## 3 BEM Simulations  
The commercial code VA One [29] was selected for the numerical simulations. In particular, the BEM module of VA One was selected since the current modelling was referred to an exterior  
Figure 1: Layers of electrospun silica/PVP blanket.  
acoustic problem, in which a diffuse acoustic field was generated in the surrounding of an aircraft seat. This assumption allowed to strongly simplify the modelling strategy, even if the downside was that, assuming a fully reverberant aircraft cabin with the noise uniformly radiated to passengers, causes an increasing approximation in the lower part of the frequency range considered.  
Figure 2 shows the initial CAD model of two aircraft seats, whereas Figure 3 shows the simplified seat modelling, comprising just headrest, backrest, and cushion. The remaining structural and non-structural seat parts, shown in Figure 2, were preliminarily considered in the simulations and subsequently removed, since they did not give any appreciable contribute to the SPL at passengers' ears. A simplified CAD model was adopted for the BEM modeling (Figure 4), where the headrest, differently from the remaining parts, is modelled with the new innovative material. Figure 4 also highlights the spherical data recovery surfaces, with a radius equal to 4 cm, in order to provide a spaced average of SPLs (rather than a less meaningful point assessment). The headrests were modelled in a flat and a folded configuration (Figures 3 and 4) and were alternatively adopted in the simplified modelling of the seat.  
The considered frequency range was set up to 200-1600 Hz and represented by standard 1/3 rd octave bands. BEM mesh comprised triangular surface linear elements with an element size equal to nearly 10 mm for the headrest and 20 mm for the remaining parts. Thus, at least 20 nodes per wavelength were adopted when considering the maximum frequency under analysis of 1.6 kHz. BEM fluid was air, with sound speed equal to 343 m/s, mass density equal to 1.21 kg/m\({}^{3}\), and a null damping loss factor.  
The acoustic load was generated by means of a series of monopole sources, spherically distributed in the surrounding of a single seat, modeled in the abovementioned simplified way. Figure 5 shows an example of this loading conditions. All the monopole sources emitted a given sound pressure spectrum, calibrated so as to recreate a diffuse acoustic field, and having a sound pressure level representative of that existing in an aircraft cabin during flight [30]. Random phases were considered for all the sources.  
Figure 2: CAD model of two aircraft seats.  
Real and imaginary parts of acoustic impedance were inserted in the code. Impedance measurements were carried out in a Kundt's tube [25; 26; 27], thus assuming a perfectly normal incidence of sound waves: such condition rarely exists in mostly all the practical applications, but the related approximations were judged as acceptable for the current analyses.  
PVP plus silica electrospun materials and foam were separately considered for the headrest surfaces, whereas the reference foam was considered for backrest and cushion surfaces. A total of six separate models were built up in order to calculate the SPL for two distinct headrest shapes and three distinct material combinations.  
Figure 4: BEM models for the two headrest configurations.  
Figure 3: Simplified CAD models, considering both flat (**right**) and folded (**left**) headrest.