Computing natural frequencies and mode shapes of a non-uniform circular membrane

This paper presents algorithms to compute natural frequencies and mode shapes of a circular membrane with concentric or eccentric non-uniformity as found in many applications such as Indian musical drums. Algorithm for concentric non-uniformity is based on the theory of linear time varying systems whereas that for eccentric non-uniformity is developed by expressing each eigenfunction as a linear combination of eigenfunctions of the corresponding circular membrane with concentric non-uniformity. Numerical results from these approaches are corroborated by comparison with those from a finite element method and existing results in the literature.