358 J. Baqersad et al. Assemble the turbine to a tower and extract the mode shapes of the assembled system. Case 5: Assembling the Turbine to a Tower Correlate the mode shapes of the wind turbine attached to the tower with the turbine in pseudo-fixed and free-free configurations using the MAC. Case 6: Investigating the Effects of Assembling the Turbine to a Tower Extract mode contribution matrices and find the contribution of each component on the mode shapes of the wind turbine assembled to the tower. Case 7: Extracting Mode Contribution Matrix of the Wind Turbine Assembly Correlate the single cantilevered blade to the blades in the assembled wind turbine. Perturb the elastic modulus and repeat the correlation. Case 8: Correlating the Cantilevered Single Blade to theTurbineAssembly Connect the blades and develop a threebladed turbine model. Extract the modes of the turbine in a pseudo-fixed configuration. Group the modes. Case 2: Developing the Turbine Model and Extracting Modes of the Turbine Compare the effects of rotational and translational DOFs of the support on the mode shapes of the three-bladed turbine and find the more influential DOFs. Case 3: Comparing the Effects of Translational and Rotational Stiffness Obtain cross section properties of a blade from a solid finite element model. Model the blade using beam elements. Extract the modes of the single blade. Case 1: Modeling a 3D Wind Turbine Blade Using Beam Elements Change the rotational stiffness of the support of the turbine and study the variation of natural frequencies along with variation of the mode shapes. Case 4: Investigating the Effects of Rotational Stiffness of the Support Fig. 34.1 A flowchart of the work that was performed in the current paper Fig. 34.2 The solid element model of the Southwest Windpower Skystream 4.7™ blade deformations in the edgewise direction. This issue may create some difficulties when one wants to interpret whether a mode of the three-bladed turbine is flapwise or edgewise; whereas in this paper, the model is used as a sample for the study and the model does not necessarily need to exactly replicate the blade. Due to the mentioned concerns, a blade model composed of 3D beam elements was used for the current study. It should be noted that based on the previous studies mentioned in the literature [11–14, 23], using beam elements to study dynamics of wind turbine blades did not degrade the results when they were compared to other theoretical and solid element models. To develop a FE beam model, a straight beam with four different cross sections was created with the total length and weight equivalent to the original solid blade (see Fig. 34.3). While the solid model had over 100,000 DOFs, the beam model was a much simpler representation of the blade with 600 DOFs. Reducing the number of DOFs leads to significant computational savings. To accurately obtain the cross section properties of each part of the beam model, cross sections properties of the blade on the corresponding length were measured from the solid model. The cross section properties of the desired length were averaged and assigned to the beam model. Therefore, a small inconsistency between the solid model and the beam model might exist that can be attributed to the averaging that was performed on cross sections. The accuracy of the beam model to represent the dynamics of the blade was verified by comparing the mode shapes of the beam model to the solid model in free-free and cantilevered configurations. The cantilevered boundary condition is a common configuration in which the wind turbine blades are tested in laboratories and test facilities. The mode shapes of the individual blade in this configuration are correlated to the three-bladed turbine in the following sections to quantify the change of the mode shapes in the turbine model. To create the cantilevered boundary condition for the individual blade, the foremost node of the FE beam model was fixed; the same nodes of three blades were
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