Stochastic Response of Dynamical Systems with Fractional Derivative Term under Wide-Band Excitation
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-23
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Transient solution of a fractional stochastic dynamical system under wide-band noise excitation is investigated.
Generalized Harmonic Balance technique is firstly used to approximate restoring force of the given system as an amplitude-dependent form.
In this way, stochastic averaging method then can be applied to transform the system into an Ito differential equation.
Furthermore, the fractional derivative in the integral-differential form can be equivalent to a combination of periodic functions after the averaging procedure.
As the following, Galerkin method therein is utilized to obtain the transient probability density functions by solving associated Fokker-Planck-Kolmogorov (FPK) equation.
As an example, the Rayleigh oscillator is studied to illustrate the efficiency and accuracy of the proposed approaches.
Numerical results show that exact stationary solution and transient solution derived from Galerkin method are in good agreement with those from Monte Carlo Simulation.
American Psychological Association (APA)
Zhao, Jun-Feng. 2016. Stochastic Response of Dynamical Systems with Fractional Derivative Term under Wide-Band Excitation. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1112904
Modern Language Association (MLA)
Zhao, Jun-Feng. Stochastic Response of Dynamical Systems with Fractional Derivative Term under Wide-Band Excitation. Mathematical Problems in Engineering No. 2016 (2016), pp.1-9.
https://search.emarefa.net/detail/BIM-1112904
American Medical Association (AMA)
Zhao, Jun-Feng. Stochastic Response of Dynamical Systems with Fractional Derivative Term under Wide-Band Excitation. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-9.
https://search.emarefa.net/detail/BIM-1112904
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112904