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

TL;DR

This paper explores how differential geometry can be applied to nonlinear acoustic wave propagation in Reissner beams, offering a geometric framework to model complex phenomena without artificial nonlinearities.

Contribution

It introduces a geometric approach using Lie groups and covariant methods to model nonlinear acoustic propagation in Reissner beams, enhancing understanding of intrinsic nonlinear phenomena.

Findings

Geometric interpretation simplifies nonlinear acoustic modeling.

Lie group symmetries enable reduction of complex models.

The covariant approach provides a unified framework for analysis.

Abstract

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.