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Forced Vibrations of Circular Plates: From Periodic to Chaotic Motions

[+] Author Affiliations
Cyril Touzé

Unité de Mécanique (UME), Palaiseau, France

Olivier Thomas

CNAM-LMSSC, Paris, France

Marco Amabili

McGill University, Montreal, QC, Canada

Paper No. DETC2010-28259, pp. 817-825; 9 pages
doi:10.1115/DETC2010-28259
From:
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4413-7 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME

abstract

A numerical study of the transition from periodic to chaotic motions in forced vibrations of circular plates, is proposed. A pointwise harmonic forcing of constant excitation frequency Ω and increasing values of the amplitude is considered. Perfect and imperfect circular plates with a free edge are studied within the von Kármán assumptions for large displacements (geometric non-linearity). The transition scenario is observed for different excitation frequencies in the range of the first eigenfrequencies of the plate. For perfect plate with no specific internal resonance relationships, a direct transition to chaos is at hand. For imperfect plate tuned so as to fulfill specific internal resonance relations, a coupling between internally resonant modes is first observed. The chaotic regime shows an attractor of large dimension, and thus is studied within the framework of wave turbulence.

Copyright © 2010 by ASME

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