Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric and External White Noise Excitations: Part II

[+] Author and Article Information
Y. K. Lin, Guoqiang Cai

Center for Applied Stochastics Research, Florida Atlantic University, Boca Raton, FL 33431

J. Appl. Mech 55(3), 702-705 (Sep 01, 1988) (4 pages) doi:10.1115/1.3125852 History: Received March 23, 1987; Revised March 25, 1988; Online July 21, 2009


A systematic procedure is developed to obtain the stationary probability density for the response of a nonlinear system under parametric and external excitations of Gaussian white noises. The procedure is devised by separating the circulatory portion of the probability flow from the noncirculatory flow, thus obtaining two sets of equations that must be satisfied by the probability potential. It is shown that these equations are identical to two of the conditions established previously under the assumption of detailed balance; therefore, one remaining condition for detailed balance is superfluous. Three examples are given for illustration, one of which is capable of exhibiting limit cycle and bifurcation behaviors, while another is selected to show that two different systems under two differents sets of excitations may result in the same probability distribution for their responses.

Copyright © 1988 by ASME
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