# Modal Identification of Train Passenger Seats Based on Dynamic Tests and Output-Only Techniques
## 1 Introduction
The biodynamic response of the human body is cross-axis-coupled, i.e., inducing vibration in one axis may lead to a response in another axis. Significant body movements in the fore-and-aft direction are produced during vertical excitation. This way, seat transmissibility is cross-axis-coupled. Additionally, the influence of subjects' physical characteristics, such as weight, on the resonance frequency and seat transmissibility has been evaluated by several authors. Multiple studies developed using subjects with varying mass ranges reported unaffected results. Increasing the loading on the seat surface (by the subject's weight) tends to increase the foam's dynamic stiffness. This foam behaviour explains the absence of the subject's weight's effect on seat transmissibility [29; 30; 31; 32]. Transmissibility differs in direction, particularly in the vertical, fore-and-aft, and lateral directions, and location, namely the seat surface and seatback. Several laboratory experiments have demonstrated a vertical transmissibility peak at 4-6 Hz when sitting upright with seatback support [23; 33; 34]. However, these experiments did not implement transmissibility tests in traditional train seats. Instead, a single rigid seat frame with distinct characteristics from the ones of a current train seat, such as frame dimensions and support points, was considered. In addition, the foam was freely placed on top of the seat surface without any restricting cover [23; 33; 34; 32]. The constraint conditions of the foam are crucial to correctly address the influence of the foam thickness variation on the transmissibility of the seat, particularly on the evaluation of its dynamic stiffness [34]. Regarding seat cushion properties, changing foam thickness has generally been found to have the most prominent and predictable effects on seat transmissibility. Doubling the foam thickness roughly halves its stiffness, leading to increased transmissibility and discomfort. [PERSON] and [PERSON] [23] conducted a study to observe the effect of foam thickness on seat transmissibility. Increasing the thickness from 40 to 80 mm reduced the transmissibility from the range of 4-7 Hz to 3-5 Hz, respectively. Resonance frequencies were found equal to 3-4 Hz, for 40 mm foam, decreasing to 2-3 Hz for 80 mm foam. The experimented individuals did not have contact with the backrest [25]. A similar tendency was reportedby [PERSON] et al. [35] where a higher transmissibility resonance was observed when the seat surface foam increased from 60 mm to 80 mm, and posteriorly to 100 mm. In turn, changing the foam hardness (composition and density) does not present any significant effect on seat transmissibility. Due to hysteresis loss, density affects the static comfort instead of the seat transmissibility. [PERSON] and [PERSON] [13] examined seat transmissibility by considering four foam cushions with equal dimensions but varying densities (from 45 to 65 kg/m\({}^{3}\)). Seat transmissibility did not present significative differences, contrary to what was observed with the subjects' comfort judgments. Therefore, those judgment differences were related to the static seat comfort [13]. Based on the limitations of the previous experiments, this study aims to give clear contributions about some aspects that presently, according to the authors' knowledge, are not sufficiently addressed in the existing literature, particularly:  
* Development of an experimental test setup on a real train environment. This way, the influence of the flexible seat base, instead of the currently rigid base used in laboratory experiments, as well as the influence of the carbody/bogies resonance movements, are considered on the seat dynamic performance. In addition, this dedicated experimental setup can clearly distinguish the seat frame's structural movements from the foam's local vibrations. * Accurate characterisation of modal parameters of the seat structural frame and surface foam for different types of seats belonging to Alfa Pendular and Intercity trains, including standard and comfort seats.