# Railway Substructure Modeling Approach for Modal Analysis Using Multibody Simulation
## 2 Materials and Methods
### Underlying Premise and Main Concept  
Before describing the main concept behind the proposed MS, this subsection presents an important premise permitting the underlying logic that was used in its design, in terms of physical and mechanical principles. The premise in question is: \"The values of the natural frequencies of the soil layers beneath a railway track do not directly depend on the presence of a railway vehicle on said track\". This means that the observable values of the natural frequencies of the soil layers do not directly change due to the presence of a vehicle above those layers, and do not change based on the modal parameters of the vehicle. This statement does not disregard the expected smaller changes in the values of the resonance frequencies from the soil layers due to the dynamic interaction between the two mechanical systems in question (i.e., the railway infrastructure and vehicle). Instead, it just states that there is no direct change in these natural frequencies caused by the presence of a railway vehicle, since the characteristic frequencies of a linear mechanical system are independent from the properties of the excitation source used to assess them [18]. This concept is applicable here as an approximation of this complex multi-element system, for the purpose of modal analysis, in the same way that it is acceptable in the context of analyzing other common engineering structures [20]. This premise has been clearly presented here first, due to its relevance to the topic under study, since this is something that is not commonly stated in the bibliography that deals with the natural frequencies of soil layers in the railway context [4; 19; 21]. In an MBS model, using only rigid-type body elements, there is an inherent detachment between the mechanical properties of a body element and its geometric dimensions. While overall mass can be established using a body's geometry and its density, parameters related with other mechanical properties cannot be directly linked to body elements (e.g., Young's modulus). These other mechanical properties are usually simulated through other element types, such as springs and dampers. In the present context, this means that there is a disconnection between the geometry/mass of a subgrade layer body element and its equivalent stiffness characteristics. Furthermore, this means that the natural frequency values of the simulated subgrade layer are dependent on the combination of the imposed mass of the subgrade body element and the stiffness of the associated spring element, which have no intrinsic relationship. This is in opposition to other modeling software (e.g., FEM model), where the mechanical properties of a subgrade layer can be intrinsically established during model setup. Thus, in an MBS model, the subgrade's mechanical properties are not fully linked to enable an adequate simulation of the subgrade's natural frequencies. Another aspect related to this issue is the difficulty in obtaining realistic values for the modal properties of a soil layer, as opposed to a common steel beam, which hinders the option of simply imposing these values on an MBS model. The proposed MS overcomes these issues by providing a set of theoretical models that result in a fully determined system for the subgrade layer element's geometry to be used in an MBS model. More specifically, by selecting a cylindrical shape for the body elements of the railway's layered elements (e.g., a subgrade layer and a ballast layer) and some input parameters related with their mechanical properties, this MS provides an equation that gives the diameter of these cylindrical elements as a function of subgrade layer height. As previously explained, the proposed MS represents a potential innovation in the specific field of soil layer modeling in the railway context, which is denoted by both the combined model and the geometry shape choice, since the authors did not find any similar solution in the consulted bibliography.