1/3 subharmonic response of Duffing oscillator under periodic and random excitations

The subharmonic response of one third order of Duffing oscillator under harmonic and random excitations is investigated for the first time by a technique combining the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function for Fokker-Planck equation. The averaged equations are linear zed so that the stationary density function of the approximate response can be found exactly by the technique of auxiliary function. The one third order subharmonic response obtained by the present technique is validated by numerical simulation. The significant contribution of this work is that it may lead to a new trend in investigating subharmonic oscillators in random nonlinear systems.