## 2 Potential Applications of Aeroacoustic Metamaterials
### Absorption and Dissipation  
Typically, the strategy adopted to reduce the exposure of citizens to aircraft noise is based on the minimization of the sound energy at ground location, hence shrinking the area inside the critical isophonic curves. Reducing the noise level provides a major contribution to the alleviation of community noise [40]. As stated above, engines are a significant source of noise under all flight conditions, largely dominating during take-off and being comparable to airframe noise during landing. Among the engine sources, fan noise is one of the biggest component in the overall noise (see Figure 2), and its relative importance has increased in the last twenty years as the bypass ratio of modern turbofan engines have increased. This latter development has been led by the need to reduce the specific fuel consumption, but has, as a side effect, also reduced the jet noise, in comparison to the other noise components. For modern aircraft, most of the engine noise attenuation is provided by liners, which are absorbing panels positioned in the internal walls of the nacelle that are designed to reduce both broadband and tonal noise. The basic single degree-of-freedom liner is typically made by an hard-backed honeycomb and behaves like a quarter-wavelength resonator, covered by a perforated plate that, on one side, enhances the sound absorption of the liner and on the other, maintains the aerodynamic flow as cleanly as possible on the walls of the nacelle. Liner design is one of the most active research field in aeronautics and recently, metamaterials have started to be taken into consideration for future and more effective absorbing panels for liners, adopting e.g., dual-resonant materials covered by microperforated panels [42; 43] or variable depth liners with spherical inclusions and microporous panels embedded within melamine [44]. The most desired effect that could be possibly achieved by adopting metamaterial-inspired liners is low frequency absorption, i.e., in the range of 100-1000 Hz, which is difficult to achieve with classical approaches, due to the long wavelengths of sound involved at those frequencies. Several authors have proposed new metamaterials for low frequency noise absorption that are of interest and could possibly be applied to the design of new liners. Some example sare shown in Figure 3, such as thin film membranes with rigid platelets, as presented in [15], in which the incident acoustic wave is dissipated at the resonance of a cavity system due to enhanced energy concentration at discontinuities in the slope of the displacement profile. Space-coiling metamaterials have been proposed as dissipative media with proven sound absorption ability, in combination with microperforated panel coverings [39; 45; 46]. One of the advantages promised by such design is a deep sub-wavelength functionality, often reached by exploiting Fabry-Perot resonance in long, coiled, narrow channels (Figure 4), which enhance dissipation phenomena at resonant frequency. Another valuable contribution in this field is the work by [PERSON] et al. [47], who derived a \"causality\" constraint that dictates trade-off conditions between the sample thickness, frequency bandwidth and magnitude of absorption in the low frequency range and presented a design strategy to realize the target absorption coefficient profile with the minimum possible thickness. Resonance and viscous dissipation was also exploited in a very interesting design by [PERSON] et al. [48]. A series of different acoustic Helmholtz resonators was obtained by inserting inclined  
Figure 2: Typical distribution of aircraft noise between different sources during take-off and approach. Picture from [41]. microporous septa in a honeycomb structure with a microperforated panel on top (see Figure 5).