Investigation of a non-linear system under partially prescribed random excitation

The problem of non-linear systems excited by random forces with known power spectral density functions and unspecified probability structure is considered. Sufficient, but not necessary, conditions on the input under which the response can be a Gaussian process are investigated. The approach is illustrated by investigating the hardening spring cubic oscillator under wide and narrow band excitations. The non-Gaussian probability density of the input that leads to Gaussian response is determined.