The random response of nonlinear dynamic systems involving stochastic coefficients is examined. A non-Gaussian closure scheme is outlined and employed to resolve an observed contradiction of the results obtained by other techniques. The method is applied to a system possessing nonlinear damping. The stationary response is obtained by numerical integration of the closed differential equations of the moments (up to fourth order). An interesting feature of the numerical results reveals the existence of a jump in the response statistic functions. This new feature may be attributed to the fact that the non-Gaussian closure more adequately models the nonlinearity, and thus results in characteristics that are similar to those of deterministic nonlinear systems. The results are compared with solutions derived by the Gaussian closure and stochastic averaging method.
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December 1985
Research Papers
Stochastic Response of Nonlinear Dynamic Systems Based on a Non-Gaussian Closure
R. A. Ibrahim,
R. A. Ibrahim
Texas Tech University, Department of Mechanical Engineering, Lubbock, Texas 79409
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A. Soundararajan,
A. Soundararajan
Texas Tech University, Department of Mechanical Engineering, Lubbock, Texas 79409
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H. Heo
H. Heo
Texas Tech University, Department of Mechanical Engineering, Lubbock, Texas 79409
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R. A. Ibrahim
Texas Tech University, Department of Mechanical Engineering, Lubbock, Texas 79409
A. Soundararajan
Texas Tech University, Department of Mechanical Engineering, Lubbock, Texas 79409
H. Heo
Texas Tech University, Department of Mechanical Engineering, Lubbock, Texas 79409
J. Appl. Mech. Dec 1985, 52(4): 965-970 (6 pages)
Published Online: December 1, 1985
Article history
Received:
June 1, 1984
Revised:
December 1, 1984
Online:
July 21, 2009
Citation
Ibrahim, R. A., Soundararajan, A., and Heo, H. (December 1, 1985). "Stochastic Response of Nonlinear Dynamic Systems Based on a Non-Gaussian Closure." ASME. J. Appl. Mech. December 1985; 52(4): 965–970. https://doi.org/10.1115/1.3169176
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