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

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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.

Original languageEnglish (US)
Article number103553
JournalMechanics Research Communications
StatePublished - Jul 2020

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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