窄带随机噪声作用下Duffing振子的双峰稳态概率密度

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

研究了Duffing振子在窄带随机噪声激励下的系统响应的双峰稳态概率密度问题.用多尺度法分离了系统的快变项,得到了系统慢变项满足的随机微分方程.用线性化方法求出了双峰稳态概率密度的表达式.数值模拟表明本文提出的方法是有效的.

The principal resonance of Duffing oscillator under the narrow-band random external excitation is investigated. The method of multiple scales is 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 is then calculated by perturbation analysis in the resonant case. These two functions are combined by using the probability of realization of the two stable stationary solutions to calculate the double-peak probability density function approximately. Theoretical analyses are verified by numerical results.