Forced vibrations of circular plates: from periodic to chaotic motions

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.
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Cyril Touzé, Olivier Thomas, Marco Amabili. Forced vibrations of circular plates: from periodic to chaotic motions. ASME IDETC 2010 International Design Engineering Technical Conferences, Aug 2010, Montreal, Canada. ⟨10.1115/DETC2010-28259⟩. ⟨hal-01148760⟩

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