## 1 Introduction
The excitation force was measured with the force cell mounted between the electro-magnetic shaker and the beam, and the vibrations of the beam were measured with the three accelerometers mounted in its middle and at the two ends. The main structure of the experimental system presented above, namely the 1:6 scale model of the Shinkansen vehicle carbody reduced to an aluminium beam, supported on two air springs, was also used by [PERSON] et al. [65, 66] to investigate the effectiveness of an active carbody vibration control method. This method is based on the combined use of piezoelectric actuators and linear actuators. Linear actuators were used to reduce rigid vibration modes (first and second vibration modes) and piezoelectric actuators to reduce flexible vibration modes (third, fourth, and fifth vibration modes). The method proposed by [PERSON] et al. [67] involves increasing the structural damping of light carbody of high-speed trains using the viscoelastic patches (through Constrained Layer Damping--CLD). The research methodology is based on experimental modal analysis of scaled aluminium beam corresponding to a portion of the floor of a light rail vehicle (see Figure 4) to which different CLDconfigurations were added. To identify the CLD configuration that provided the highest absolute and specific modal damping, several solutions were compared regarding the type of constraint layer (uniform or honeycomb), viscoelastic layer thickness, location, covered area, and continuity between patches. The scale model corresponding to a portion of the floor of the railway vehicle shown in Figure 4 consisted of two webs having a width of 130 mm and a length of 5078 mm. These dimensions were chosen so that the stiffness per unit width of the scale model is the same as that of the railway vehicle floor. Figure 5 shows different types of CLD patches used. Type A represents the beam without CLD, and types B and C were constructed by attaching a rigid aluminium sheet (uniform or honeycomb) to a layer of viscoelastic polymer. The constraint layer used for type B corresponded to an aluminum sheet with a length of 2500 mm, a width of 125 mm and a thickness of 6 mm. For type C, a honeycomb with a thickness of 20 mm was used, made of aluminum foil with a thickness of 0.08 mm, having a hexagonal cell with a size of 6.4 mm. The honeycomb was sandwiched between two aluminum sheets of different  
Figure 3: Scale model of a Shinkansen vehicle [60, 63, 64]. thicknesses, the thicker one being the furthest from the aluminum beam. For types B and C, two different thicknesses were used for the viscoelastic polymer layer, 1 mm, and 2 mm, respectively. Twelve different cases of partial treatment of the aluminium beam with CLD were thus obtained, which were evaluated experimentally. These cases are represented schematically in Figure 6.  
In a research project developed by a team in Japan, an experimental system was built that includes a 1:12 scale model of the Maglev vehicle carbody [68,69]. This experimental system, named MAGMOX (Figure 7), was designed to study different methods of reducing vehicle vibration. The carbody was made of aluminium and thus designed to be flexible enough to be used for bending vibration studies. At each end, the carbody was supported by helical springs on a bogie. Coil springs shaped the vehicle's secondary suspension. The vehicle carbody was specially designed to have the natural frequency of the first vertical bending mode below 50 Hz, which is the maximum vibration frequency that can be generated by the motion base. Two carbodies were built, one with the natural frequency of the first vertical bending mode of 45 Hz and the other with the frequency of 50 Hz. The length (2 m) and width (0.25 m) of both types of carbodies were equivalent to about 1/12 the length and width of a full-scale vehicle. The heights of the two types of carbodies were reduced to 30 mm and 35 mm, respectively, because it was necessary to minimize the second-order cross-sectional moment.