response of duffing oscillator with time delay subjected to combined harmonic and random excitations

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2017
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Abstract
This paper aims to investigate the stationary probability density functions of the Duffing oscillator with time delay subjected to combined harmonic and white noise excitation by the method of stochastic averaging and equivalent linearization. By the transformation based on the fundamental matrix of the degenerate Duffing system, the paper shows that the displacement and the velocity with time delay in the Duffing oscillator can be computed approximately in non-time delay terms. Hence, the stochastic system with time delay is transformed into the corresponding stochastic non-time delay equation in Ito sense. The approximate stationary probability density function of the original system can be found by combining the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function. The response of Duffing oscillator is investigated. The analytical results are verified by numerical simulation results.
Reference Key
hao2017mathematicalresponse Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;D. N. Hao;N. D. Anh
Journal journal of power sources
Year 2017
DOI
10.1155/2017/4907520
URL
http://dx.doi.org/10.1155/2017/4907520
Keywords
civil engineering (general)mathematics engineering (general)

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