Geometric diffusion of energy and comparison with the vibrational conductivity approach

Alain Le Bot (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

The vibrational conductivity approach is sometimes used to evaluate the spatial repartition of the energy density of dynamical structural/acoustic systems in high frequency range. This is a significant improvement of the Statistical Energy Analysis which only provides a single energy value per sub-system. However, this model is based on the underlying assumption that the wave field is constructed as a superposition of plane waves. This hypothesis may fail for largely non diffuse fields. This paper is devoted to the study of other types of waves. The fields are still described in terms of energy quantities which are solved using a differential equation written along the "streamlines of energy". Results strongly depend on the geometry of these streamlines. Whenever this geometry is known, for instance for plane, cylindrical and spherical waves, the differential equation may be solved. The plane wave case is in good agreement with the vibrational conductivity approach, whereas a large class of other waves are generated by this equation. Some numerical simulations illustrate these facts.

Mots clés: Vibration; Energy; High frequency; Statistical Energy Analysis

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Alain Le Bot. Geometric diffusion of energy and comparison with the vibrational conductivity approach. Journal of Sound and Vibration, 1998, 212, pp.637-647. ⟨hal-00468900⟩