The spectral density of the nonlinear damping model: Single DOF case

The spectral density and the correlation function of the following single DOF nonlinear damping model is investigated: , where is a small parameter. A formula for the spectral density is established with accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first-order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly.