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

Abstract : Nonlinear vibrations of a steelpan are experimentally studied. Modal analysis reveals the existence of numerous modes displaying internal resonances of order two and three, 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 a simple model displaying 1:2:2 internal resonance is 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 complex shape frequency response functions. This ease in transferring energy and coupling modes is a key feature for explaining the peculiar tone of the steelpan.