A proof of the completeness of Lamb modes

被引：3

作者：

Akian, Jean-Luc ^{[1
]}

机构：

[1] Univ Paris Saclay, ONERA, F-92322 Chatillon, France

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2022年 / 45卷 / 03期

关键词：

completeness; Lamb modes; resolvent;

D O I：

10.1002/mma.7860

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1402 / 1419

页数：18

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