On Double Peak Probability Density Functions of a Duffing Oscillator to Combined Deterministic and Random Excitations

RONG Hai-wu; WANG Xiang-dong; MENG Guang; XU Wei; FANG Tong

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(11): 1373-1379

RONG Hai-wu, WANG Xiang-dong, MENG Guang, XU Wei, FANG Tong. On Double Peak Probability Density Functions of a Duffing Oscillator to Combined Deterministic and Random Excitations[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1373-1379.

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On Double Peak Probability Density Functions of a Duffing Oscillator to Combined Deterministic and Random Excitations

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

Received Date: 2004-09-03
Rev Recd Date: 2006-08-07
Publish Date: 2006-11-15

Abstract

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.
- Duffing oscillator,
- double peak probability density function,
- multiple scale method,
- lin-earization method

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References(10)

References

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