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.
- Bessel functions
- free plate