Non-Stationary Response of a Stochastic System With Fractional Derivative Damping Under Gaussian White-Noise Excitation

LI Wei; ZHAO Jun-feng; LI Rui-hong; Natasa Trisovic

doi:10.3879/j.issn.1000-0887.2014.01.007

Volume 35 Issue 1

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LI Wei, ZHAO Jun-feng, LI Rui-hong, Natasa Trisovic. Non-Stationary Response of a Stochastic System With Fractional Derivative Damping Under Gaussian White-Noise Excitation[J]. Applied Mathematics and Mechanics, 2014, 35(1): 63-70. doi: 10.3879/j.issn.1000-0887.2014.01.007

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Non-Stationary Response of a Stochastic System With Fractional Derivative Damping Under Gaussian White-Noise Excitation

doi: 10.3879/j.issn.1000-0887.2014.01.007

¹School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China;²Department of Applied Mathematics, School of Natural and Applied Sciences,Northwestern Polytechnical University, Xi’an 710072, P.R.China;³Department of Mechanics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade 11000, Serbia

Funds: The National Natural Science Foundation of China（11302157；11202155）

Received Date: 2013-06-03
Rev Recd Date: 2013-10-27
Publish Date: 2014-01-15

Abstract

Abstract

Non-stationary response of a nonlinear stochastically dynamical system with fractional derivative damping under Gaussian white-noise excitation was investigated. Based on the equivalent linearization method, the original nonlinear system was converted to a linear system with respect to the vibration amplitude and phase, then the stochastic averaging method was applied to obtain the FPK equation, in which the fractional derivative was approximated by a periodic function. The approximate non-stationary response of the FPK equation was derived with Galerkin method. Numerical results verify the efficiency and correction of the proposed method.
- non-stationary response,
- fractional derivative,
- stochastic averaging method,
- Galerkin method

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References

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