Stochastic stability of a fractional viscoelastic column under bounded noise excitation

The stability of a viscoelastic column under the excitation of stochastic axial compressive load is investigated in this paper. The material of the column is modeled using a fractional Kelvin–Voigt constitutive relation, which leads to that the equation of motion is governed by a stochastic fraction...

Full description

Saved in:
Bibliographic Details
Published in:Journal of sound and vibration 2014-03, Vol.333 (6), p.1629-1643
Main Authors: Deng, J., Xie, W.-C., Pandey, M.D.
Format: Article
Language:English
Subjects:
Dynamical systems
Excitation
Mathematical analysis
Mathematical models
Noise
Stability
Stochasticity
Viscoelasticity
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:The stability of a viscoelastic column under the excitation of stochastic axial compressive load is investigated in this paper. The material of the column is modeled using a fractional Kelvin–Voigt constitutive relation, which leads to that the equation of motion is governed by a stochastic fractional equation with parametric excitation. The excitation is modeled as a bounded noise, which is a realistic model of stochastic fluctuation in engineering applications. The method of stochastic averaging is used to approximate the responses of the original dynamical system by a new set of averaged variables which are diffusive Markov vector. An eigenvalue problem is formulated from the averaged equations, from which the moment Lyapunov exponent is determined for the column system with small damping and weak excitation. The effects of various parameters on the stochastic stability and significant parametric resonance are discussed and confirmed by simulation results.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2013.11.019