Normal Modes and Modal Reduction in Exterior Acoustics

The Helmholtz equation for exterior acoustic problems can be solved by the finite element method in combination with conjugated infinite elements. Both provide frequency-independent system matrices, forming a discrete, linear system of equations. The homogenous system can be understood as a quadrati...

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Bibliographic Details
Published inJournal of theoretical and computational acoustics Vol. 26; no. 3; p. 1850029
Main Authors Moheit, Lennart, Marburg, Steffen
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 01.09.2018
World Scientific Publishing Co. Pte., Ltd
Subjects
Acoustics
Eigenvalues
Finite element method
Helmholtz equations
Mathematical analysis
Matrix methods
Mode superposition method
Reduction
Sound pressure
infinite element method
modal reduction
Exterior acoustics
normal modes
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ISSN2591-7285
2591-7811
2591-7811
DOI10.1142/S2591728518500299

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Summary:The Helmholtz equation for exterior acoustic problems can be solved by the finite element method in combination with conjugated infinite elements. Both provide frequency-independent system matrices, forming a discrete, linear system of equations. The homogenous system can be understood as a quadratic eigenvalue problem of normal modes (NMs). Knowledge about the only relevant NMs, which — when doing modal superposition — still provide a sufficiently accurate solution for the sound pressure and sound power in comparison to the full set of modes, leads to reduced computational effort. Properties of NMs and criteria of modal reduction are discussed in this work.
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ISSN:2591-7285
2591-7811
2591-7811
DOI:10.1142/S2591728518500299