Vibrational modes of circular free plates under tension

L. M. Chasman

Research output: Contribution to journalArticle

7 Scopus citations


The vibrational frequencies of a plate under tension are given by the eigenvalues ω of the equation Δ 2u - τΔu = ωu. This article determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes - the eigenfunctions of the lowest nonzero eigenvalue - are identified and found to have simple angular dependence.

Original languageEnglish (US)
Pages (from-to)1877-1895
Number of pages19
JournalApplicable Analysis
Issue number12
StatePublished - Dec 1 2011
Externally publishedYes


  • Bessel functions
  • bi-Laplace
  • free plate

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