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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article number051030
JournalJournal of Computational and Nonlinear Dynamics
Volume12
Issue number5
DOIs
Publication statusPublished - 2017 Sep 1

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Duffing Oscillator
Linearization
Excitation
White noise
Linearization Method
Nonlinear Algebraic Equations
Nonlinear equations
Nonlinear Oscillator
Nonlinear systems
Time-average
Gaussian White Noise
Nonlinear Systems
Monte Carlo Simulation
Predict
Coefficient

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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abstract = "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.",
author = "Ren-Jung Chang",
year = "2017",
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language = "English",
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journal = "Journal of Computational and Nonlinear Dynamics",
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AB - 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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