Phase plane for narrow band random excitation of a duffing oscillator

Abstract

The response of a Duffing oscillator to narrow band random excitation is consedered. It is shown that multiple values of the response can occur at some frequencies for very narrow excitation bandwidths, but these reduce to a single value as the bandwidth is increased. Time histories of quantities such as mean square displacement are obtained from the time dependent Fokker Planck equation. Smoothed time histories of mean square velocity and displacement are plotted on a phase plane. The phase plane can show either one sink, or two sinks and a saddle point as in the sinusoidal case, but again, excitation bandwith determines whether or not multiple sinks occur.