This work investigates the stability of axially moving media subjected to parametric excitation resulting from tension and translation speed oscillations. Each of these excitation sources has spectral content with multiple frequencies and arbitrary phases. Stability boundaries for primary parametric instabilities, secondary instabilities, and combination instabilities are determined analytically through second-order perturbation. The classical result that primary instability occurs when one of the excitation frequencies is close to twice a natural frequency changes as a result of multiple excitation frequencies. Unusual interactions occur for the practically important case of simultaneous primary and secondary instabilities. While sum type combination instabilities occur, no difference type instabilities are detected. The nonlinear limit cycle amplitude that occurs under primary instability is derived using the method of multiple scales.
Parametric Instability of Axially Moving Media Subjected to Multifrequency Tension and Speed Fluctuations
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Aug. 26, 1999; final revision, June 27, 2000. Associate Editor: A. K. Mal. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Parker, R. G., and Lin, Y. (June 27, 2000). "Parametric Instability of Axially Moving Media Subjected to Multifrequency Tension and Speed Fluctuations ." ASME. J. Appl. Mech. January 2001; 68(1): 49–57. https://doi.org/10.1115/1.1343914
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