## 2 Methods and the Data  
The dynamic load on the bearing structure of an open car at operational load modes can be reduced through some improvements. One of them is the application of elastic, viscous honeycomb panels between the vertical sheets of the intermediate, end, and bolster beams; the intermediate beams are made of a boxed section (Figures 2 and 3). The proposed solution was substantiated in this study into the dynamic load of the bearing structure of a rail car at operational modes operating on main lines. This study also deals with the determination of the dynamic load of a car transported via a train ferry. The calculation included the common load diagrams for the bearing structure of a car transported via a train ferry:  
* Angular displacements around the longitudinal axle \(X\) at the angle \(\theta\) (rolling motion) (Figure 4). At the same time, it was taken into account that the car was symmetrically fixed on the deck with eight ties (four on each side). The ship's centre of gravity was at the centre of its displacement (\(YZ\) coordinate system). The \(Y^{\prime}Z^{\prime}\) coordinate system was portable. Under the action of a perturbing influence Pc on the car with a certain height \(h_{c}\), it was displaced at angle \(\theta\). * The turning motion of the train ferry loaded with cars while approaching the dock. Figure 4: Diagram of movements of the open car body during oscillations of the train ferry. Figure 3: Improved frame of an open car. Figure 2: Section of the cross bearer of an open car frame: (**a**) standard structure; (**b**) improved structure. The dynamic loads on the bearing structure of a car transported via a train ferry were determined with a mathematical model developed by the authors of the article; it characterizes the angular displacement of a train ferry loaded with cars during rolling [10,15]. \[ \begin{array}{l}\frac{D}{12\cdot g}\cdot\left(B^{2}+4\cdot z_{g}^{2}\right) \cdot\ddot{q}_{1}+\\ \quad l_{\theta}\cdot\ddot{q}_{2}+c\cdot\frac{b}{2}\cdot q_{2}+\beta\cdot\frac {b}{2}\cdot\dot{q}_{2}=p_{k}\cdot\frac{b_{k}}{2}+F_{\theta}\end{array}  \tag{1}\]  
where \(q_{1}\) and \(q_{2}\) are the generalized coordinates corresponding to the angular displacement of the train ferry and the bearing structure of a car around the longitudinal axle, respectively, \(D\) is the ship displacement; \(B\) is the breadth of the train ferry; \(z_{g}\) is the coordinate of the centre of gravity of the train ferry; \(\Lambda_{\theta}\) is the coefficient of resistance to the oscillations of the train ferry; \(p^{\prime}\) is the static motion of the wind relative to the upper projection of the train ferry loaded with cars; \(h\) is the hull height; \(F(t)\) is the force to the train ferry loaded with rail cars on the decks; \(\beta\) is the coefficient of viscous resistance of a honeycomb panel; \(c\) is the stiffness of a honeycomb panel; \(b\) is the width of the bearing structure of a car; \(p_{c}\) is the wind pressure to the bearing structure of a car; \(h_{c}\) is the height of the bearing structure of a car; and \(F_{\theta}\) is the moment of the forces acting between the bearing structure and the deck. The disturbing effect takes the form of a trochoidal law of motion of a sea wave, which has the following form [15]:  
\[F(t)=a+R\cdot\varepsilon^{k\cdot b}\cdot\sin(k\cdot a+\omega\cdot t)+b-R\cdot \varepsilon^{k\cdot b}\cdot\cos(k\cdot a+\omega\cdot t) \tag{2}\]  
where \(a\) and \(b\) are the horizontal and vertical coordinates of the centre of the trajectory along which the particle rotates, which here have the coordinates \(x\) and \(z\), respectively; \(R\) is the radius of the trajectory along which the particle moves, m; \(\omega\) is the frequency of the sea wave; and \(k\) is the frequency of the trajectory of the disturbing effect. Significantly, the mathematical model built by the authors of this article can be used to determine the dynamic loads acting on the car transported via various train ferries and water zones where they operate.