Scattering by coupled resonating elements in air

TL;DR

This paper investigates the scattering properties of coupled resonating elements in air, combining analytical models, experimental data, and approximations to understand low-frequency resonances and band-gap effects in arrays of composite scatterers.

Contribution

It introduces an analytical model for coupled resonators with N-slits, confirms a simple square root relation for resonant frequencies, and demonstrates band-gap effects in periodic arrays.

Findings

Resonant frequencies depend on the number of slits as a square root.

Coupled resonators produce significant insertion loss peaks.

Band-gap effects are observed below the first Bragg frequency.

Abstract

Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of these scatterers in air has been investigated analytically and through laboratory experiments. The composite scatterer forms a system of coupled resonators and gives rise to multiple low frequency resonances. The corresponding analytical model employs polar angle dependent boundary conditions on the surface of the N-slit cylinder. The solution inside the slits assumes plane waves. It is shown also that in the low-frequency range the N-slit rigid cylinder can be replaced by an equivalent fluid layer. Further approximations suggest a simple square root dependence of the resonant frequencies on the number of slits and this is confirmed by data. The observed resonant phenomena are associated with Helmholtz-like behaviour of the resonator for which the radius and width of the openings are much smaller than the wavelength. The problem of scattering by a finite periodic array of such coupled resonators in air is solved using multiple scattering techniques. The resulting model predicts band-gap effects resulting from the resonances of the individual composite scatterers below the first Bragg frequency . Predictions and data confirm that use of coupled resonators results in substantial insertion loss peaks related to the resonances within the concentric configuration. In addition, for both scattering problems experimental data, predictions of the analytical approach and predictions of the equivalent fluid layer approximations are compared in the low-frequency interval.