Kalimba tine boundary condition models

The kalimba or African thumb piano is a musical instrument with thin metal tines plucked by the thumbs at their free end. The opposite end is secured to a wood resonator with a three-point clamp that provides downward force in the middle, between points of upward force at the bridge and the back bar. The simplest model is an Euler-Bernoulli thin beam, free at the plucked end and clamped at the mount. Chapman [J. Acoust. Soc. Am 131, 945 (2012)] explored the benefits to modeling the bridge as a simply supported point, with a clamped condition at the load point in the middle. Considerations in the present work are related to the modes of vibration of the resonator box. (i) The bridge is the point where vibration is transmitted to the resonator box, itself designed to better radiate sound, and thus the mechanical impedance at that point provides a complex boundary condition to be implemented in the tine model. (ii) Measurements of the attack of the kalimba tones include harmonic content not predicted by the thin beam model; recent work on this “offset” boundary condition is approached computationally, extending beyond the theoretical thin beam model.