Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams

Joël Bensoam (1)

1 STMS - Sciences et Technologies de la Musique et du Son

Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics through the concepts of differential geometry can help to address the non-linear phenomena in their intrinsic qualities. This results in a field of research aimed at establishing and solving dynamic models purged of any artificial nonlinearity by taking advantage of symmetry properties underlying the use of Lie groups. The geometric constructions needed for reduction are presented in the context of the "covariant" approach.

Mots clés: Acoustic; Reissner beam; Lie group; geometry

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]; Vibrations [physics.class-ph]; Vibrations [physics.class-ph]; Physique mathématique [math-ph]

Joël Bensoam. Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams. 2013. ⟨hal-00807030⟩