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

Authors:
  • RHRong Hai-Wu
    Rong Hai-Wu
  • WXWang Xiang-Dong
    Wang Xiang-Dong
  • XWXu Wei
    Xu Wei
  • MGMeng Guang
    Meng Guang
  • FTFang Tong
    Fang Tong
  • (1(1)佛山大学数学系，佛山528000;(2)佛山大学数学系，佛山528000;上海交通大学振动、冲击、噪声国家重点实验室，上海200030;(3)上海交通大学振动、冲击、噪声国家重点实验室，上海200030;(4)西北工业大学数学系，西安710072
    (1)佛山大学数学系，佛山528000;(2)佛山大学数学系，佛山528000;上海交通大学振动、冲击、噪声国家重点实验室，上海200030;(3)上海交通大学振动、冲击、噪声国家重点实验室，上海200030;(4)西北工业大学数学系，西安710072
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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.