Extended field method free vibration solutions

An apparent paradox involving the relation between the plate bending natural frequencies of two elastic plates when one plate encloses the other is examined and dispelled. Specifically it is shown (1) that the extended field method of analysis can exactly, or with excellent numerical convergence, calculate plate bending eigenvalues, and (2) that the extended field method forced vibration solutions are not compromised by the singularities at the eigenvalues of the extended plate.