Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances
Résumé
The scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section is
studied from a modal formalism by emphasizing the role of the symmetries. More precisely, as the
symmetry is broken in the transition from the infinite circular cylinder to the elliptical one, the
splitting up of resonances is observed both theoretically and experimentally. This phenomenon can
be interpreted using group theory. The main difficulty stands in the application of this theory
within the framework of the vectorial formalism in elastodynamics. This method significantly
simplifies the numerical treatment of the problem, provides a full classification of the resonances,
and gives a physical interpretation of the splitting up in terms of symmetry breaking. An
experimental part based on ultrasonic spectroscopy complements the theoretical study. A series of
tank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, in
the frequency range 0kr50, where kr is the reduced wave number in the fluid. The symmetry
is broken by selecting various cylinders of increasing eccentricity. More precisely, the greater
the eccentricity, the higher the splitting up of resonances is accentuated. The experimental
results provide a very good agreement with the theoretical ones, the splitting up is
observed on experimental form functions, and the split resonant modes are identified on angular
diagrams.
Domaines
Acoustique [physics.class-ph]
Origine : Fichiers produits par l'(les) auteur(s)
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