Natural Mode Resonances in the Plane Wave Scattering from an Infinite Thin Resistive Plate with a Circular Hole

In this paper, the natural mode resonances of an infinite thin resistive plate with a circular hole excited by an impinging plane wave are analyzed. By using the generalized boundary conditions and introducing suitable unknowns related to the azimuthal harmonics of the effective surface current density, the problem is formulated as an infinite set of independent one-dimensional dual integral equations in the Hankel transform domain. The discretization and analytical regularization of such integral equations are achieved by means of the Helmholtz-Galerkin technique. Once the unknowns are reconstructed, the resonance frequencies are readily individuated by the peaks of the total scattering cross-section.