## 3 Experimental Study of Squeal Noise
### Preliminary Analysis  
The preliminary analysis of the tests carried out is conducted in two steps. Firstly, the evolution of the mean square pressure as a function of distance for each microphone from the braking system (which corresponds to the origin of squeal noise) is estimated by analyzing the experimental results of the temporal evolution of the squeal noise. For each microphone, the mean square of the temporal signal is estimated for \(15.5\) s \(<t<36\) s (i.e., on the phase of the braking test when the squeal noise is generated). Figure 4 shows a cloud of points obtained from the measurements carried out in one braking test. A decrease in the signal almost proportional to the square of the distance is observed (i.e., the decrease is more precisely identified as equal to \(\frac{1}{r!.34}\)). This result allows us a regorous conduct of our study, knowing that the experimental results are not related to external disturbances (such as unwanted reflections due to non-controlled experimental conditions, for example). Figure 3: Positioning of the 117 microphones in the plane of the digital microphone antenna. Secondly, Figure 5 illustrates the spectrogram obtained from one typical evolution of squeal noise by considering one microphone of the digital antenna. A Fourier transform is calculated with a time window \(\Delta t=\frac{0.1}{3}\) s, the sampling frequency of the measurements being 56,250 Hz. It can be observed without any ambiguity that the squeal noise generated for \(t>15.5\) s is mainly composed of one fundamental frequency \(f_{1}=610\) Hz and the associated harmonic components denoted by \(f_{2}=2f_{1}=1220\) Hz, \(f_{3}=3f_{1}=1830\) Hz, \(f_{4}=4f_{1}=2440\) Hz and \(f_{5}=5f_{1}=3050\) Hz. These results are of course in agreement with those of previous studies [25; 26]. Moreover, some additional phenomena due to thermal effects can also be the cause of complex secondary transient phenomena during squeal events. This is characterized by several additional second-order contributions corresponding to frequencies that decrease during squeal events (as observed in the frequency ranges \([900;1200]\) Hz and \([1200;1600]\) Hz). For more details on these unexpected thermal effects on squeal events, the reader can refer to [27]. For the rest of the study, we focus on frequencies \(f_{1},f_{2},f_{3},f_{4}\) and \(f_{5}\) that correspond to the main contributions of squeal noise. Moreover, to illustrate the effectiveness of the methodology to reconstruct the acoustic field from measurements in the near field, the results presented in the following sections are proposed only at \(t=24\) s (denoted by the red lines in Figure 2 or the dashed line in Figure 5) for which the five frequencies of interest are clearly visible. The acoustic phenomenon of squeal over the entire duration of the braking test remains outside the scope of this study and will be the subject of future work. Nevertheless, we check that the acoustic behavior remains relatively the same for several seconds. Hence, the results proposed here are not specific for one specific time interval (i.e., \(t=24\) s) but remain valid during squeal events. It should be noted that the potential links between the emergence of friction-induced vibrations and squeal noise in the near-field and far-field were discussed in depth previously in [26]. Although the frequency signature observed in vibration is similar to that analyzed on radiated noise during transient and stationary squeal events, it is observed that the largest frequency contributions of squeal noise are not necessarily the largest frequency contributions of the friction-induced vibrations detected on the two pads, the disc and the caliper. It can therefore be concluded that there is no obvious link between the acoustic levels and the vibration levels for each frequency contribution. In addition, for a more detailed comment on the phenomena of friction-induced vibrations during squeal events, the interested readers should refer to [25].