Uncertainty quantification of mechanical stiffnesses in a base-shake sine test of a spacecraft

The aim of this thesis is to analyze how unpredictable perturbations on the mechanical stiffness of the components of a shaker assembly could influence the resonance frequency and dynamic characteristics of a satellite in a base-shake sine test. In order to manage stochastic perturbations, we introduced ordinary differential equations with uncertain parameters and then we presented the solving method clarifying their advantages and disadvantages with numerical experiments. This thesis is organized in four main chapters: in the first, we describe the physical system under examination with its geometrical approximations, while in the second chapter we introduce the methods of uncertainty quantification by comparing the results obtained on a benchmark case of aggregation/dispersion of a particle system identified by their speed in space. The use of a case-example like this one is preparatory to understand some choices and hypotheses made through the thesis. The third and fourth chapters present the construction of the mathematical model and its motion equations using a rigorous formalism of Analytical Mechanics. Then numerical results of systems of deterministic parameter equations are presented. Finally, the stochastic methods presented within chapter 2 are applied to the physical system, assuming the stiffness of the oil meatus perturbed by a random variable with an assigned probability distribution.