作　　者： ; ; ; ; ;

机构地区： 上海交通大学理学院数学系

出　　处： 《物理学报》 2005年第6期2557-2561,共5页

摘　　要： 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.

关 键 词： 非线性振子 双峰稳态概率密度 多尺度法 线性化方法 随机微分方程 单自由度

领　　域： [理学] [理学] [理学] [理学]