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TECHNICAL PAPERS

Parametric Instability of Axially Moving Media Subjected to Multifrequency Tension and Speed Fluctuations

[+] Author and Article Information
R. G. Parker, Y. Lin

Department of Mechanical Engineering, The Ohio State University, 206 W. 18th Avenue, Columbus, OH 43210-1107

J. Appl. Mech 68(1), 49-57 (Jun 27, 2000) (9 pages) doi:10.1115/1.1343914 History: Received August 26, 1999; Revised June 27, 2000
Copyright © 2001 by ASME
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References

Figures

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First mode (ω1=2.95) stability boundaries of an axially moving string caused by three parametric excitation combinations for γ=0.25: (a) single excitation Ω1, (b) two excitations Ω2=2Ω12=0.3, and (c) two excitations Ω2=(1/2)Ω12=0.3
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Dependence of the second mode (ω2=2π(1−γ02)) moving string principal instability region on translation speed for (a) single excitation, Ω1≈2ω2, (b) two excitations, Ω1≈2ω2 and Ω2=(1/2)Ω1≈ω22=0.3
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Dependence of the second mode (ω2=2π(1−γ02)) moving string secondary instability region on translation speed for (a) single excitation, Ω1≈ω2, (b) two excitations, Ω1≈ω2 and Ω2=2Ω1≈2ω22=0.3
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Moving string stability boundaries of first (ω1=3.071) and second mode (ω2=6.142) sum-type combination instability (Ω1≈ω12) for two parametric tension excitations. Dotted curves denote first-order perturbation, and solid curves denote second-order perturbation.
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Time histories and spectra of the modal response under first-mode primary instability with single frequency tension excitation. (a) analytical approximation, (b)–(d) numerical integration of coupled equations from a three-mode Galerkin discretization. γ=0.4,ω1=0.84π,ε1=0.35,σ=−0.2,Ω1=2ω1−2ε1σ=1.68π.
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Comparison among numerical results (* ), first-order perturbation (dots) and second-order perturbation (solid curves) of the first mode (ω1=2.76) primary instability region of an axially moving string under two parametric tension excitations. γ=0.35, ε2=0.35.
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Continuous dependence on excitation amplitudes of the first mode (ω1=3.07) primary instability region of an axially moving string under two parametric tension excitations. Ω2=7,γ=0.15.

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