## 1 Introduction
The carbody was modelled as a Euler-Bernoulli beam, while lumped parameter models were used for the bogie chassis, wheelsets and suspension elements. The anti-bending bars were modelled as ideal elastic elements, neglecting their bending effect. Figure 2 shows an example regarding the change in the dynamic behaviour of the carbody when fitted with an anti-bending bar system; the calculated speed was 270 km/h. First, the figure graphs show the acceleration power spectral density (acceleration is weighted accordingly _Guidelines for Evaluating Passenger Comfort In Relation to Vibration in Railway Vehicles_ to reflect the sensitivity of the human being to vertical vibrations [23]) for the carbody variant without anti-bending bar system (red line) at the carbody centre (Figure 2a), above the front bogie (Figure 2b) and above the rear bogie (Figure 2c). The carbody centre without anti-bending bars exhibits an absolute maximum at 8 Hz in the acceleration power spectral density corresponding to the bending frequency. This peak is larger than the one due to the carbody bounce located at approx. 1.17 Hz. Above the bogies, a peak at 1.4 Hz due to the pitch motion is added next to the bounce peak and surpasses the bending peak. The vibration behaviour of the carbody with the anti-bending bar system changes radically in terms of the importance of the carbody bending vibration as shown by the three variants depicted in Figure 2. The anti-bending bar system is sized so that the bending frequency of carbody reaches 10 Hz (blue line), 12 Hz (green line) and 14 Hz (yellow line). The effect of the anti-bending bar system is to increase the bending frequency of the carbody and reduce the acceleration in the frequency range corresponding to its bending, thus contributing to the improvement of ride comfort, especially in the middle of the carbody. The method of reducing vertical vibrations with the help of the anti-bending bar system is advantageous due to the simplicity of the construction whose manufacturing, assembly and maintenance costs are reduced. From the point of view of an anti-bending bar system design, the parameters of the anti-bending bars are calculated by starting from the bending natural frequency of the vehicle carbody and forcing it to reach a convenient value above 12 Hz so that the ride comfort in vertical vibrations is assured. To demonstrate the feasibility of the new concept of reducing the vibration of the carbody of the railway vehicles using an anti-bending bar system, an original dedicated experimental scale demonstrator system was proposed in ref. [24]. Figure 3 shows the diagram of the experimental scale demonstrator system for the carbody with anti-bending bar system, which consists of the scale model of the vehicle carbody, which is placed on four elastic rubber elements (suspension elements); rubber is a material often used in the suspension of railway vehicles [25; 26]. Figure 2: Influence of the anti-bending bar system in terms of PSD of the carbody acceleration at 270 km/h: (**a**) at the carbody centre; (**b**) above the front bogie; and (**c**) above the rear bogie [17]. The scale model of the carbody is an aluminium plate sized so that the first bending eigenfrequency of the beam-spring assembly is in the typical range where the natural bending frequency of the carbody on the vehicle suspension is usually found. The anti-bending bar system is mounted under the aluminium beam on its sides. In paper [24], a discrete-continuous-type model like that used in ref. [17] was presented and utilised to evaluate the influence of the anti-bending bar system on the frequency response function of the reduced scale model of the vehicle carbody. The use of scale models of the railway vehicle carbody to experiment in laboratory conditions with different vibration reduction methods is widely used due to the advantages of these models over 1:1 scale model, the most important of which is related to the cost of manufacturing and equipping for tests.