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Parametric Instability in a Stationary String With a Periodically Varying Length

[+] Author Affiliations
K. Wu, W. D. Zhu

University of Maryland, Baltimore County, Baltimore, MD

Paper No. DETC2014-35522, pp. V008T11A077; 15 pages
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 26th Conference on Mechanical Vibration and Noise
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4641-4
  • Copyright © 2014 by ASME


Parametric instability in a stationary string with a periodically varying length is investigated. The free linear vibration of a stationary string with a constant tension, a fixed boundary, and a periodically moving boundary is studied first. The parametric instability in the string features a bounded displacement and an unbounded vibratory energy, and parametric instability regions in the parameter plane are classified as period-i (i ≥ 1) parametric instability regions. If the periodic boundary movement profile of the string satisfies certain condition, only period-1 parametric instability regions exist. However, parametric instability regions with higher period numbers can exist for a general periodic boundary movement profile. A corresponding nonlinear model that consider coupled transverse and longitudinal vibrations of the string are introduced next. Responses and vibratory energies of the linear and nonlinear models are calculated for both stable and unstable cases using the finite difference method. The mechanism of the parametric instability is explained in the linear model and through axial strains in the nonlinear model.

Copyright © 2014 by ASME
Topics: String



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