Complicated dynamics exhibited by thin shells displaying numerous internal resonances: application to the steelpan

Abstract : Nonlinear vibrations of a steelpan, a musical instrument from the Caribbean islands, are experimentally and theoretically studied. Modal analysis reveals the existence of numerous modes displaying internal resonances, enabling the structure to transfer energy from low or high frequency modes. The complicated dynamics in forced vibrations is precisely measured by following the different harmonics of the responses. Energy transfers are explained in light of high order couplings, and simple models displaying 1:2:2 and 1:2:4 internal resonance are fitted to the experiments. The measurements reveals that mode couplings are activated for very low amplitudes of order 1/25 times the thickness, and that numerous modes are rapidly excited, giving rise to frequency responses with complex shape. This ease in transferring energy is a key feature for explaining the peculiar tone of the steelpan. The identified 1:2:4 model is finally used to recover the time oscillations of an impacted note in normal playing condition, resulting in a perfect agreement for the first four harmonics.
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Olivier Thomas, Mélodie Monteil, Cyril Touzé. Complicated dynamics exhibited by thin shells displaying numerous internal resonances: application to the steelpan. European Nonlinear Dynamics conference ENOC 2014, Jul 2014, Vienna, Austria. ⟨hal-01134689⟩

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