# Acoustic Metamaterials in Aeronautics

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## Abstract

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## 1. Introduction

## 2. Potential Applications of Aeroacoustic Metamaterials

#### 2.1. Absorption and Dissipation

#### 2.2. Reflection

#### 2.3. Noise Trapping

#### 2.4. Scattering Abatement (Cloaking)

## 3. Challenges

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Metasurface design of a Schroeder Diffuser from [26]: diffuse scattering is achieved through a deep sub-wavelength metasurface. Each cell adds a different and random arranged phase-shift in the reflected field. In (

**a**,

**b**) the standard and the metasurface designs are compared. The simulated far-field scattering pattern for a flat plate and for the metasurface diffuser are shown in (

**c**,

**d**) in terms of sound pressure level (the arrow indicates the incident acoustic perturbation) evidencing the achieved metabehavior.

**Figure 2.**Typical distribution of aircraft noise between different sources during take-off and approach. Picture from [41].

**Figure 3.**Various metamaterial designs for low-frequency absorption: (

**a**) a membrane decorated with added platelets and displacement related to the first three eigenfrequencies of the structure from [47]; (

**b**) a dual resonant metamaterial composed of Helmholtz’s resonators, and a perforated sheet adopted as an innovative liner in [43]; (

**c**,

**d**) two different space-coiling designs, respectively from [45] and [46]. The dissipation of acoustic energy is fundamental in each design.

**Figure 4.**The original “optimal” absorbing metamaterial obtained by Yang et al. The unit cell is composed of 16 resonant channels differing in length and folded to compact the sample (image from [47]).

**Figure 5.**Image from [48]. An absorbing metamaterial composed of various different Helmholtz resonators separated by microporous septa. The reference values for parameters are ${d}_{1}$, ${t}_{2}$, ${d}_{2}$, T = 1 mm, ${t}_{1}$ = 2 mm, ${b}_{1}$ = 3.6 mm, ${b}_{2}$ = 4 mm, H = 20 mm, and these can be tuned to obtain the maximum absorption at the desired frequency (e.g., an absorption peak at 580 Hz is obtained with H = 60 mm ${d}_{2}$ = 0.2 mm and ${d}_{1}$ = 1.3 mm).

**Figure 7.**Shaping the reflection field, from [22,23]. The unit cell is easily parametrized (

**a**) to obtain a phase shift profile (

**b**, colors indicate the phase of the reflected field when a plane wave is incoming) combining different cells in an array (

**c**). An arbitrary shape can be obtained, imposing different phase shift profiles, $\varphi \left(y\right)$, to the reflected field (

**d**).

**Figure 8.**Noise trapping unit cell, from [63] and the functioning scheme of a noise trapping concept. The incident wave is allowed to pass through the metamaterial, and it is steered by the phase array into an absorbing material. The reflected fraction of the sound cannot escape and multiple reflections and absorption occur.

**Figure 9.**A pentamode material as realized by Kadic [69] with 3D laser lithography. The unit elements are linked to each other with connections that are 0.55 $\mathsf{\mu}$m thick.

**Figure 10.**Acoustic cloaking in the presence of flow. The classic transformation acoustic theory defines a metamaterial that fails during abate scattering for the Mach number M ≠ 0 (

**a**). A correction of metamaterial parameters, as derived in [92], can recover the cloaking effect, even for M = 0.3 (flow incoming from the right) (

**b**).

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**MDPI and ACS Style**

Palma, G.; Mao, H.; Burghignoli, L.; Göransson, P.; Iemma, U. Acoustic Metamaterials in Aeronautics. *Appl. Sci.* **2018**, *8*, 971.
https://doi.org/10.3390/app8060971

**AMA Style**

Palma G, Mao H, Burghignoli L, Göransson P, Iemma U. Acoustic Metamaterials in Aeronautics. *Applied Sciences*. 2018; 8(6):971.
https://doi.org/10.3390/app8060971

**Chicago/Turabian Style**

Palma, Giorgio, Huina Mao, Lorenzo Burghignoli, Peter Göransson, and Umberto Iemma. 2018. "Acoustic Metamaterials in Aeronautics" *Applied Sciences* 8, no. 6: 971.
https://doi.org/10.3390/app8060971