Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances

International audienceThe scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section isstudied from a modal formalism by emphasizing the role of the symmetries. More precisely, as thesymmetry is broken in the transition from the infinite circular cylinder to the elliptical one, thesplitting up of resonances is observed both theoretically and experimentally. This phenomenon canbe interpreted using group theory. The main difficulty stands in the application of this theorywithin the framework of the vectorial formalism in elastodynamics. This method significantlysimplifies 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. Anexperimental part based on ultrasonic spectroscopy complements the theoretical study. A series oftank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, inthe frequency range 0kr50, where kr is the reduced wave number in the fluid. The symmetryis broken by selecting various cylinders of increasing eccentricity. More precisely, the greaterthe eccentricity, the higher the splitting up of resonances is accentuated. The experimentalresults provide a very good agreement with the theoretical ones, the splitting up isobserved on experimental form functions, and the split resonant modes are identified on angulardiagrams