Formulation of an equation of diffusion for heterogeneous rods
Résumé
A new formulation for predicting the energy flow in heterogeneous rods id developed on the basis of an equation of diffusion. It succeeds in surpassing traditional studies for homogeneous ones, for which vibratory responses are often easily known by simple displacement formulation. However, one stays difficult to describe the mechanical behavior for heterogeneous structures: in this case, the energy flow is governed by structural damping, as for homogeneous medium, but by discontinuities too. The study presented here proposes to identify for heterogeneous structures a factor of diffusion involving proportionality between transmitted power and energy gradient. An equation of diffusion is then formulated considering an energetic balance. The formulation is semi-local, that is spatial average is locally made to take into account several heterogeneities in studied element. An analytical formulation is first developed for rod with area discontinuities. The proposed theoretical factor of diffusion is in good agreements with the numerical predictions.
Domaines
Vibrations [physics.class-ph]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...