STOCHASTIC RESPONSE OF DUFFING OSCILLATOR WITH FRACTIONAL OR VARIABLE-ORDER DAMPING

This paper introduces a numerical technique for the estimation of stochastic response of the Dung oscillator with fractional or variable or- der damping and driven by white noise excitation. The Wiener-Hermite ex- pansion is integrated with the Grunwald-Letnikov approximation in case of fractional order damping and with Coimbra approximation in case of variable- order damping. The numerical solver was tested and validated with the an- alytic solution and with Monte-Carlo simulations. The developed technique was shown to be ecient in simulating the stochastic non-linear dierential equations with fractional or variable order derivatives.