TL;DR
This paper provides a concise mathematical proof demonstrating the completeness of Lamb modes and related modes, utilizing advanced theorems on elliptic systems and eigenvector completeness.
Contribution
It offers a new, simplified proof of Lamb mode completeness based on established theorems, clarifying a fundamental aspect of wave propagation in elastic plates.
Findings
Proof confirms the completeness of Lamb modes.
Utilizes Agranovich-Vishik theorem on elliptic systems.
Applies Locker’s criterion for eigenvector completeness.
Abstract
The aim of this paper is to give a precise proof of the completeness of Lamb modes and associated modes. 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.
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