Optimal Design and Physical Modelling of Mallet Percussion Instruments
Luı́s Henrique · 2003
Summary At the present time, instruments are mostly designed by trial and error procedures, which are inefficient and costly. In the first part of this paper we present an approach, based on finite-element eigen-analysis coupled with optimization procedures, which enable the computation of optimal instrument shapes in order to obtain a target set of modal frequencies. We briefly discuss various optimization approaches, deterministic and stochastic, in relation with computational efficiency and effectiveness. A satisfying compromise has been found by describing the shape of the vibrating components in terms of orthogonal shape-functions, and then optimizing their amplitude coefficients using a deterministic optimization scheme. Beyond enabling a systematic and cost-effective way of improving conventional instrument designs, an obvious advantage of optimization is the possibility of developing non-conventional instruments with new sound qualities. We illustrate the various aspects discussed by optimizing vibraphone or marimba-type bars, for several modal target sets. In the second part of this paper, we turn towards the sound synthesis of percussion bars. Here, the nonlinear physical modelling is based on a modal representation of the unconstrained bar. Such approach addresses the spatial aspects of the problem, being well suited for both non-dispersive and dispersive systems – which is the case of the flexural waves of interest here. Only the vibratory responses will be simulated, without an explicit accounting of sound radiation phenomena or of the coupling between vibrating bars and acoustic resonators. We illustrate the computational method with numerical simulations (sounds and animations) of marimba and vibraphone bars, for both classic and non-orthodox geometries.