## 1 Introduction
Additionally, the proposed method has the advantage that it involves the use of a simple mechanical system, which does not require high manufacturing, implementation, and maintenance costs. The main element of the demonstrative experimental system is the scale model of the vehicle carbody, reduced to a beam, on which the anti-bending bars are mounted. For the vibration study of the experimental model of the vehicle carbody, it is represented by an original theoretical model developed based on the Euler-Bernoulli beam theory. This theory is widely used in the railway field to model the vehicle carbody [13; 29; 37], wheelset [75], or rail [76; 77]. To determine the dimensions of the experimental model of the carbody, the dimensions of the real carbody of a passenger vehicle are taken as a starting point and the following original criteria are introduced: the convenient adoption of the scaling factor of the dimensions of the real carbody from the point of view of the practical realization of the experimental model of the carbody, ensuring the buckling stability of the demonstrative experimental system, achieving the natural frequency of the vertical bending of the real carbody, and avoiding the interference of the bounce vibration with the vertical bending vibration of the experimental model of the carbody. As shown above, achieving a vertical bending frequency of the experimental model of the carbody with anti-bending bars, convenient from the point of view of ride comfort, is the main condition underlying the dimensioning of the anti-bending bars. Added to this is the condition that the vertical bending vibration of the anti-bending bar do not interfere with the vertical bending vibrations of the experimental model of the carbody. At the end of Section 3, the results of the numerical simulations on the frequency response function of the acceleration of the experimental model of the carbody without/with anti-bending bars are presented. Based on these results, the effectiveness of the anti-bending bars in reducing the vertical bending vibrations of the experimental model of the carbody is analysed for different constructive dimensions of the anti-bending bars. The theoretical results presented show that there are premises for the next stage of the research, namely the experimental verification of the functionality of the method of reducing vertical bending vibrations of the railway vehicle carbody with the help of the anti-bending bar system, using the experimental model of the carbody integrated in the special demonstrative experimental system conceived. The original elements of the paper can be found in Section 3 and consist mainly of: the conception of a new demonstrative experimental system dedicated to testing in the laboratory the effectiveness of the method of reducing vertical bending vibrations of the carbody of railway vehicles with the help of the system consisting of two anti-bending bars; development of the theoretical model of the experimental model of the carbody with anti-bending bars; development of methodologies for dimensioning the experimental model of the carbody and the anti-bending bars; analysis of the effectiveness of the anti-bending bars in reducing the vertical bending vibrations of the experimental carbodymodel and increasing the resonance frequency of the vertical bending vibrations based on numerical simulations. Applications of Scale Models in Experimental Research on the Reducing of Vertical Vibrations of the Railway Vehicle Carbody  
In the last 20 years, several methods have been developed to reduce the vertical vibration of the carbody of the railway vehicles with impact on ride comfort. Exploring the specialized literature on this topic, we identified several experimental studies carried out on scale models that confirmed the effectiveness of some passive or active methods of damping the vibrations of the railway vehicle carbody or have validated solutions to optimize the constructive elements of the vehicle that lead to the minimization of the flexible vibrations of the carbody.