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Tim e-domain Wave Propagation in Rigid Porous Media using Equivalent Fluid Model with a Quadratic Nonlinearity

Moufid, Ilyes and Matignon, Denis and Roncen, Remi and Piot, Estelle Tim e-domain Wave Propagation in Rigid Porous Media using Equivalent Fluid Model with a Quadratic Nonlinearity. ( In Press: 2022) In: 10th European Nonlinear Dynamics Conference (ENOC), 17 July 2022 - 22 July 2022 (Lyon, France).

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Abstract

The acoustic properties of rigid porous media can be described by the equivalent fluid model (EFM) in the frequency domain, involving complex-valued functions. These physical quantities can be irrational, which leads to fractional derivatives in the time domain. Besides, this model is built with a constant flow resistivity, which is known to grow linearly with the flow velocity in the Forchheimer regime. Hence, a correction on the EFM is made according to the Darcy-Forchheimer law, leading to a more general model with an additional nonlinear term. Here, an approach is presented to formulate the EFM equations with the Forchheimer’s correction in the time domain, where the fractional derivatives described by causal convolution are approximated by additional differential equations. It results in a nonlinear system on which an energy-based analysis is performed to ensure its stability under suitable conditions.

Item Type:Conference or Workshop Item (Paper)
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE)
Laboratory name:
Funders:
ONERA and ISAE-SUPAERO, through EUR TSAE under grant ANR-17-EURE-0005.
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Deposited On:20 Sep 2021 13:23

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