Vibrational modes of circular free plates under tension

Details Vibrational modes of circular free plates under tension Vibrational modes of circular free plates under tension

2010-04-19

arxiv.org/abs/1004.3316v1

Mathematics

Analysis of PDEs

17 pages. To be submitted for publication shortly.

Scientific paper

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper 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.

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