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The aim of this paper is to give a precise proof of the completeness of Lamb modes of an elastic isotropic plate. This proof is relatively simple and short but relies on two powerful mathematical theorems. The first one is a theorem on elliptic systems with a parameter due to Agranovich and Vishik. The second one is a theorem due to Locker which gives a criterion to show the completeness of the set of generalized eigenvectors of a Hilbert–Schmidt discrete operator.

A proof of the completeness of Lamb modes