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On double peak probability density functions of duffing oscillator to combined deterministic and random excitations

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Abstract

The principal resonance of Duffing oscillator to combined deterministic and random external excitation was 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 obtain the double peak probability density function. The theoretical analysis are verified by numerical results.

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Authors and Affiliations

  1. Department of Mathematics, Foshan University, Foshan, 528000, Guangdong Province, P. R. China

    Rong Hai-wu  (戎海武) (Professor) & Wang Xiang-dong  (王向东)

  2. The State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiaotong University, Shanghai, 200030, P. R. China

    Rong Hai-wu  (戎海武) (Professor) & Meng Guang  (孟光)

  3. Department of Mathematics, Northwestern Polytechnical University, Xi’an, 710072, P. R. China

    Xu Wei  (徐伟) & Fang Tong  (方同)

Authors
  1. Rong Hai-wu  (戎海武)
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  2. Wang Xiang-dong  (王向东)
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  3. Meng Guang  (孟光)
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  4. Xu Wei  (徐伟)
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  5. Fang Tong  (方同)
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Corresponding author

Correspondence to Rong Hai-wu  (戎海武).

Additional information

Communicated by ZHANG Shi-sheng

Project supported by the National Natural Science Foundation of China (Key Program) (No.10332030) and the Natural Science Foundation of Guangdong Province of China (No.04011640)

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Rong, Hw., Wang, Xd., Meng, G. et al. On double peak probability density functions of duffing oscillator to combined deterministic and random excitations. Appl Math Mech 27, 1569–1576 (2006). https://doi.org/10.1007/s10483-006-1115-z

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  • DOI: https://doi.org/10.1007/s10483-006-1115-z

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2000 Mathematics Subject Classification

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