The eigenspectra of Indian musical drums
  In a family of drums used in the Indian subcontinent, the circular drum head is made of material of non-uniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the non-uniform membrane are harmonic. In this work we model the drum head by a non-uniform membrane whose density varies smoothly between two prescribed values. Using a Fourier-Chebyshev spectral collocation method we obtain the eigenmodes and eigenvalues of the drum head. For a suitable choice of parameters, which we find by optimising a cost function, the eigenspectra obtained from our model are in excellent agreement with experimental values. Our model and the numerical method should find application in numerical sound synthesis. 
G. Sathej and R. Adhikari