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arXiv · 1004.3316

Vibrational modes of circular free plates under tension

L. M. Chasman
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Abstract

The vibrational frequencies of a plate under tension are given by the eigenvalues $ω$ of the equation $Δ^2u-τΔu=ωu$. 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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L. M. Chasman. 2010-04-19. Vibrational modes of circular free plates under tension. https://doi.org/10.1080/00036811.2010.534727

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