Asymptotic Distribution of Eigenvalues of a Constrained Translating String

[+] Author and Article Information
W. D. Zhu

Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

C. D. Mote

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

B. Z. Guo

Department of Applied Mathematics, Beijing Institute of Technology, Beijing, China

J. Appl. Mech 64(3), 613-619 (Sep 01, 1997) (7 pages) doi:10.1115/1.2788937 History: Received November 20, 1995; Revised September 09, 1996; Online October 25, 2007


A new spectral analysis for the asymptotic locations of eigenvalues of a constrained translating string is presented. The constraint modeled by a spring-mass-dashpot is located at any position along the string. Asymptotic solutions for the eigenvalues are determined from the characteristic equation of the coupled system of constraint and string for all constraint parameters. Damping in the constraint dissipates vibration energy in all modes whenever its dimensionless location along the string is an irrational number. It is shown that although all eigenvalues have strictly negative real parts, an infinite number of them approach the imaginary axis. The analytical predictions for the distribution of eigenvalues are validated by numerical analyses.

Copyright © 1997 by The American Society of Mechanical Engineers
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