of non-Gaussian random processes, is considered. The non-Gaussian processes are obtained as nonlinear combinations of a vector of mutually correlated, stationary, Gaussian random processes. The Von Mises stress in a linear vibrating structure under stationary Gaussian loadings is a typical example for such processes. The crux of the formulation lies in developing analytical approximations for the joint probability density function of the non-Gaussian process and its instantaneous first and second time derivatives. Depending on the nature of the problem, this requires the evaluation of a multidimensional integration across a possibly irregular and disjointed domain. A numerical algorithm, based on first order reliability method, is developed to evaluate these integrals. The approximations for the peak distributions have applications in predicting the expected fatigue damage due to combination of stress resultants in a randomly vibrating structure. The proposed method is illustrated through two numerical examples and its accuracy is examined with respect to estimates from full scale Monte Carlo simulations of the non-Gaussian process.
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e-mail: s.gupta@tudelft.nl
e-mail: p.h.a.j.m.vangelder@tudelft.nl
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June 2008
Research Papers
Probability Distribution of Peaks for Nonlinear Combination of Vector Gaussian Loads
Sayan Gupta,
Sayan Gupta
Assistant Professor
Department of Applied Mechanics,
e-mail: s.gupta@tudelft.nl
Indian Institute of Technology Madras
, Chennai 600036, India
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P. H. A. J. M. van Gelder
P. H. A. J. M. van Gelder
Associate Professor
Department of Civil Engineering,
e-mail: p.h.a.j.m.vangelder@tudelft.nl
Technical University of Delft
, Stevinweg 1, P.O. Box 5048, 2600 GA Delft, The Netherlands
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Sayan Gupta
Assistant Professor
Department of Applied Mechanics,
Indian Institute of Technology Madras
, Chennai 600036, Indiae-mail: s.gupta@tudelft.nl
P. H. A. J. M. van Gelder
Associate Professor
Department of Civil Engineering,
Technical University of Delft
, Stevinweg 1, P.O. Box 5048, 2600 GA Delft, The Netherlandse-mail: p.h.a.j.m.vangelder@tudelft.nl
J. Vib. Acoust. Jun 2008, 130(3): 031011 (12 pages)
Published Online: April 8, 2008
Article history
Received:
July 14, 2006
Revised:
January 31, 2007
Published:
April 8, 2008
Citation
Gupta, S., and van Gelder, P. H. A. J. M. (April 8, 2008). "Probability Distribution of Peaks for Nonlinear Combination of Vector Gaussian Loads." ASME. J. Vib. Acoust. June 2008; 130(3): 031011. https://doi.org/10.1115/1.2890404
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