Speaker: Christian Hafner (ICGA)
Given a target shape and a target frequency, we automatically synthesize shapes that exhibit this frequency as part of their natural spectrum while resembling the target shape as closely as possible.
We propose three shape parametrization methods that afford meaningful degrees of freedom in the design of instruments such as marimbas and bells. The design space is based on the representation of a solid as the volume enclosed by an outer surface and an inner offset surface.
In order to evaluate the natural frequency spectrum of a solid, we employ finite element modal analysis and evaluate the suitability of different element types. We propose a fabrication method for the production of optimized instruments by an amateur craftsperson using sand or rubber molds.
The efficiency of our method is demonstrated by the production of a simple tin bell and a more complicated bell in the shape of a rabbit. We achieve agreement with the predicted pitch frequencies of 2.8% and 6% respectively.
These physical results are supplemented by a number of computational results that explore the optimization of harmonic ratios and the influence of mesh resolution and mesh smoothness on the accuracy of the finite element model.