## 2 Methodology
Figure 2 presents the oscillograms of the forces, \(S\) (Figure 2a) and \(S_{B}\) (Figure 2b); rail deflection, \(\omega_{p}\) (Figure 2c); and bending moment, \(M_{P}\) (Figure 2d), at the section \(x=1.5\) m, as well as \(\omega_{p1}\) (Figure 2e) and \(M_{P1}\) (Figure 2f) at a speed of \(C=140\) km/h. In this figure and all subsequent ones, solid lines represent graphs considering the influence of adjacent wheelsets, while dashed lines depict results without considering this influence. The graphs indicate that the effect of adjacent wheelsets on the \(S\) forces in the suspension system is insignificant. However, adjacent wheelsets exert a somewhat greater influence (around 10%) on the interaction forces, \(S_{B}\), and bending moments, \(M_{P}\) and \(M_{P1}\), and an even more significant effect on the amplitude values of rail deflections, \(\omega_{p}\) and \(\omega_{p1}\) (up to 20%). Similar conclusions were obtained from the analysis of oscillograms of wheelset accelerations and displacements; rail deflections, \(\omega_{p}\); and bending moments, \(M_{P}\), at other rail sections. Figure 2: Oscillograms of \(S\) forces and bending moment, \(M_{P}\). At lower vehicle speeds, the influence of adjacent wheelsets decreases. However, under different railcar parameters, this influence may be more significant. Figure 3 presents graphs showing the dependence of the maximum values of forces \(S\) and \(S_{B}\) on the vehicle speed. The results indicate that the influence of adjacent wheelsets on the forces and displacements occurring at speeds up to 140 km/h is insignificant and can be neglected. It is important to note that this study considers only perturbations (11) with spectral components containing frequencies up to 20 Hz. This conclusion is obtained at the specified parameters of the rails and the base. Figure 4 shows the graphs of the dependence of the maximum values of the forces \(S\) and \(S_{B}\). at \(C=140\) km/h from some parameters: base elastic modulus, \(u_{1}\) (Figure 4a), the reduced linear mass of the rails; and the base, \(m_{w}\) (Figure 4b). Vertical lines on these graphs indicate the values corresponding to the initial parameters. As seen from the graphs, the influence of the considered parameters on the forces \(S\) and \(S_{B}\) is insignificant. The effect of adjacent wheelsets can be neglected across the entire range of parameter variations at the given speed and railcar characteristics. Thus, the results of this study on the oscillations of a four-axle freight wagon moving along a beam resting on a continuous inertial viscoelastic foundation and on discrete inertial viscoelastic \"supports\" indicate that the forces acting on the wagon, rail deflections, and bending moments are similar in both cases at speeds up to 140 km/h. Furthermore, the forces arising in the central suspension system remain comparable even at speeds up to 180 km/h. This can be seen from the results of the calculations performed Table 1. This conclusion is supported by Table 2, which presents the values of forces \(S\) and \(S_{B}\) for the continuum model, considering (first row) and disregarding (second row) the influence of adjacent wheelsets. Figure 3: Graphs of the dependence of the maximum values of forces \(S\) and \(S_{B}\) on vehicle speed. The numerator represents the forces during unloading, while the denominator corresponds to the forces during overloading. The results presented in Table 2 were obtained for an irregularity depth of \(d=5\) mm. All other rows in Table 2 show the force values determined from solving the problem of wagon oscillations, considering the track as a system with lumped parameters. Let us represent the rail as a system with lumped parameters and consider it an oscillatory element, where the input is a stationary vertical force, \(P_{(t)}=P_{0}e^{i\omega t}\), applied at section \(x=0\), and the output is the deflection at an arbitrary section, \(\mathbf{x}\). Figure 4: (**a**) Graph of the maximum values of forces S and \(S_{B}\) versus the track modulus of elasticity.