The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude an...The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude and phase. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method. These two one-peak-density functions were combined using the probability of realization of the two stable stationary solutions to obtain the double peak probability density function. The theoretical analysis are verified by numerical results.展开更多
基金Project supported by the National Natural Science Foundation of China (Key Program) (No.10332030)the Natural Science Foundation of Guangdong Province of China (No.04011640)
文摘The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude and phase. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method. These two one-peak-density functions were combined using the probability of realization of the two stable stationary solutions to obtain the double peak probability density function. The theoretical analysis are verified by numerical results.
