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Research Papers

Extension of Nonlinear Stochastic Solution to Include Sinusoidal Excitation—Illustrated by Duffing Oscillator

[+] Author and Article Information
R. J. Chang

Department of Mechanical Engineering,
National Cheng Kung University,
Tainan 70101, Taiwan
e-mail: rjchang@mail.ncku.edu.tw

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 29, 2017; final manuscript received June 1, 2017; published online July 12, 2017. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 12(5), 051030 (Jul 12, 2017) (9 pages) Paper No: CND-17-1138; doi: 10.1115/1.4037105 History: Received March 29, 2017; Revised June 01, 2017

A new non-Gaussian linearization method is developed for extending the analysis of Gaussian white-noise excited nonlinear oscillator to incorporate sinusoidal excitation. The non-Gaussian linearization method is developed through introducing a modulated correction factor on the linearization coefficient which is obtained by Gaussian linearization. The time average of cyclostationary response of variance and noise spectrum is analyzed through the correction factor. The validity of the present non-Gaussian approach in predicting the statistical response is supported by utilizing Monte Carlo simulations. The present non-Gaussian analysis, without imposing restrictive analytical conditions, can be obtained by solving nonlinear algebraic equations. The non-Gaussian solution effectively predicts accurate sinusoidal and noise response when the nonlinear system is subjected to both sinusoidal and white-noise excitations.

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Figures

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Fig. 1

Cyclostationary mean response of state x1

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Fig. 2

Cyclostationary variance response of state x1 by different approaches

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Fig. 3

Gaussian and non-Gaussian prediction of cyclostationary time average of variance response

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Fig. 4

Gaussian correction factor for non-Gaussian linearization

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Fig. 5

Estimation of mean physical power spectrum of noise response under unit-amplitude sinusoidal excitation with ω0=2π(0.2)rad/s and white-noise excitation with 2q = 4 by different approaches

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