Stochastic Response of Dynamical Systems with Fractional Derivative Term under Wide-Band Excitation

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...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical problems in engineering 2016-01, Vol.2016 (2016), p.1-9
Main Author: Zhao, Jun-Feng
Format: Article
Language:English
Subjects:
Agreements
Applied mathematics
Computer simulation
Derivatives
Differential equations
Dynamical systems
Efficiency
Engineering
Excitation
Galerkin method
Galerkin methods
Integrals
Mathematical analysis
Mathematical models
Mathematical problems
Methods
Monte Carlo simulation
Noise
Oscillators
Periodic functions
Probability density functions
Researchers
Stochasticity
Studies
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2016/9638523