A stable, unified model for resonant Faraday cages

Area of Science:

• Acoustics and Wave Propagation
• Mathematical Modeling
• Computational Physics

Background:

• Periodic arrays of Dirichlet wires create effective transmission conditions for wave propagation.
• Previous asymptotic analyses yielded frequency-dependent transmission conditions, complicating practical applications, especially in the time domain.
• Acoustic Faraday cages delimited by such arrays exhibit resonance phenomena.

Purpose of the Study:

• To demonstrate the validity and effectiveness of a unified transmission model for wave propagation through periodic Dirichlet wires.
• To provide a simplified model applicable regardless of proximity to resonance frequencies.
• To implement and exemplify the model in both harmonic and time-domain regimes.

Main Methods:

• Asymptotic analysis to derive transmission conditions.
• Development and validation of a unified model applicable across a range of frequencies.
• Explicit solutions for harmonic regime analysis.
• Time-domain numerical implementation with a focus on scheme stability.

Main Results:

• The unified model accurately reproduces the effects of periodic Dirichlet wires, including acoustic Faraday cage resonance.
• The model's validity is confirmed across different frequency regimes, unlike previous approaches.
• The time-domain formulation ensures numerical stability.

Conclusions:

• The unified model offers a robust and simpler alternative for studying wave propagation with periodic structures.
• This work facilitates more accessible and stable numerical simulations in acoustics and related fields.
• The findings are significant for understanding wave phenomena in resonant structures.