This paper develops a theory for the sound absorption and scattering of perforated slit absorbers. A rigid plane, perforated periodically in one dimension with absorbing slits, scatters incoming sound waves as discrete wave components in different directions. The absorbing slits are assumed to be line-like in the sense that their width is much shorter than the wavelengths. The equation for the sound field is solved in the wavenumber domain. The slits are described with an impedance description, assuming local reaction of the slits (typically a Helmholtz resonator). The solution is found by means of an inverse transform, back to the spatial domain. This results in an explicit formulation of the sound field, including a sum consisting of components that either radiate energy in discrete directions or are surface waves. A similar sum is also included in a term that can be interpreted as radiation impedance. The explicit expressions for the absorption and scattering coefficients are found with the aid of the radiating part of the scattered and reflected field. Numerical results of the absorption and scattering coefficients are presented. The result is verified with finite element method and compared with the result from an alternative general formulation of the problem.
Acoustic metamaterials have emerged as alternative solutions to achieve useful physical effects that differ from the ones obtained with traditional materials. In terms of sound absorption, previous works have addressed their potential as compact surfaces with high performance. Nevertheless, studies on their angle-dependent behavior are scarce. In this work, an analytic model and a numerical model to estimate the performance of periodic surfaces with unit cells composed of 2D Helmholtz resonators are presented. By making use of these modeling tools, the absorption of surfaces with one and three different resonators is studied as a function of both incidence angle and frequency. Changes in the incidence angle can cause variation of the maximum absorption coefficient, the frequencies at which the maximum performance is observed, and the frequency range of significant absorption. Furthermore, the rate at which the performance changes as a function of the incidence angle is larger as the angle increases. Given the angle dependency of these absorbers, a strategy to optimize the dimensions of the surface elements to maximize the absorption performance for predefined ranges of incidence angles and frequencies is presented.
It has been shown in several recent publications that acoustic materials consisting of a combination of resonators tuned to different frequencies can render high absorption coefficient values over an extended frequency range while maintaining compactness. This makes them attractive
solutions for applications in which low frequency sound control is needed, and/or when there are significant space constraints. Nevertheless, the acoustic performance of these surfaces varies with the angle at which a wave impinges on the surface. The changes in the absorption characteristics
with the incidence angle occur both on the maximum absorption coefficient, and on the effective frequency bandwidth. Numerical optimization is a tool that can help realize designs with a large degree of geometrical freedom, and using this framework we have demonstrated an array of coupled
2D Helmholtz resonators that is less sensitive to changes in the incidence angle.
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