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Article

Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

[+] Author and Article Information
Chung Hwan Kim

Samsung Electronics Co., Ltd, Maetan 3-Dong, Suwon, Gyeonggi-Do 442-742, Koreae-mail: ch74.kim@samsung.com

Chong-Won Lee

Center for Noise and Vibration Control (NOVIC), Department of Mechanical Engineering KAIST, Science Town, Daejeon 305-701, Koreae-mail: cwlee@novic.kaist.ac.kr

N. C. Perkins

Mechanical Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2125e-mail: ncp@umich.edu

J. Vib. Acoust 127(1), 36-43 (Mar 21, 2005) (8 pages) doi:10.1115/1.1857924 History: Received May 24, 2003; Revised December 23, 2003; Online March 21, 2005
Copyright © 2005 by ASME
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References

Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley, New York.
Kim, C. H., Perkins, N. C., and Lee, C. W., 2003 (to appear), “Parametric Resonance of Plates in a Sheet Metal Coating Process,” J. Sound Vib.
Kim, C. H., 2003, “Vibration Analysis of Thin Plate Under Time Varying Tension and External Excitation in Sheet Metal Coating Process,” Ph.D. dissertation, KAIST.
Chia, Ch-Y., 1980, Nonlinear Analysis of Plates, McGraw-Hill, New York.
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Figures

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Power spectra of the response obtained from the simulation results of the cubic nonlinear single degree-of-freedom plate model with parametric excitation having a frequency of 2ω0 and (a) without external excitation, (b) ωr/2π=2.5 Hz, (c) ωr/2π=3.0 Hz, (d) ωr/2π=3.5 Hz
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Frequency-response curves: single frequency parametric excitation in the neighborhood of ω≈2ω0 and single frequency external excitation at ωr
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Frequency-response curves: single frequency parametric excitation in the neighborhood of ω≈ωr±ω0 and single frequency external excitation at frequencies ωr;K1=0.054 and K2=0.017
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Evolution of the amplitude and phase to the steady-state solution: triple-frequency parametric excitation and a single-frequency external excitation
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(a) Amplitude and (b) phase of frequency-response: triple-frequency parametric excitation with φ123=0 and a single-frequency external excitation
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Frequency-response curves for triple-frequency parametric excitation and a single-frequency external excitation for (a) (φ123)=(0,π/2,0), (0,0,π/2); (b) (φ123)=(0,3π/2,0), (0,0,3π/2); (c) (φ123)=(π/2,0,0); (d) (φ123)=(3π/2,0,0)
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Frequency-response curves for double-frequency parametric excitation and a single-frequency external excitation for (a) φ1=0,φ2=0; (b) φ1=0,φ2=π/2; (c) φ1=0,φ2=π; (d) φ1=π/2,φ2=0. (e) φ1=π,φ2=0; (f) φ1=3π/2,φ2=0; (g) φ1=2π,φ2=0.
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Response amplitude vs φ1 and φ2
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Time-frequency map of vibration data 2
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Time-frequency map of dynamic tension data 2. Enlarged sections of the data in the lower half are shown in the upper half for the three resonance regions, 2fn,fn+fr, and fn−fr.

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