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
Citation: 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

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
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
  • 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.
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