Stochastic response of dynamical systems with fractional derivative term under wide-band excitation
type: Item
instance of: scholarly article
title: Stochastic response of dynamical systems with fractional derivative term under wide-band excitation
zbMATH Open document ID: 1400.60088
DOI: 10.1155/2016/9638523
author: Junfeng Zhao
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34C26
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60G22
zbMATH DE Number: 6953827
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/9638523
OpenAlex ID: W2549426722
Wikidata QID: Q59141314
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description: scientific article; zbMATH DE number 6953827