(Bi)-orthogonality relation for eigenfunctions of self-adjoint operators. (2nd September 2019)

• Record Type: Journal Article
• Authors: Ledet, L. S.; Sorokin, S. V.
• Is Part Of: Philosophical transactions. Volume 377:Number 2156(2019)
• Publication Date: 2019-09-02
• Subjects: bi-orthogonality relation -- reciprocity relation -- self-adjoint operator -- fluid-loaded plate -- energy flow; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2019.0112
• Languages: English
• ISSNs: 1364-503X

Abstract

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)'.