Uncertainty Quantification in the Dynamics of Wind-Turbine Curved Blades Within the Formulation of Iso Geometric Analysis

Abstract

In this paper we study the dynamics of wind-turbine blades constructed with resin-fiber reinforced composites with uncertainties. The constructive process of these structures, although conceived to be carried out mostly with robust automatic machines, cannot avoid the presence of a number of details that lead to unexpected spurious mechanical behavior. In this type of structures the source of uncertainty can be found in geometric, material and mechanical aspects. In order to study the uncertain dynamics of these structures, we employed a composite curved beam model formulated in the context of iso-geometric analysis. The model incorporates, variable curvature and geometrical variability within the cross-section. It serves as a mean deterministic approach to the studies on stochastic dynamics and uncertainty quantification, which are objectives of this article. The computational procedure to quantify the uncertainty in the beam dynamics involves the introduction of random variables related to material or geometric properties such as elasticity moduli, material density, wall thickness and fiber angle along the axis of the beam. The probability density functions (PDF) of the random variables are derived appealing to the Maximum Entropy Principle according to given knowledge about the variability of the uncertain parameters. Then, a probabilistic model is constructed with the basis of the deterministic model and both discretized with finite element approaches. Once the probabilistic model is constructed, the plain Monte Carlo and a Latin Hypercube sampling are employed to carry out random realizations. With the aim to seek the sensitivity of the uncertain parameters, a number of possible scenarios are evaluated.