Analysis, simulation and impedance operator of a nonlocal model of porous medium for acoustic control

Emmanuel Montseny (1, 2) , Céline Casenave (3, 4)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 UT3 - Université Toulouse III - Paul Sabatier
3 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
4 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

The problem under consideration relates to a model of a porous wall devoted to aircraft motor noise reduction. For such a medium, the parameters of the propagation equation depend on the frequency. Then, the associated time-model involves non rational convolution operators, which make the model complex from both analysis and simulation points of view. In this paper, based on the so-called di usive representation of con- volution operators, a time-local formulation of the porous wall model, well adapted to analysis and numerical simulation, is established and analyzed. Then its associated impedance operator is computed. Fi- nally, some numerical results relating to the time-domain simulation of the porous wall and its impedance operator are given.

Mots clés: porous medium; acoustics waves; boundary control; impedance operator; non rational operator; diffusive representation; state representation; dissipativity

Domaines: Automatique / Robotique; Vibrations [physics.class-ph]; Vibrations [physics.class-ph]; Automatique

Emmanuel Montseny, Céline Casenave. Analysis, simulation and impedance operator of a nonlocal model of porous medium for acoustic control. Journal of Vibration and Control, 2015, 21 (5), pp. 1012-1028. ⟨10.1177/1077546313493815⟩. ⟨hal-00854312⟩