On Double Peak Probability Density Functions of a Duffing Oscillator to Combined Deterministic and Random Excitations
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摘要: 研究Duffing振子在谐和与随机噪声联合作用下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．数值模拟表明提出的方法是有效的．Abstract: The principal resonance of Duffing oscillator to combined deterministic and random external excitation is investigated.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 obtained the double peak probability density function.The theoretical analyses are verified by numerical results.
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