Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control

A. Y T Leung; H. X. Yang; J. Y. Chen

doi:10.1016/j.compstruc.2014.01.015

Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control

A. Y T Leung
, H. X. Yang
, J. Y. Chen

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

17 Citations (Scopus)

Abstract

We investigate the steady state response of a simply supported viscoelastic column subject to axial harmonic excitation. The viscoelastic material is modeled in fractional derivative Kelvin sense. The equation of motion is derived and discretized by the Galerkin approximation resulting in a generalized Mathieu-Duffing equation with time delay. Bifurcations in parametric excitation can be eliminated by appropriate feedback gain and time delay. The bifurcating behavior for various fractional orders and material ratios are also investigated. New criteria of stability determination are established. Based on the Runge-Kutta method, numerical results are obtained and compared with analytical solutions for verification. © 2014 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	47-55
Journal	Computers and Structures
Volume	136
Online published	18 Feb 2014
DOIs	https://doi.org/10.1016/j.compstruc.2014.01.015
Publication status	Published - May 2014

Research Keywords

Fractional Mathieu-Duffing oscillator
Parametric bifurcation
Time delay
Viscoelastic column

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title = "Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control",

abstract = "We investigate the steady state response of a simply supported viscoelastic column subject to axial harmonic excitation. The viscoelastic material is modeled in fractional derivative Kelvin sense. The equation of motion is derived and discretized by the Galerkin approximation resulting in a generalized Mathieu-Duffing equation with time delay. Bifurcations in parametric excitation can be eliminated by appropriate feedback gain and time delay. The bifurcating behavior for various fractional orders and material ratios are also investigated. New criteria of stability determination are established. Based on the Runge-Kutta method, numerical results are obtained and compared with analytical solutions for verification. {\textcopyright} 2014 Elsevier Ltd. All rights reserved.",

keywords = "Fractional Mathieu-Duffing oscillator, Parametric bifurcation, Time delay, Viscoelastic column",

author = "Leung, \{A. Y T\} and Yang, \{H. X.\} and Chen, \{J. Y.\}",

year = "2014",

month = may,

doi = "10.1016/j.compstruc.2014.01.015",

language = "English",

volume = "136",

pages = "47--55",

journal = "Computers and Structures",

issn = "0045-7949",

publisher = "Elsevier Ltd.",

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TY - JOUR

T1 - Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control

AU - Leung, A. Y T

AU - Yang, H. X.

AU - Chen, J. Y.

PY - 2014/5

Y1 - 2014/5

N2 - We investigate the steady state response of a simply supported viscoelastic column subject to axial harmonic excitation. The viscoelastic material is modeled in fractional derivative Kelvin sense. The equation of motion is derived and discretized by the Galerkin approximation resulting in a generalized Mathieu-Duffing equation with time delay. Bifurcations in parametric excitation can be eliminated by appropriate feedback gain and time delay. The bifurcating behavior for various fractional orders and material ratios are also investigated. New criteria of stability determination are established. Based on the Runge-Kutta method, numerical results are obtained and compared with analytical solutions for verification. © 2014 Elsevier Ltd. All rights reserved.

AB - We investigate the steady state response of a simply supported viscoelastic column subject to axial harmonic excitation. The viscoelastic material is modeled in fractional derivative Kelvin sense. The equation of motion is derived and discretized by the Galerkin approximation resulting in a generalized Mathieu-Duffing equation with time delay. Bifurcations in parametric excitation can be eliminated by appropriate feedback gain and time delay. The bifurcating behavior for various fractional orders and material ratios are also investigated. New criteria of stability determination are established. Based on the Runge-Kutta method, numerical results are obtained and compared with analytical solutions for verification. © 2014 Elsevier Ltd. All rights reserved.

KW - Fractional Mathieu-Duffing oscillator

KW - Parametric bifurcation

KW - Time delay

KW - Viscoelastic column

UR - https://www.scopus.com/pages/publications/84894384935

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84894384935&origin=recordpage

U2 - 10.1016/j.compstruc.2014.01.015

DO - 10.1016/j.compstruc.2014.01.015

M3 - RGC 21 - Publication in refereed journal

SN - 0045-7949

VL - 136

SP - 47

EP - 55

JO - Computers and Structures

JF - Computers and Structures

ER -

Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control

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Research Keywords

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