Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, June 20, 2001; final revision, Sept. 25, 2001. Associate Editor: N. C. Perkins.

Consider the following equation of motion
$x¨+2αx[˙1+ηt]+Ω2x[1+ξt]=ζt$
(1)
where $ξt,$$ηt,$$ζt$ are Gaussian white noises (in the Stratonovich sense) with spectral densities $Kξξ,$$Kηη,$$Kζζ,$ respectively. The two parametric white noises, $ηt$ and $ξt,$ are correlated, with cross-spectral density $Kξη.$ The objective is to obtain the spectral density (PSD) of the response $xt,$ which exists if $xt...$