# Modal Identification of Train Passenger Seats Based on Dynamic Tests and Output-Only Techniques
## 3 Case Study: Alfa Pendular
### Results
#### 3.2.1 Transmissibility Curves  
Transmissibility curves were evaluated using MATLAB scripts validated in previous works [55]. These curves were obtained based on the information from accelerometers 1 and 6, both at the z-axis. Due to the similarity between experiments and to obtain a cleaner presentation, only 1 experiment per subject is presented. Figure 7 shows the transmissibility curves for the three subjects (S1, S2, and S3) considering the comfort (Figure 6(a)) and standard (Figure 6(b)) seats. It is possible to observe the resonance peaks (marked by red circles) and the antiresonance peaks (marked by blue circles). Table 2 summarises the main resonance and antiresonance peaks for the comfort and standard seats. Due to its intensity, it is expected that some of these frequencies cannot induce a different type of movement. Comfort seat transmissibilities are characterised by resonance frequencies of 0.20, 1.37-1.56, 2.54, and 4.69-4.88 Hz. It should be pointed out that the higher-amplitude transmissibility peaks occur at low frequencies, namely 0.20 and 1.37-1.56 Hz. The antires \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Subject** & **Gender** & **Age (Years)** & **Weight (kg)** & **Height (m)** \\ \hline
**S1** & Female & 25 & 58 & 1.70 \\ \hline
**S2** & Male & 26 & 80 & 1.87 \\ \hline
**S3** & Male & 39 & 115 & 1.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Subjects’ characteristics. onance values are found between 0.39-0.59 and 4.30-4.69 Hz. Despite the inter-subject variability, no significant differences are found between the transmissibility resonances and antiresonances frequency values when comparing all subjects' results. These conclusions comply with the ones found by [PERSON] and [PERSON] [32]. Regarding standard seat transmissibility, the results are also similar for all analysed subjects. Resonances of 0.20, 1.76, 2.34-2.73, and 4.30-4.69 Hz and antiresonances equal to 0.78-1.37 and 3.52-4.30 Hz characterise this class. Higher transmissibility resonances are obtained for 0.20 and 1.76 Hz. Those transmissibility peaks are higher than the ones of the comfort seat. This result agrees with the conclusions derived from the studies performed by [PERSON] and [PERSON] [23] and [PERSON] et al. [35], where the transmissibility peak values decreased for higher foam thicknesses. As aforementioned, the comfort seat has a seat surface thickness of 190 mm, whereas the standard seat thickness is equal to 130 mm. The previously mentioned studies evaluated the effect of foam thickness on less thick foams, namely 40, 60, 80, and 100 mm. Therefore, the AP seat foam thickness is higher than those of the previous studies. Following the reported trend, comparing those results with the present ones, lower transmissibility frequencies in the present results were observed. Figure 6: Experimental test setup: (**a**) seat pad location and experimental test; (**b**) accelerometers distribution along seat frame structure. Each number represents the modal node used on ARteMIS software (see Section 3.2.2). The transmissibility frequency resonance peaks presented in this study are lower than those presented by other authors [23; 32; 33; 34], who found vertical transmissibility frequencies around 4.30 Hz. However, the experiments reported in the bibliography were performed in laboratory conditions instead of using a real railway vehicle. More specifically, those tests considered a single seat with a simplified rigid metallic structure (with a mass of approximately 1000 kg) composed of 4 vertical rigid columns and a free foam on top of the surface without covering it nor restricting its movement. In turn, the train seats instrumented in this study present a leather cover with a large seam hem. The cover significantly modifies the foam vibration transmission by restricting the foam cellular morphology movements. Therefore, the vibration absorption is clearly distinct when compared to the free foam of the laboratory experiments.