Random response of a strongly nonlinear oscillator with internal and external excitations

A second order oscillator with nonlinear restoring force and nonlinear damping is con-sidered: it is subject to both external and internal (parametric) excitations of Gaussian white noise type. The nonlinearities are chosen in such a way that the associated Fok-ker-Planck-Kolmogorov equation is solvable in the steady state. Different choices of some system parameters give rise to different and interesting shapes of the joint prob-ability density function of the response, which in some cases appears to be multimodal. The problem of the determination of the power spectral density of the response is also addressed by using the true statistical linearization method.