Abstract
In a family of drums used in the Indian subcontinent, the circular drum head is made of material of nonuniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the nonuniform membrane are harmonic. In this work the drum head is modeled as a nonuniform membrane whose density varies smoothly between two prescribed values. The eigenmodes and eigenvalues of the drum head are obtained using a high-resolution numerical method. The mathematical model and the numerical method are able to handle both concentric and eccentric nonuniformities, which correspond, respectively, to the dayan and the bayan drums. For a suitable choice of parameters, which are found by optimizing the harmonicity of the drum, the eigenspectra obtained from the model are in excellent agreement with experiment. The model and the numerical method should find application in numerical sound synthesis.
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