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A New Method for the Calculation of the Mechanical Behaviour of Arbitrarily Shaped Membranes

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A finite element method for the calculation of the static and dynamic mechanical behaviour of membranes with arbitrary geometrical shape is introduced. The differential equation governing membrane waves, and the differential equation governing acoustic wave propagation in fluid media exhibit identical structure, so finite elements of a membrane type were implemented on the basis of standard fluid finite elements. The results obtained were tested against analytical solutions available for regular shaped membranes, as well as data available in the literature for the eigenfrequencies of L-, 1-, cross- and elliptically shaped membranes.

Zusammenfassung

Es wird eine Finite-Element-Methode zur Berechnung des statischen und dynamischen Verhaltens von Membranen mit beliebiger Berandungsgeometrie vorgestellt. Aufgrund der Identität der Differentialgleichungen für Membranschwingungen und der Wellengleichung für Schallwellen in gasförmigen bzw. fluiden Medien konnten die finiten Membranelemente auf der Basis von fluiden finiten Elementen entwickelt werden. Die finiten Membranelemente wurden anhand von aus der Literatur bekannten Eigenfrequenzen fur L-, I- und kreuzförmige sowie elliptische Membranen verifiziert.

Sommaire

On présente une méthode d'éléments finis pour calculer le comportement mécanique statique et dynamique de membranes de forme géométrique arbitraire. L'equation differentielle régissant les ondes dans les membranes et l'équation regissant la propagation des ondes acoustiques en milieu fluide montrent des structures identiques, de sorte qu'on a pu établir les éléments finis pour la membrane sur la base des éléments finis pour un fluide standard. Les résultats obtenus ont été vérifiés par comparaison avec des solutions analytiques disponibles pour des membranes de formes régulières ainsi qu'avec des données publiées concernant les fréquences propres de membranes en forme de L, de I, de croix et d'ellipses.
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Document Type: Research Article

Publication date: February 1, 1991

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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