Multiple local resonators periodic design for interior noise control

Nowadays, an aircraft project cannot neglect noise consideration for interior and exterior noise. Furthermore, exterior acoustic disturbance is crucial in terms of noise pollution and regulations, while interior annoyances due to acoustic sources should be avoided (or at least minimized), in order to upgrade travel conditions and comfort for passengers. The frame of an aircraft is generally made by thin structures of aluminum or composite materials, which are surely perfect materials for their main function but inadequate for acoustic insulation purposes. Hence, acoustic solutions must be introduced, but they should guarantee great performances without requiring excessive weight and/or space increase. Acoustic metamaterials are designed to take into account these boundaries, by assembling complex cells with a proper arrangement, shape or geometry aimed at reducing sound disturbance [1–2]. This approach, even through the use of conventional materials, allows to produce systems which exhibit extraordinary properties, such as negative refraction, sub-wavelength imaging, cloaking, one-way transmittance. Meta-material can be designed through basic acoustic objects like Helmholtz Resonators [3], porous materials [4], quarter-wavelength tubes [5] and Dynamic Vibrating Absorbers (DVA) [6]. The main advantage of acoustic metamaterial is the design flexibility: indeed, each sub-system can be useful for a specific purpose (and of course less effective for others). For instance, acoustics resonators like Helmholtz Resonators and Dynamic Vibrating Absorbers have great performance when they are applied for the suppression of tonal sources; acoustic resonators are characterized by tunable resonance frequencies that can completely delete the source sound disturb. In contrast, a porous layer can suppress high-frequency noise; however, it works as a damper either, hence its coupling with an acoustic resonator will affect the correct behavior of the resonator in correspondence of its resonance frequency. Furthermore, a considerable number of applications are related to absorb the sound energy, while others are principally deployed when the sound wave should be not transmitted (transmission loss applications). For instance, a transmission loss application can be the one in Figure 1: a double-plate system made by coupling a structural panel with a panel employed for sound suppression (acoustic panel). The acoustic panel is divided in multiple sub-structures, which are tuned through appropriate boundary conditions (BCs). Each sub-structure is helpful to arise the transmission loss of the whole model at a specific tunable frequency. In contrast, a model like this is not useful for absorption objectives. Another acoustic metamaterial design can be otherwise successful for sound absorption but not the best option for transmission loss applications. An example is herein presented (Figure 2), made by three labyrinthine resonators (LRs), where each LR has a tunable resonance frequency similar but not equal to the others, in order to increase the bandwidth of influence and ensure good absorption properties in a specific range of frequency instead of being productive just in a narrow bandgap. In this work, different acoustic metamaterial solutions are numerically studied and compared, in order to highlight benefits and drawbacks of each objects in terms of sound absorption and transmission loss.