Numerical Studies of Elastic-Disk Contour Modes Lacking Axial Symmetry

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Abstract
The eigenvalue problem for axially asymmetric contour extensional modes of thin elastic disks with planar isotropy has been solved numerically. This solution includes determination of the dimensionless eigenvalues and the associated particle‐displacement eigenfunctions with normalization coefficients. Results are presented in tabular form for modes having angular index less than 10 and for values of Poisson's ratio between 0.25 and 0.50. The 68 modes of this class, which are graver than the fourth axially symmetric mode, have been considered. The resulting orthonormal modes are ideal for eigenfunction expansion (i.e., generalized Fourier series) solutions of elastic disks driven by axially asymmetric forces. Quantitative studies of axially asymmetric electroded piezoelectric disks also become feasible.

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