Response’s Probabilistic Characteristics of a Duffing Oscillator under Harmonic and Random Excitations - Anh, Nguyen Dong; V.L., Zakovorotny; Hao, Duong Ngoc (VNU Journal of Science: Mathematics - Physics, 2014)
Abstract: Response’s probabilistic characteristics of a Duffing oscillator subjected to combined harmonic and random excitations are investigated by a technique combining the stochastic averaging method and the equivalent linearization method. The harmonic excitation frequency is taken to be in the neighborhood of the system’s natural frequency. The original equation is averaged by the stochastic averaging method in Cartesian coordinates. Then the equivalent linearization method is applied to the nonlinear averaged equations so that the equations obtained can be solved exactly by the technique of auxiliary function. The theoretical analyses of Duffing oscillator are validated by numerical simulation. Keywords: Duffing, averaging method, equivalent linearization, harmonic excitation, random excitation.