Dynamic analysis of structures subjected to parametric and nonparametric uncertainties

The variations in the dynamic behavior of structures can be modeled by finite elements with the inclusion of uncertainties as parametric variations of the input data. Parametric models are not always feasible, mainly due to the high computational cost required for the numerical solution. In this work, uncertainties are applied directly to the global stiffness, mass and damping matrices of the finite element model using a nonparametric approach by means of the Random Matrix Theory. The definition of the randomness level for the problem requires a prior knowledge of the result dispersion generated by the uncertainties of the input parameters, what is often not available. The results dispersion is then estimated through a parametric analysis in the low frequency range, which is feasible due the coarser finite element mesh required to solve the lower order vibration modes. After the model calibration, the nonparametric model is used to predict the dynamic behavior of the structure throughout the frequency range of interest.