A linear stochastic differential equation of order N with colored noise random coefficients and random input is studied. An approximate expression for the autocorrelation of the response is derived in terms of the statistical properties of the random coefficients and input. This is achieved by using an expansion method known as the Born expansion (Feynman, 1962). Feynman diagrams are used as a short hand notation. In the particular case where the coefficients are white noise processes, the expansion method yields identical results to those obtained using an alternate method in a companion paper (Benaroya and Rehak, 1989). The expansion method is also used to demonstrate that white noise coefficients are statistically uncorrelated from the response.
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March 1989
Research Papers
Response and Stability of a Random Differential Equation: Part II—Expansion Method
H. Benaroya,
H. Benaroya
Applied Science Division, Weidlinger Associates, 333 Seventh Avenue, New York, N. Y. 10001
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M. Rehak
M. Rehak
Applied Science Division, Weidlinger Associates, 333 Seventh Avenue, New York, N. Y. 10001
Search for other works by this author on:
H. Benaroya
Applied Science Division, Weidlinger Associates, 333 Seventh Avenue, New York, N. Y. 10001
M. Rehak
Applied Science Division, Weidlinger Associates, 333 Seventh Avenue, New York, N. Y. 10001
J. Appl. Mech. Mar 1989, 56(1): 196-201 (6 pages)
Published Online: March 1, 1989
Article history
Received:
June 23, 1986
Revised:
May 11, 1988
Online:
July 21, 2009
Citation
Benaroya, H., and Rehak, M. (March 1, 1989). "Response and Stability of a Random Differential Equation: Part II—Expansion Method." ASME. J. Appl. Mech. March 1989; 56(1): 196–201. https://doi.org/10.1115/1.3176045
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