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TECHNICAL BRIEFS

Eigenvalue Estimation Using Linearly Dependent Eigenfunctions

[+] Author and Article Information
Keh-Yang Lee, Anthony A. Renshaw

Dept. of Mechanical Engng., Columbia University, M/C 4703, New York, NY 10027

J. Vib. Acoust 122(4), 464-466 (Jun 01, 2000) (3 pages) doi:10.1115/1.1310327 History: Received July 01, 1999; Revised June 01, 2000
Copyright © 2000 by ASME
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References

Wickert,  J. A., and Mote,  C. D., 1991, “Response and Discretization Methods for Axially Moving Materials,” Appl. Mech. Rev., 44, pp. S279–S284.
Lee, K.-Y., and Renshaw, A. A., 1999, “Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions,” ASME 1999 Design Engineering Technical Conference, Las Vegas, NV, September, 1999.
Renshaw,  A. A., 1997, “Modal Decoupling of Systems Described by Three Linear Operators,” J. Appl. Mech., 64, pp. 238–240.
Lancaster, P., 1966, Lambda-Matrices and Vibrating Systems, Pergamon Press, Oxford, UK.
Wickert,  J. A., and Mote,  C. D., 1990, “Classical Vibration Analysis of Axially Moving Continua,” J. Appl. Mech., 57, pp. 738–744.
Perkins,  N. C., 1990, “Linear Dynamics of a Translating String on an Elastic Foundation,” J. Vibr. Acoust., 112, pp. 2–7.
Perkins,  N. C., and Mote,  C. D., 1987, “Three-Dimensional Vibration of Travelling Elastic Cables,” J. Sound Vib., 114, pp. 325–340.

Figures

Grahic Jump Location
Absolute error of eigenvalue estimate of the smallest magnitude eigenvalue for damped moving string as a function of N.c=0.3 and v=0.25. Circle=proposed method; +=Galerkin’s method with un=sin(nπx);X=Galerkin’s method with unn.
Grahic Jump Location
Absolute error of eigenvalue estimate of the smallest magnitude eigenvalue for elastically supported moving string as a function of N.μ=10 and v=0.25. Same symbols as Fig. 1.
Grahic Jump Location
Absolute error of eigenvalue estimate of the smallest magnitude eigenvalue for moving cable as a function of N.m2=0.3 and v=0.25. Same symbols as Fig. 1.

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