ABSTRACT This work aims to study the transversal motion of a car’s chassis, modeled by a beam and supported at its ends by two sets of spring-damper elements. A finite differences method is utilized along with Robin boundary conditions to solve the mathematical modeling. The constants of the boundary conditions are modeled by a fuzzy parameter obtained through a 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 of this study is based on considering the spring’s elastic constant as a relevant instrument acting in the system, due to the fact that analytic formula to perform these calculations, does not consider the time of use. Indeed, the vehicle’s mechanical components might have their properties altered due to the fatigue process, for example. The impacts of the car dynamics’s property evolution might induce undesirable passenger’s discomfort up to the vehicle performance loss. The results showed that the time of use of the spring influences the vehicle’s displacement due to the loss of stiffness, thus affecting its stability.

ABSTRACT Treatment with antiviral drugs for human immunodeficiency virus type 1 (HIV-1) infection causes a rapid reduction in plasma viral load. Viral decline occurs in several stages and provides information on important kinetic constants of virus replication in vivo and pharmacodynamic properties. We present a mathematical model that not only considers the intracellular phase of the viral life cycle, defined as the time between the infection of a cell and the production of new viral particles, but we also consider that this parameter together with the virus decay are interactive fuzzy numbers.