On the application of bi-orthogonality relations for analysis of linear dynamic systems

Lasse S. Ledet*, Sergey V. Sorokin*

*Kontaktforfatter

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

3 Citationer (Scopus)

Abstract

This paper derives a new class of modal decompositions of Somigliana's identities for a certain class of problems displaying symmetry and uniformity such as, for instance, elastic vibration problems including the effect of fluid loading. The decompositions are shown to lead to a number of new analytical results relating to homogeneous and inhomogeneous boundary value problems in whichever realm of physics, for example, free and forced vibration problems in a bounded domain, and also to unify many known results which have previously been obtained by other methods. At every stage, the mathematical analysis is shown to correspond to physical concepts relating to standing waves, transmission of energy and bi-orthogonality. Details are given for a number of examples in elastodynamics and vibro-acoustics, of which the fluid-loaded membrane provides particularly clear demonstrations of the power of the method in a non-trivial setting.

OriginalsprogEngelsk
Artikelnummer115020
TidsskriftJournal of Sound and Vibration
Vol/bind465
ISSN0022-460X
DOI
StatusUdgivet - 20 jan. 2020

Bibliografisk note

Funding Information:
A special thanks to Prof. C. J. Chapman from Keele University for helpful discussions and suggestions to the paper. The financial support from the Innovation Fund Denmark and Grundfos Holding A/S is gratefully appreciated. Appendix A

Funding Information:
A special thanks to Prof. C. J. Chapman from Keele University for helpful discussions and suggestions to the paper. The financial support from the Innovation Fund Denmark and Grundfos Holding A/S is gratefully appreciated.

Publisher Copyright:
© 2019 Elsevier Ltd

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