bComputational acoustic modeling laboratory, CIRMMT, McGill University
The natural frequencies of marimba bars are tuned by removing material from the bottom of the bar. Three partials are typically tuned, though less are tuned for higher notes. With only three or fewer partials to tune, many different bar geometries may produce the desired frequencies. As a result, bar geometries can show significant variation between brands, with each manufacturer employing their own tuning approach, honed over many years of experience. This work uses 3D finite element analysis to investigate tuning marimba bar geometry, with an aim to inform manufacturing methods. Optimization techniques, including genetic algorithms, are employed to evaluate and improve bar geometries. The preferred geometries tune the desired frequencies, while also scoring well on secondary evaluation criteria. These secondary criteria include: separating the frequencies of torsional modes from those of the tuned modes, prioritizing symmetry, and producing shapes similar to professional marimba bars. Models are developed using the open-source finite element program Calculix. Optimization routines are written in Python. The programs are interfaced to coordinate model execution. Functions are created to identify mode shapes based on displaced geometry. These functions provide resilience against any modal reordering, allowing the optimization routines to run unsupervised over significant changes in geometry.
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