# Modal Identification of Train Passenger Seats Based on Dynamic Tests and Output-Only Techniques
## 3 Case Study: Alfa Pendular
### Results
#### 3.2.2 EFDD Method  
The modal identification was also performed using the EFDD method available in the ARTeMIS(r) software [56]. Once the inter-subject variability did not notice any significant alteration in transmissibility analysis, the EFDD method was performed only for subject S1. The natural frequencies estimated from the EFDD method and transmissibility functions are equal once the latter is the base for identifying the natural modes. Figure 8 shows the first two curves of the average normalised singular values of the spectral density matrices of subject S1 considering the comfort seat test. In this figure, it is possible to observe the peaks corresponding to the identified frequencies and mode shapes. The seat modal parameters, namely the natural frequencies and modal configurations, are depicted in Figure 9, where \(f\) represents the average value of each natural frequency. The figure represents each modal configuration by the front and lateral views. Moreover, the undeformed structure is represented in blue, while the deformed structure is red-coloured. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Subject**} & \multicolumn{2}{c}{**Comfort**} & \multicolumn{2}{c}{**Standard**} \\ \cline{2-5}  & **Resonance** & **Antiresonance** & **Resonance** & **Antiresonance** \\  & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** \\ \hline \multirow{4}{*}{**S1**} & 0.20 & 0.59 & 0.20 & 1.37 \\ \cline{2-5}  & 1.37 & 4.49 & 1.76 & 3.91 \\ \cline{2-5}  & 2.54 & & 2.34 & \\ \cline{2-5}  & 4.88 & & 4.69 & \\ \hline \multirow{4}{*}{**S2**} & 0.20 & 0.39 & 0.20 & 1.17 \\ \cline{2-5}  & 1.56 & 4.69 & 1.76 & 3.52 \\ \cline{2-5}  & 2.54 & & 2.34 & \\ \cline{2-5}  & 4.88 & & 4.30 & \\ \hline \multirow{4}{*}{**S3**} & 0.20 & 0.39 & 0.20 & 0.78 \\ \cline{2-5}  & 1.37 & 4.30 & 1.76 & 4.30 \\ \cline{2-5}  & 2.54 & & 2.73 & \\ \cline{2-5}  & 4.69 & & 4.69 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main resonance and antiresonance frequency values for comfort and standard seats of AP train. Figure 8: EFDD method: average normalised singular values of the spectral density matrices regarding AP comfort seat. As expected, each vibration mode corresponds to a different seat movement. Mode 1 with a frequency equal to 0.20 Hz is related to the vertical foam local movements. Mode 2, with a frequency of 1.37 Hz, is possibly associated with a global movement of the vehicle carbody, which induces a rigid body motion on the seat structure, with a slight foam movement in the vertical and longitudinal directions. This longitudinal component is associated with distorsional movements of the foam layer. Concerning the AP train natural frequencies, [PERSON] et al. [55], based on a forced vibration test of the carbody, estimated the frequency values of the three rigid body modes of the carbody, associated with rolling, bouncing, and pitching movements, ranging between 1.0 Hz and 1.6 Hz, which are in full compliance with Mode 2's physical interpretation. It should be highlighted that the 0.59 Hz antiresonance frequency identified on the transmissibility curve matches the same movements as Mode 2. Mode 3, with a frequency around 3 Hz, is associated with rigid body movements of the seat frame due to the flexibility provided by the connection elements between the seat and the carbody. This modal configuration has similar movements to the ones of Mode 2. Mode 4 demonstrates a seat movement transition. Characterised by this antiresonance frequency, the seat frame presents a quite well-defined bending movement coupled with a torsion movement, as stated by the longitudinal movement of the seat foam. The bending of the seat frame is naturally mobilised by the externally induced vibration and the mass of the passenger (Figure 10). At this frequency value, the foam layer strictly follows the movement of the seat frame without any type of independent vibration, being comparable to the result obtained by [PERSON] [55], 4.23 Hz, conducted in the same environment but on a pre-renovation seat and with a simplified experimental setup.