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