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Updated: Jan 20, 2026

Calibration Procedures for Orthogonal Superposition Rheology
Published on: November 18, 2020
(Bi)-orthogonality relation for eigenfunctions of self-adjoint operators
1Research 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)'.
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