Fuzzy Boundary for Beams Vibrations in Vehicles

Abstract

The aim of this work is to study the transversal motion of a car's chassis, modeled by a beam and supported at its ends by two set of spring-damper element. We use a finite differences method with Robin boundary conditions at the ends to solve the mathematical modeling. The boundary conditions constants are modeled by a fuzzy parameter, which is obtained through Fuzzy Rule-Based System (FRBS) acting on the different vibrations of the model depending on the number of spirals and time of use of the spring. The contributions in this study come in the sense of considering the elastic constant of the spring as a relevant instrument acting in the system, because the analytical formula to perform these calculations does not take into consideration the time of use of it. Indeed, the mechanical components of the vehicle might have their properties altered due to fatigue process, for example. The impacts of the property evolution in the car dynamics might induce undesirable passenger's discomfort up to the vehicle performance lost. The results showed that the time of use of the spring influences the displacement of the vehicle, due to the loss of stiffness, thus affecting its stability.