Abstract
As much of metamaterials’ properties originate from resonances, the novel characteristics displayed by acoustic metamaterials are a narrow bandwidth and high dispersive in nature. However, for practical applications, broadband is often a necessity. Furthermore, it would even be better if acoustic metamaterials can display tunable bandwidth characteristics, e.g., with an absorption spectrum that is tailored to fit the noise spectrum. In this article we present a designed integration strategy for acoustic metamaterials that not only overcomes the narrow-band Achilles’ heel for acoustic absorption but also achieves such effect with the minimum sample thickness as dictated by the law of nature. The three elements of the design strategy comprise: (a) the causality constraint, (b) the determination of resonant mode density in accordance with the input target impedance, and (c) the accounting of absorption by evanescent waves. Here, the causality constraint relates the absorption spectrum to a minimum sample thickness, derived from the causal nature of the acoustic response. We have successfully implemented the design strategy by realizing three structures of which one acoustic metamaterial structure, comprising 16 Fabry-Perot resonators, is shown to exhibit near-perfect flat absorption spectrum starting at 400 Hz. The sample has a thickness of 10.86 cm, whereas the minimum thickness as dictated by the causality constraint is 10.55 cm in this particular case. A second structure demonstrates the flexible tunability of the design strategy by opening a reflection notch in the absorption spectrum, extending from 600 to 1000 Hz, with a sample thickness that is only 3 mm above the causality minimum. We compare the designed absorption structure with conventional absorption materials/structures, such as the acoustic sponge and micro-perforated plate, with equal thicknesses as the metamaterial structure. In both cases the designed metamaterial structure displays superior absorption performance in the target frequency range.
Highlights
Even in the 21st century, acoustic noise can still be a pernicious problem
The relevant limit in the case of acoustic absorption is that imposed by the causality principle, which, combined with the resonant mode density determination based on the target absorption spectrum for a structure backed by a reflecting substrate, is shown to yield a self-consistent strategy for achieving absorption
For a fixed d and a desired absorption level, what is the broadest possible frequency range possible? But perhaps the most-often encountered scenario would be: For a target absorption spectrum A(λ), what would be the minimum sample thickness achievable? Below we show examples for what can be achieved from this perspective, but first it is necessary to consider the requirement of impedance matching for a sample, which is the complementary consideration to the causality constraint in our strategy to design a structure with a tunable absorption spectrum
Summary
Even in the 21st century, acoustic noise can still be a pernicious problem. An obvious question facing the scientific and engineering community is: How can we do better to remediate this problem?. Much less-known consequence of the causality principle is that for any electromagnetic absorption spectrum, there is a minimum sample thickness [4,5]. A somewhat interesting aspect of Equation (1) is that only the bulk modulus appears in the causality constraint (in the electromagnetic case only the magnetic permeability appears in the causality constraint), whereas it is well known in acoustics that there are two material parameters: bulk modulus and mass density. This is attributed to the fact that in the derivation, it is necessary to take the zero-frequency limit. The present approach differs by delineating the ultimate limit as dictated by natural law, and using such constraint as part of the design strategy to achieve tunable absorption by design
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