# Modal Identification of Train Passenger Seats Based on Dynamic Tests and Output-Only Techniques
## 4 Case Study: Intercity Train
### Results
#### 4.2.2 EFDD Method  
The EFDD method was applied using ARteMIS(r) software [56]. Based on the assumption of AP seats, the modal analysis was conducted only for S1. Figure 19 shows the first two curves of the average normalised singular values of the spectral density matrices of the S1 comfort seat experiment, where it is possible to observe the peaks corresponding to the identified frequencies and mode shapes. Figure 16: Experimental setup: (**a**) seat pad location; (**b**) accelerometers on seat frame structure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Subject**} & \multicolumn{3}{c}{**Comfort**} & \multicolumn{3}{c}{**Standard**} \\ \cline{2-5}  & \begin{tabular}{c} **Resonance** \\ **(Hz)** \\ \end{tabular} & \begin{tabular}{c} **Antiresonance** \\ **(Hz)** \\ \end{tabular} & \
\begin{tabular}{c} **Resonance** \\ **(Hz)** \\ \end{tabular} &
\begin{tabular}{c} **Antiresonance** \\ **(Hz)** \\ \end{tabular} \\ \hline \multirow{2}{*}{**S1**} & \multicolumn{2}{c}{0.59} & 1.37 & 0.20 & 0.59 \\ \cline{2-5}  & 4.30 & & 0.78 & 2.54 \\ \cline{2-5}  & \multicolumn{3}{c}{4.88} \\ \hline \multirow{4}{*}{**S2**} & \multicolumn{3}{c}{0.20} & 1.37 & 0.20 & 1.17 \\ \cline{2-5}  & 4.49 & & 1.56 & 2.93 \\ \cline{2-5}  & \multicolumn{3}{c}{4.88} \\ \hline \multirow{2}{*}{**S3**} & \multicolumn{2}{c}{0.20} & 1.95 & 0.20 & 0.59 \\ \cline{2-5}  & 4.69 & & 0.78 & 2.34 \\ \cline{2-5}  & \multicolumn{3}{c}{5.27} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main resonance and antiresonance frequency values for comfort and standard seats of Intercity trains. Figure 17: Transmissibility curves of Intercity train seat: (**a**) comfort seat; (**b**) standard seat. Figure 19: EFDD method: average normalised singular values of the spectral density matrices regarding Intercity comfort seat. Figure 18: Seatback (X-axis)/Floor (Z-axis) transmissibility: (**a**) comfort seat; (**b**) standard seat. The seat movements derived from the vibration modes are represented in Figure 20, where \(f\) represents the average value of the natural frequency. As estimated, each mode corresponds to a different seat movement. Frequencies lower than 0.59 Hz are characterised by vertical and longitudinal foam movements and seatback local bending movements. This frequency matches the one identified as a prominent resonance on the fore-and-aft seatback transmissibility curve. This factor validates the applied methodology and the experimental setup and reveals a strong connection between the transmissibility curve and the modal identification. Mode 1 is deeply connected with foam movements, which represents a dependency on the foam's capacity to absorb vibration. Mode 2 is associated with a global movement of the vehicle carbody. This induces a rigid body movement on the seat frame, coupled with foam distortions in the vertical and longitudinal directions and seatback local bending. Concerning the standard seat experiment, Figure 21 illustrates the first two curves of the average normalised singular values of the spectral density matrices, where it is possible to observe the peaks corresponding to the identified frequencies and mode shapes. Figure 22 illustrates the seat movements derived from the vibration modes, where \(f\) represents the average value of the natural frequency. Figure 21: EFDD method: average normalised singular values of the spectral density matrices regarding Inrectity standard seat. Figure 20: Comfort seat experimental modal parameters, where the front and lateral views are presented. Mode 1 is characterised by the foam's incapacity to absorb low-frequency vibrations (<0.20 Hz), while Mode 2 combines that foam incapacity with seatback local bending movements. Mode 3 demonstrates rigid body movements induced by the carbody, associated with seatback local bending movements and foam vertical and longitudinal motion. As on the other analysed seats, the last mode is defined by a combination of the remaining modes.