A stable, unified model for resonant Faraday cages

We study some effective transmission conditions able to reproduce the effect of a periodic array of Dirichlet wires on wave propagation, in particular when the array delimits an acoustic Faraday cage able to resonate. In the study of Hewett & Hewitt (2016 Proc. R. Soc. A 472, 20160062 (doi:10.1098/rspa.2016.0062)) different transmission conditions emerge from the asymptotic analysis whose validity depends on the frequency, specifically the distance to a resonance frequency of the cage. In practice, dealing with such conditions is difficult, especially if the problem is set in the time domain. In the present study, we demonstrate the validity of a simpler unified model derived in Marigo & Maurel (2016 Proc. R. Soc. A 472, 20160068 (doi:10.1098/rspa.2016.0068)), where unified means valid whatever the distance to the resonance frequencies. The effectiveness of the model is discussed in the harmonic regime owing to explicit solutions. It is also exemplified in the time domain, where a formulation guaranteeing the stability of the numerical scheme has been implemented.