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 Ka´rma´n 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.
- Design Engineering Division and Computers in Engineering Division
Forced Vibrations of Circular Plates: From Periodic to Chaotic Motions
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Touze´, C, Thomas, O, & Amabili, M. "Forced Vibrations of Circular Plates: From Periodic to Chaotic Motions." Proceedings of the 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. pp. 817-825. ASME. https://doi.org/10.1115/DETC2010-28259
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