On double-peak probability density functions of a Duffing oscillator under narrow-band random excitations

Abstract

The principal resonance of Duffing oscillator under the narrow-band random exter nal excitation is investigated. The method of multiple scales is used to determi ne the equations of modulation of amplitude and phase. The one-peak probability density function of each of the two stable stationary solutions is then calculat ed by perturbation analysis in the resonant case. These two functions are combin ed by using the probability of realization of the two stable stationary solutions to calculate the double_peak probability density function approximately. Theor etical analyses are verified by numerical results.