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On Superharmonic Resonances of Nonlinear Nonuniform Beams

[+] Author Affiliations
Dumitru I. Caruntu

University of Texas - Pan American, Edinburg, TX

Paper No. SMASIS2008-599, pp. 495-500; 6 pages
doi:10.1115/SMASIS2008-599
From:
  • ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
  • Smart Materials, Adaptive Structures and Intelligent Systems, Volume 2
  • Ellicott City, Maryland, USA, October 28–30, 2008
  • Conference Sponsors: Aerospace Division
  • ISBN: 978-0-7918-4332-1 | eISBN: 978-0-7918-3839-6
  • Copyright © 2008 by ASME

abstract

Superharmonic resonances of nonlinear forced bending vibrations of moderately large curvature of nonuniform cantilever beams of rectangular cross section and a sharp end are reported. Cantilevers of constant width and parabolic thickness variation are considered in this paper. Method of multiple scales is directly applied to the governing partial-differential equation of motion and boundary conditions. Two problems, zero- and first-order problem, result. Solving the zero-order problem, the linear modes are obtained in terms of hypergeometric functions by using the factorization method. The first-order problem provides the amplitude and phase evolution equation and consequently the superharmonic frequency response of the nonlinear system.

Copyright © 2008 by ASME

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