(Bi)-orthogonality relation for eigenfunctions of self-adjoint operators-Reference-Cited by-同舟云学术

(Bi)-orthogonality relation for eigenfunctions of self-adjoint operators

Published:2019-09-02 Issue:2156 Volume:377 Page:20190112
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Ledet L. S.¹^ORCID,Sorokin S. V.¹

Affiliation:

1. Research group of Solid and Computational Mechanics, Aalborg University, Fibigerstraede 16, 9220, Aalborg, Denmark

Abstract

The bi-orthogonality relation for eigenfunctions of self-adjoint operators is derived. Its composition is explained in view of the structure of a characteristic equation and of the energy flow components. Application of the bi-orthogonality relation for solving forcing problems is generalized and the connection between the bi-orthogonality relation and the virtual wave method is highlighted. Technicalities are illustrated in a non-trivial example of propagation of free/forced cylindrical waves in a thin elastic plate under heavy fluid loading. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

Funder

Innovation Fund Denmark and Grundfos Holding A/S

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2019.0112

Reference17 articles.

1. Orthogonality relations for Lamb waves;Bobrovnitskii YI;Sov. Acoust. Phys.,1973

2. Orthogonality relation for the Rayleigh–Lamb modes of vibration of a plate

3. Generation of symmetric Lamb waves by non-uniform excitations

4. The Generation of Waves in a Semi-Infinite Plate by a Smooth Oscillating Piston

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