Acoustic waves in a perforated cylinder

A lumped parameter approach to the problem of acoustic wave scattering by a perforated cylinder has been presented. The proposed framework enables analytical evaluation of the scattering amplitudes of all harmonics and derivation of the dispersion relations for the guided wave propagating inside the cylinder. The lumped parameter boundary condition enables straightforward estimation of the effect of different perforation patterns on the scattering characteristics and internal resonances of the perforated cylinder. The derived equations were treated analytically and validated numerically. It was demonstrated how the proposed theory can be applied for estimation of the fundamental frequency of a two-dimensional Helmholtz resonator with the complex configurations of openings. The predictions are in good agreement with the previously published results.