The response and distribution of maxima of a non-linear oscillator with band limited excitation

Abstract

The response of an oscillator with a non-linear spring is considered when the excitation force is white noise filtered through a first order low pass filter. When the damping is light, one term in the Fokker-Planck equation for the joint density function of displacement, velocity and acceleration is negligibly small. The resulting approximate Fokker-Planck equation can be solved exactly. An equivalent damping that keeps the power input to the oscillator constant is used to extend the range of validity of the approximate solution. A density function for the distribution of maxima is obtained that covers both narrow band and broad band response. A numerical example of the non-linear maxima distribution is calculated for the case of an oscillator with a bilinear spring.