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TECHNICAL PAPERS

Spatial Discretization of Axially Moving Media Vibration Problems

[+] Author and Article Information
Rajesh K. Jha, Robert G. Parker

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210-1107

J. Vib. Acoust 122(3), 290-294 (Mar 01, 2000) (5 pages) doi:10.1115/1.1303847 History: Received May 01, 1999; Revised March 01, 2000
Copyright © 2000 by ASME
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References

Mote,  C. D., 1965, “A Study of Bandsaw Vibrations,” J. Franklin Inst., 279, pp. 430–444.
Barakat,  R., 1967, “Transverse Vibrations of a Moving Thin Rod,” J. Acoust. Soc. Am., 43, pp. 533–539.
Hwang,  S. J., and Perkins,  N. C., 1992, “Supercritical Stability of an Axially Moving Beam. Part 2: Vibration and Stability Analysis,” J. Sound Vib., 154, pp. 397–409.
Parker,  R. G., 1999, “Supercritical Speed Stability of the Trivial Equilibrium of an Axially Moving String on an Elastic Foundation,” J. Sound Vib., 221, No. 2, pp. 205–219.
Wickert,  J. A., and Mote,  C. D., 1991, “Response and Discretization Methods for Axially Moving Materials,” Appl. Mech. Rev., 44, pp. 279–284.
Chen,  J. S., 1997, “Natural Frequencies and Stability of an Axially Traveling String in Contact with a Stationary Load System,” J. Vib. Acoust., 119, pp. 152–157.
Meirovitch,  L., 1974, “A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems,” AIAA J., 12, pp. 1337–1342.
D’Eleuterio,  G. M., and Hughes,  P. C., 1984, “Dynamics of Gyroelastic Continua,” ASME J. Appl. Mech. 51, pp. 415–422.
Wickert,  J. A., and Mote,  C. D., 1990, “Classical Vibration Analysis of Axially Moving Continua,” ASME J. Appl. Mech., 57, pp. 738–744.
Huseyin,  K., 1976, “Standard Forms of the Eigenvalue Problems Associated With Gyroscopic Systems,” J. Sound Vib., 45, No. 1, pp. 29–37.
Courant, R., and Hilbert, D., 1953, Methods of Mathematical Physics, Vol. 1, Interscience Publishers, New York, pp. 61–65.
Perkins,  N. C., 1990, “Linear Dynamics of a Translating String on Elastic Foundation,” J. Vib. Acoust., 112, pp. 3–13.
Parker,  R. G., and Sathe,  P. J., 1999, “Exact Solutions for the Free and Forced Vibration of a Spinning Disk-Spindle System,” J. Sound Vib., 223, No. 3, pp. 445–465.
Lengoc,  L., and McCallion,  H., 1996, “Transverse Vibration of a Moving String: A Comparison Between the Closed-Form Solution and the Normal-Mode Solution,” J. Syst. Eng., 6, pp. 72–78.
Wickert,  J. A., 1992, “Nonlinear Vibration of a Traveling Tensioned Beam,” Int. J. Nonlinear Mech., 27, pp. 503–517.
Mockensturm,  E. M., Perkins,  N. C., and Ulsoy,  A. G., 1996, “Stability and Limit Cycles of Parametrically Excited, Axially Moving Strings,” J. Vib. Acoust., 118, pp. 346–351.
Pakdemirli,  M., and Ulsoy,  A. G., 1997, “Stability Analysis of an Axially Accelerating String,” J. Sound Vib., 203, pp. 815–832.
Parker, R. G., and Lin, Y., 2000, “Parametric Instability of Axially Moving Media Subjected to Multi-Frequency Tension and Speed Fluctuations,” J. Appl. Mech., accepted.

Figures

Grahic Jump Location
Measure of independence of sets of complex conjugate moving string eigenfunction pairs for varying speeds ν
Grahic Jump Location
Configuration space discretization of a stationary string using moving string eigenfunctions. (○) denote discretization results and solid lines denote the exact eigenvalues of the stationary string.
Grahic Jump Location
Discretization of an axially moving string on elastic foundation with κ=50. Figures (a) and (b) show results for ν=0.5 and ν=0.75, respectively. (⋄) -N terms of stationary string eigenfunctions, (○) -configuration space form using N complex conjugate moving string eigenfunction pairs, and (▵) - state space form with 2N complex conjugate moving string eigenfunction pairs. Horizontal solid lines denote the lowest three exact eigenvalues.
Grahic Jump Location
Configuration space discretization of an axially moving string on elastic foundation (κ=20) showing incorrect flutter predictions. (○) denote eight cc pairs of moving string eigenfunctions and solid lines denote exact eigenvalues.
Grahic Jump Location
Discretization of a simply supported, axially moving, tensioned beam (γ=0.1). (⋄) - six terms of stationary beam eigenfunctions, (○) - six cc pairs of moving string eigenfunctions, and ( * ) - six cc pairs of modified moving string eigenfunctions with α=2. Solid lines denote exact eigenvalues.

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