1.
Philos Trans A Math Phys Eng Sci
; 377(2156): 20190112, 2019 Oct 21.
Article
in English
| MEDLINE
| ID: mdl-31474209
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)'.