35 Effects of Boundary Conditions on the Structural Dynamics of Wind Turbine Blades. Part 2: Edgewise Modes 371 Fig. 35.2 The solid element model of the Southwest Windpower Skystream 4.7™ blade Fig. 35.3 A schematic of the beam model with four different cross sections emulating the Skstream blade (left); edgewise natural frequencies below 40 Hz and their corresponding mode shapes of the beam model in a cantilevered boundary condition (right) 35.2.1 Case 1: Modeling a 3D Wind Turbine Blade Using Beam Elements A solid element model of a Skystream 4.7™ wind turbine from Southwest Windpower was initially developed in Abaqus™ [20] as shown in Fig. 35.2. The finite element model of the single blade showed a strong correlation to the experimental measurements [9, 21]. In order to study effects of the boundary conditions on the dynamics of the wind turbine, the solid element model was simplified using beam elements (see Fig. 35.3). This simplification reduces the computation time and leads to an easier interpretation of the results. It should be noted that using beam element to study dynamics of wind turbine does not degrade the results based on the previous studies [1, 2, 22, 23]. The beam model of the blade consisted of several beam elements with four different cross section properties. The section properties were extracted from the solid element model. The accuracy of the beam model to represent the dynamics of the blade was verified by comparing the modes of the beam model to the solid model in free-free and cantilevered configurations. 35.2.2 Case 2: Developing the Turbine Model and Extracting Modes of the Turbine in a Pseudo-Fixed Configuration In order to develop a finite element model of the turbine, three individual beam models of the blades were rigidly connected together after arranging the blades in the appropriate positions that form the three-bladed turbine. The rigid connection replicates the performance of the hub that is significantly stiffer than the blades (blades were made of plastic with elastic modulus of 15.8 GPa; hub consisted of a very thick cast aluminum part with elastic modulus of 72.4 GPa, and a steel plate with elastic modulus of 180 GPa). An eigensolution was performed on the three-bladed turbine model in a pseudo-fixed configuration to extract the mode shapes and natural frequencies. The fully fixed condition (i.e. setting the rotational DOFs of the center point to zero) leads each blade to have isolated dynamic behavior. As the modes of the three-bladed assembly with interactions among the blades were targeted, the pseudo-fixed condition rather than the fully fixed condition was used for the analysis. In the pseudo-fixed configuration, very stiff springs connect the center point to the ground. All the edgewise mode shapes of the three-bladed turbine below 100 Hz in a pseudo-fixed configuration are shown in Fig. 35.4 (the modes in this frequency span were selected for the current study). The edgewise modes can be categorized as either collective or differential modes. The collective modes are the modes with the same phase on three blades such as modes 1 and 4. The other modes are called differential modes because the blades do not have the same phase.
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