Vibrational modes of circular free plates under tension

Abstract

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

17 pages. To be submitted for publication shortly.

References in corpus (2)

• An isoperimetric inequality for the fundamental tone of free plates
• An Isoperimetric Inequality for Fundamental Tones of Free Plates

Cited by in corpus (4)

• An isoperimetric inequality for the fundamental tone of free plates
• An isoperimetric inequality for fundamental tones of free plates with nonzero Poisson's ratio
• Nodal properties of eigenfunctions of a generalized buckling problem on balls
• Spectral analysis of a generalized buckling problem on a ball