**5. Transmissibility**

Passengers spend most of their time seated; thus, vibration is transmitted to the user due to the contact with the seat and floor. This way, the seat is essential to reduce vibration transmission and increase passengers' comfort. The seat and human body's dynamic responses affect seat vibration transmission as they constitute a coupled dynamic system [10, 11, 33, 35, 37, 56]. Therefore, seat dynamics are quantified regarding transmissibility, which verifies seat efficiency in vibration discomfort and is an indicator of ride comfort. The seat transmissibility presents the ratio of vibration at the user-seat interface and the floor, according to Eq. (5):

$$H(f) = \frac{G\_\bullet(f)}{G\_i(f)}\tag{5}$$

where *H*(*f*) represents the transmissibility, *G*o(f) is the output acceleration at the seat-user interface, and *G*i(f) represents the input acceleration at the floor [57].

Transmissibility differs in direction (vertical, fore-and-aft, and lateral) and location (seat surface and seatback). Laboratory experiments demonstrated a vertical transmissibility peak between 4 and 6 Hz when sitting upright with backrest support [57–60]. However, these studies did not implement transmissibility tests on train seats. Instead, they considered a rigid seat frame with distinct characteristics of the standard train seat, such as frame dimensions and support points. Moreover, in opposition to the natural rail environment, the experimented seats are individual instead of double, and the foam is placed on top of the surface without a restricting cover [57–60]. These are essential parameters because seat transmissibility is affected by the physical properties of the foam, such as thickness, density, or yield strength [59]. Doubling the foam thickness roughly halves its stiffness; thus, transmissibility and discomfort also increase. Patelli and Griffin [57] conducted a study where foam thickness's effect on transmissibility was observed. When the thickness increased from 40 to 80 mm, the transmissibility reduced from 4 to 7 Hz to 3–5 Hz, respectively, with maximum frequencies of 3–4 Hz for the 40 mm foam and 2–3 Hz for the 80 mm foam. In this study, the individuals did not have contact with the backrest [58]. Zhang et al. [61] also reported a similar tendency and observed higher transmissibility when the seat pan foam was increased from 60, 80, and 100 mm.

The stomach has a resonance frequency between 2 and 20 Hz; thus, passengers may feel sick if the seat transmits vibration within that range.

Ribeiro [62] performed transmissibility tests on Alfa Pendular trains in 2012 before the train renovation using the same method as the one used in this study. Transmissibility peaks around 4.3 Hz were found. At that time, seats were covered by tissue without seams instead of the leather covers with seams now used [54]. Moreover, Ribeiro numerically identified the rigid body frequencies of the carbody and bogie. The former reported frequencies under 1.42 Hz, whilst frequencies between 4 and 12 Hz characterize the latter [62].

To properly quantify the dynamic performance of the Pendolino seats, transmissibility tests were conducted on its two-seat classes, namely, comfort and touristic. **Figure 2** illustrates both seat types. The main difference regarding those seats is their dimensions, especially the seat surface thickness. The comfort class seat has a thickness of 190 mm, whereas the touristic class has a thickness of 130 mm. Moreover, the

**Figure 2.** *Pendolino seats: (a) comfort seat, (b) touristic seat.*


**Table 9.** *Subjects' characteristics.*

2017 renovation introduced significant changes to seat covers and foams. All foams were replaced with new ones, and a leather cover with seams was introduced [54].

A set of dedicated experimental tests were accomplished. According to **Table 9**, four volunteers (two males and two females), aged between 9 and 39, weighing 33–115 kg and 1.33–1.87 m in height, participated in the study. The subjects sat in a normal posture, placed both hands on their thighs, and made complete contact with the seatback.

Two seats, one of each class, were instrumented. Seats had the same exact location in the vehicle, particularly near the bogie. Acceleration at the seat surface was measured using a three-axial seat pad accelerometer (PCB 356B41). Uniaxial accelerometers (PCB 393A03) were placed on the floor (1 unit) and the metallic support frame (4 units) for measuring the acceleration at the seat frame. Accelerometers were positioned as shown in **Figure 3**.

The data acquisition system was composed of a NI cDAQ-9172 with NI 9234 IEPE modules connected to a PC to acquire and record data measurements. The vibration was induced by a group of people randomly walking and jumping nearby the seat. A time series of 3 minutes with a sampling frequency of 2048 Hz, posteriorly decimated at 100 Hz, was saved. Data processing was performed using MATLAB scripts previously validated.

**Figure 3.** *Accelerometer positioning: (a) seat frame and floor accelerometers, (b) seat surface pad.*
