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

@inproceedings{Bensoam2013DifferentialGA,
  title={Differential Geometry Applied to Acoustics: Non Linear Propagation in Reissner Beams},
  author={Jo{\"e}l Bensoam},
  booktitle={International Conference on Geometric Science of Information},
  year={2013}
}
  • J. Bensoam
  • Published in
    International Conference on…
    3 April 2013
  • Mathematics
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… 
1 Citations

Non Linear Propagation in Reissner Beams: An Integrable System?

In the seventies, Arnold has a geometric approach by considering a dynamical system as a map taking values in an abstract Lie group, and this multi-symplectic approach can be related to the study of harmonic maps for which two dimensional cases can be solved exactly.

References

SHOWING 1-10 OF 36 REFERENCES

Modelling and numerical simulation of strings based on lie groups and algebras applications to the nonlinear dynamics of Reissner Beams

A nonlinear string can be modelled as a prestressed beam using Reissner's assumptions. Namely, that plane sections normal to the neutral axis remain plane but that their displacements and rotations

Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms

The long-term dynamic response of non-linear geometrically exact rods under-going finite extension, shear and bending, accompanied by large overall motions, is addressed in detail. The central

Riemannian Geometry

THE recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Riemann proposed the generalisation, to spaces of any order, of Gauss's

The Nonlinear Dynamics of Filaments

Recently developed techniques involving linear and nonlinear analyses that enable one to study, insome detail, the actual dynamics of filament instabilities and the localized structures that can ensue are reviewed.

Towards a classification of Euler–Kirchhoff filaments

Euler–Kirchhoff filaments are solutions of the static Kirchhoff equations for elastic rods with circular cross sections. These equations are known to be formally equivalent to the Euler equations for