## 1 Introduction
### Results of the Numerical Simulations  
In this section, 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 vibration of the experimental model of the carbody is analysed. The numerical simulation parameters of the experimental model of the carbody without anti-bending bars are those presented in Table 2. The following loss factors are also considered: \(\eta_{zc}=0.12\)--for elastic rubber elements and \(\eta_{c}=\eta_{b}=0.01\)--for the experimental model of the carbody and anti-bending bars. Figure 17 shows the component of the frequency response function of the acceleration of the experimental model of the carbody corresponding to the vertical bending, highlighted in Equation (55) as \(\overline{H}_{cT_{c}}\), calculated in the middle of the experimental model of the carbody (diagram a) and above the elastic supports (diagram b). The results were obtained for anti-bending bars of length 900 mm, positioned at \(h_{b}=40\) mm from the neutral axis of the experimental model of the carbody, and four diameter values, namely 5 mm, 6 mm, 7 mm and 8 mm. To verify the effectiveness of the anti-bending bars, the acceleration response function component of the experimental model of the carbody without anti-bending bars was also represented on the diagrams, calculated with the relation  
\[\overline{H}_{cT_{c}}(x,\omega)=\omega^{2}X_{c}(x)\frac{(\omega^{2}M_{c}-4 \overline{k}_{zc})\xi+4\overline{k}_{zc}\varepsilon}{(-\omega^{2}M_{c}+4 \overline{k}_{zc})(-\omega^{2}M_{mc}+\overline{k}_{mc}+4\overline{k}_{zc} \varepsilon^{2})-16\overline{k}_{zc}^{2}\varepsilon^{2}}. \tag{57}\]  
It was noted the increase in the resonance frequency of the vertical bending of the experimental model of the carbody when the diameter of the anti-bending bars increased, results that are consistent with the observations are presented in Figure 16.  
The increase in the resonance frequency of the vertical bending of the experimental model of the carbody was the result of the stiffening of the system because of the increase in the rigidity of the anti-bending bars when their diameter increased. The effectiveness of the anti-bending bars in reducing the vertical bending vibrations of the experimental model of the carbody was highlighted both in the middle of the experimental model of the carbody and above the elastic supports. By introducing the anti-bending bars, a significant reduction in the peaks of the response function of the acceleration corresponding to the vertical bending was obtained at the vertical bending frequency of the experimental model of the carbody. The reduction became more important as the diameter of the anti-bending bars increased. For example, for bars with a diameter of 5 mm, the reduction in the peak of the response function was 47% and reached 79% for bars with a diameter of 8 mm. Figure 17: Component of the acceleration response function of the experimental model of the carbody corresponding to the vertical bending: (**a**) at middle; (**b**) above elastic supports. It should be noted that the vertical bending vibration were more pronounced in the middle of the experimental model of the carbody than above the elastic supports. For example, for the experimental model of the carbody without anti-bending bars, at the resonance frequency of 7.90 Hz, the response function \(\overline{H}_{cT_{c}}\) had the value of 1.817 (m/s\({}^{2}\))/N in the middle of the experimental model, which was about 60% higher than above elastic supports where the value is 1.137 (m/s\({}^{2}\))/N.