Abstract
The stationary response of oscillators possessing linear damping and non-linear stiffness to the white Gaussian noise excitation is considered. The original stochastic differential equation (SDE) is used to establish relations between the system parameters and the envelope correlation function. The approximation approach is based on the moment approximation and replacement of the envelope generating SDE by the new one with analytical solution of the corresponding Fokker-Planck equation. The usefulness of the method is illustrated by application to the randomly driven Duffing oscillator.
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