Simplified mathematical model for frontal impact study

The structure of the front compartment is built to provide safety to passengers during an impact. Safety is ensured by designing structures capable of taking up much of the impact energy. During an impact, the energy of the impact is consumed by the ability of the body structure to deform. Thus, a large part of the kinetic energy of the impact is transformed into deformation energy. It ensures that decelerations are reduced in a short period of time to the limit that passengers can bear. Two mathematical models are proposed for the study of the frontal impact between two vehicles. In the mathematical model the component elements of the frontal compartmental structures are treated separately. Two simplified numerical models with two degrees of freedom are proposed. The first mathematical model is of the table-spring type, and the second is the mathematical model of the table-spring-shock absorber type. The body elements and the main subassemblies of the vehicle are considered to be two concentrated table bodies. The connection between these bodies will be made by elastic elements and damping elements. Based on Lagrange's generalized equations, the equations of motion necessary for the impact study will be obtained. Furthermore, the solving of the numerical systems of the proposed models will be done with the help of the modelling, simulation and analysis environment offered by the MATLAB Simulink software. In this environment, the main initial parameters and impact conditions between the two bodies will be established and block schemes will be built for both systems of equations. With the help of these mathematical models it is desired to determine the maximum deformation recorded by each vehicle during the frontal impact between the two.