Stochastic analysis of a cracked rod modeled via the spectral element method

The spectral element method is used to model a cracked rod, where the crack is modeled as a localized flexibility. The crack flexibility is derived using Castigliano’s theorem, and the uncertainties are modeled by the parametric probabilistic approach. The probabilistic model is constructed directly for the variable of interest, i.e., the crack flexibility. Two different probabilistic models, where the probability density functions are constructed using the Maximum Entropy Principle, are used and compared. It is shown that the model with more uncertainty is the one constructed with less information. Monte Carlo simulations are performed in order to estimate the frequency response function envelopes.