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Simultaneous Resonances of Geometric Nonlinear Nonuniform Beams

[+] Author Affiliations
Dumitru I. Caruntu

University of Texas-Pan American, Edinburg, TX

Paper No. DETC2009-86779, pp. 1397-1402; 6 pages
  • ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • San Diego, California, USA, August 30–September 2, 2009
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4898-2 | eISBN: 978-0-7918-3856-3
  • Copyright © 2009 by ASME


Simultaneous resonances, superharmonic and subharmonic, of two-term excitation nonlinear bending vibrations in the case of moderately large curvature of nonuniform cantilever beams are reported. Cantilevers of constant width and parabolic thickness variation are considered in this research. The method of multiple scales is directly applied to the governing partial-differential equation of motion and boundary conditions. Two problems, zero- and first-order, result. Using factorization method, the linear modes of the zero-order problem are obtained in terms of hypergeometric functions. The first-order problem provides the amplitude-phase evolution relationship and consequently the simultaneous resonances response.

Copyright © 2009 by ASME



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