Timoshenko Beam with Uncertainty on the Boundary Conditions

In mechanical system modeling, uncertainties are present and, to improve the predictability of the models, they should be taken into account. This work discusses uncertainties present in boundary conditions using the model of a vibrating Timoshenko beam, free in one end and pinned with rotation constrained by a linear elastic torsional spring in the other end. The Finite Element Method is used to discretize the system and two probabilistic approaches are considered to model the uncertainties: (1) the stiffness of the torsional spring is taken as uncertain and a random variable is associated to it (parametric probabilistic approach); (2) the whole stiffness matrix is considered as uncertain and a probabilistic model is constructed for the associated random matrix (nonparametric probabilistic approach). In both approaches, the probability density functions are deduced from the Maximum Entropy Principle. In the first approach only the uncertainty of a parameter is taken into account, and in the second approach, the uncertainties of the model are taken into account, globally. Both approaches are compared and their capability to improve the predictability of the system response is discussed.