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Nonlinear Parametric Resonance of a Fractional Damped Axially Moving String

[+] Author and Article Information
Tian-Zhi Yang

Department of Astronautics,
Shenyang Aerospace University,
Shenyang 110136, China
e-mail: yangtz@me.com

Xiaodong Yang

School of Mechanical Engineering,
Beijing University of Technology,
Shenyang 100022, China

Fei Chen

Department of Engineering Mechanics,
Shenyang Aerospace University,
Shenyang 110136, China

Bo Fang

Department of Astronautics, Shenyang Aerospace University,
Shenyang 110136, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received August 31, 2012; final manuscript received June 1, 2013; published online August 6, 2013. Assoc. Editor: Weidong Zhu.

J. Vib. Acoust 135(6), 064507 (Aug 06, 2013) (5 pages) Paper No: VIB-12-1248; doi: 10.1115/1.4024779 History: Received August 31, 2012; Revised June 01, 2013

Nonlinear parametric vibration of an axially accelerating viscoelastic string is investigated. The string is constituted by the fractional Kelvin model. The principal parametric resonance is analyzed by using an asymptotic approach. The modulation equation is derived from the solvability condition. Closed-form expressions of the amplitudes and the existence conditions of steady-state responses are obtained from the modulation equation. Numerical examples are presented to highlight the effects of fractional order and other system parameters on the responses.

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Grahic Jump Location
Fig. 1

Schematic of an axially moving string

Grahic Jump Location
Fig. 2

Effect of fractional order α on the steady-state responses (γ0 = 0.3, η = 0.5, e0 = 0.1, γ1 = 1)

Grahic Jump Location
Fig. 3

Effect of stiffness constant of the e0 on the steady-state responses (γ0 = 0.3, α = 0.6, η = 0.5 γ1 = 1)

Grahic Jump Location
Fig. 4

Effect of viscosity η on the steady-state responses (γ0 = 0.3, α = 0.5, e0 = 0.1, γ1 = 1)




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