Dynamic stability of an axially accelerating viscoelastic beam

Chen, Liqun; Yang, Xiao‐Dong; Chang-jun, Cheng

doi:10.1016/j.euromechsol.2004.01.002

Cited by 68 publications

(26 citation statements)

References 12 publications

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“…Chen et al [7] used the averaging method to a discretized system via the Galerkin method to analytically present the stability boundaries of the axially accelerating viscoelastic beams with clamped-clamped ends. Chen and Yang [8] used the method of multiple scales without discretization to analytically obtain the stability boundaries of the axially accelerating viscoelastic beams with pinned-pinned or clamped-clamped ends.…”

Section: Introductionmentioning

confidence: 99%

“…Chen and Yang [10] used the method of multiple scales to analytically present the vibration and stability of an axially moving beam constrained by the simple supports with rotational springs. In the works of Chen et al [7] and Chen and Yang [8,10] , the Kelvin model containing the partial time derivative was used to describe the viscoelastic behavior of beam materials.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

王波

Wang

2012

Appl. Math. Mech.-Engl. Ed.

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The weakly forced vibration of an axially moving viscoelastic beam is investigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of nontrivial steady-state response is examined via the Routh-Hurwitz criterion.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

王波

Wang

2012

Appl. Math. Mech.-Engl. Ed.

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“…For example, if the axially moving beam models a belt on a pair of rotating pulleys, the rotation vibration of the pulleys will result in a small fluctuation in the axial speed of the belt. Although there are some researches on axially accelerating beams [13][14][15][16][17][18], these researches are confined to linear models.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and chaos of an axially accelerating viscoelastic beam

Yang¹,

Chen

2005

Chaos, Solitons & Fractals

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“…Pellicano et al [14] used the approximate analytical and the experimental methods to study the primary and the parametric resonances of a power transmission belt with the fluctuation of the tension. Chen et al [15] employed the averaging method to investigate the stability problems of an axially accelerating tensioned beam under the condition of the subharmonic and combination resonances. Pakdemirli andÖz [16] adopted a perturbation technique to discuss stable regions of a simply supported axially moving beams subjected to sum-and difference-type combination resonances.…”

Section: Introductionmentioning

confidence: 99%

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

Li¹,

Tang²

2017

Mathematical Problems in Engineering

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The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton's second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff 's fractional material model are much larger than those predicted by Mote's fractional material model.

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Dynamic stability of an axially accelerating viscoelastic beam

Cited by 68 publications

References 12 publications

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

Bifurcation and chaos of an axially accelerating viscoelastic beam

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

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