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

Hai Wu Rong, Xiang Dong Wang, Guang Meng, Wei Xu, Tong Fang

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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.

Original languageEnglish
Pages (from-to)1569-1576
Number of pages8
JournalApplied Mathematics and Mechanics (English Edition)
Volume27
Issue number11
DOIs
StatePublished - Nov 2006

Keywords

  • Double peak probability density function
  • Duffing oscillator
  • Linearization method
  • Multiple scale method

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