### Dynamic Analysis of Models for Suspension Systems of Ground Vehicles with Uncertain Parameters

Claudio Gatti, Marcelo T. Piovan

#### Abstract

Land transportation vehicles have suspension systems to limit the vibrations caused by the movement. The main function of these systems is to maintain the welfare of people (in vehicles or cars) or the integrity and functionality of installed equipment (in robotic platforms). Suspension systems are constituted by damping and elastic components whose properties may have a wide variation due to the geometrical configuration, manufacturing process and assembly protocols. This entails that the dynamic response of the system is not the expected one, which implies a degree of uncertainty although the properties of the components appear to be correctly specified. In this context it is important to characterize the propagation of uncertainty of the response of the system, caused by the uncertainty of its mechanical
components: dampers, dash-pots, springs, anti-roll bars, etc. In this paper, the stochastic dynamic response of a suspension platform is analyzed. The mathematical model of the platform, characterized by 7 degrees of freedom, is derived by means of newtonian dynamics of rigid bodies. This mathematical
model is deterministic and it is adopted as the mean model for the further stochastic studies. The parameters of the system: mass, springs and dampers are considered uncertain. Second order random variables are defined for every uncertain parameter involved. The probability density functions of the random variables are derived using the Maximum Entropy Principle. Once the probabilistic model is constructed, the Monte Carlo method is employed to perform the statistical simulations. Numerical studies are carried out to show the main advantages of the modeling strategies employed, as well as to quantify the propagation of the uncertainty in the dynamics of suspension systems.

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