## 2 Materials and Methods  
In the course of this research, the modal analysis of the frame bodies was considered. The first copy was made of gray cast iron, and the second one was made of polymer concrete with topological optimization of the machine geometry. Figure 1 shows an isometric view of the part in question. This machine bed body made by Koluszki Foundry and Machinery (Koluszki, Poland) CU300 with dimensions of \(300\) mm \(\times\)\(300\) mm \(\times\)\(2000\) mm is made of gray cast iron. Casting technology imposes design limitations, consisting in the design of a cast element with the most uniform thickness of walls and ribs. The use of different thicknesses and variable cross sections of elements can lead to the occurrence of adverse effects during the casting or cooling of the casting, such as, for example, shrinkage cavities [13]. This is a significant technological limitation leading to the need to adapt the shape of the structural element to the requirements of the casting process [14]. Therefore, to increase the statistical and dynamic rigidity of the machine bed, it was proposed to use a special structure made of polymer concrete. The use of polymer concrete as a material for the machine bed is aimed at improving the dynamic properties [15] since the most favorable changes can be expected as a result of the use of a material with a better damping factor, the vibrations of which are much higher than that of cast iron. These properties also change in a positive direction as a result of an increase in the mass of the foundation bed. To answer the question of the extent to which the use of polymer concrete will affect the change in the dynamic properties of the foundation bed, studies was conducted on the basis of selected 3D models of machine bodies. The studies were carried out using the analytical module Autodesk Inventor, the application of which is based on the finite element method [16; 17; 18]. In the course of the research, a theoretical analysis was carried out for the first twenty different forms of vibrations (F1 \(\div\) F20) and the natural frequencies of the foundation bed. The mechanical properties of both samples used in the analysis of materials are presented in Table 1[19]. Figure 1: Isometric view of the frame. A very important aspect in the analysis was the adequate imposition of boundary conditions [21]. One of them was the deprivation of degrees of freedom (fixing the body of the foundation bed). The housing on the left and right has mounting holes (marked in red) with which it is bolted, and it was on these holes that fixed bonds were imposed in accordance with Figure 2, which deprived all degrees of freedom of the body relative to the substrate, both for the cast-iron body and for the body made of polymer concrete. Another very important aspect in conducting this research was to correctly set up the finite element mesh [22]. Smaller grid parameters lead to a larger number of nodes and elements, and a larger number of elements would lead to distortion of the obtained data. Thus, the optimal number of elements was chosen, while the generation time was longer, but the results obtained by mesh compaction turned out to be more accurate. When creating the computational model of the curbs, the standard procedure of generating a finite element mesh with increased density was used without losing the geometric shape of the analyzed structure. During the discretization process, second-order three-dimensional pyramidal elements were used. For a more accurate and valid distribution of internal stresses on the rails and the pedestal under the action of external forces, it is necessary to pay due attention to the quality of the superimposed finite element network. The density of the network in these parts is increased by 50% in relation to the main structure. Figures 3 and 4 show a finite element grid applied to cast iron and polymer concrete structures. The cast iron body was divided into 407,740 nodes and 231,853 elements, and the polymer concrete body--into 475,499 nodes and 277,603 elements.