## 1 Introduction
A series of studies belong to teams of Japanese researchers, whose research focused both on the possibilities of passively reducing the vibration of the railway vehicle carbody using piezoelectric elements [60; 61; 62; 63; 64] or stack type piezoelectric transducers [65], or on the active control of the vibrations of the railway vehicle carbody with piezoelectric actuators [66]. A recent study by a team of researchers from Spain aims to experimentally analyse a passive method for increasing the structural damping of light carbody of high-speed trains to improve ride comfort [67]. Other works contain detailed descriptions of experimental systems specially designed to be used in the investigation of methods of reducing structural vibrations of the railway vehicle carbody [68; 69; 70; 71; 72; 73]. The longitudinal interaction between carbody and bogie through the traction rod can influence the bending vibrations of the vehicle carbody, an aspect studied in the research focused on the effect of the flexural and twisting modes on the ride quality index of the high-speed Shinkansen railway vehicle carbody. In this context, a scale model of the vehicle was constructed to validate the numerical results [74]. In the following, a general description of these experimental systems is presented, which include scale models of the railway vehicle carbody. [PERSON] et al. used piezoelectric elements in a passive method to improve ride comfort by reducing vertical bending vibrations of the railway vehicle carbody [60; 61; 62; 63; 64]. The principle of the method is based on the property of piezoelectric elements to transform the mechanical energy of vibrations into electrical energy, which was then dissipated in a shunt circuit. Two types of shunt circuits were investigated, both designed to be used in conditions of high amplitude vibrations. For the damping of a single mode of vibration, the shunt circuit consisted of an inductor and a resistor in series, tuned for a single frequency (single-mode shunt circuit). To reduce two modes of vibration, the resistor and inductor connected in series were connected in parallel with a capacitor in series with another resistor and inductor, thus obtaining two electrical resonances (two-mode shunt circuit). The piezoelectric elements were attached to the side beams (four on each beam) of a 1:5 scale model of the carbody of a Shinkansen vehicle (Figure 3). This model had the length of 4.9 m, the width of 0.67 m, the height of 0.6 m, and the mass of 292 kg. The scale model of the carbody rested on air springs at four points corresponding to the suspension positions of a real vehicle. An electrodynamic shaker was used to generate vertical vibrations, which was mounted at one end of the scale model of the carbody. The excitation force was measured with a load cell mounted between the rod of the electrodynamic shaker and the the scale model of the carbody. To measure the vibrations of the scale model of the carbody, accelerometers were mounted on its surface. [PERSON] et al. have proposed new control method of the vibrations of the railway vehicle carbody through damping shunts, based on stack-type piezoelectric devices [65]. For this purpose, two types of shunt circuits were analysed, respectively, an LR-LRC shunt circuit and a negative capacitance shunt circuit. Effectiveness and robustness of the shunt damping systems were investigated experimentally with a 1:6 scale model of the carbody a Shinkansen vehicle. The carbody was reduced to a beam made of aluminium, having the natural frequencies of the first five modes of vibration very close to those of the carbody of the Shinkansen vehicle. The beam had a length of 4 m and a rectangular section with the width of 0.55 m and the height of 0.025 m. The mass of the beam was 150.15 kg. The beam was supported by two air springs and is excited with the help of an electro-magnetic shaker positioned at one end of it.