44 A Comparison of Common Model Updating Approaches 441 The objective function J for the model updating method using FRFs can be defined as J DX n iD0 ki 1 FRACij (44.5) Where ki indicates the weighting coefficient of the FRAC at the i-th point and j the specified point of excitation. In the following two sections the efficiency of these three model updating methods will be investigated on the Ampair 600W wind turbine’s fin as an example of simple homogeneous structure. 44.3 Measurement An impact test was performed with a standard modal analysis software under free-free condition to identify the dynamic data of the fin as the reference for the model updating. For sake of simplicity, the fin was considered being a plane surface. A measurement grid of 7 points was defined as shown in Fig. 44.1. By measurement the fin was excited in the direction perpendicular to the plane surface at point 4. The FRF of measurement points respect to the excitation point in the frequency range from 300 to 700 Hz with 1 Hz increment and the first 5 eigenmodes were extracted and used to calculate MAC and FRAC values. The measured eigenfrequencies are listed in Table 44.3. 44.4 Modeling The CAD model of the fin was provided by University of Stuttgart [9]. The geometry of this model is assumed to be properly defined. A FE model was generated in ANSYS Workbench 15.0. In order to get the best compromise between the accuracy and computing time of FEA, a mesh study was performed to find the best mesh size. The convergence of numerical eigenfrequencies is shown in Fig. 44.2. Finally a mesh with 34,584 nodes and 29,061 solid tetra elements was adapted (see Fig. 44.3). The nodes with the same location as measurement points were defined to extract mode shapes in FEA. The fin is made of steel and is considered to be homogeneous. Therefore the model of fin provides three parameters to update, namely density¡, Young’s modulus E and Poisson’s ratio ”. 44.5 Model Updating Model updating is considered as a process of minimization of the deviation of the dynamic response of FE model with respect to the truth data. In other words, the objective functions introduced in Sect. 2 must be optimized iteratively. To do so, Matlab Optimization Toolbox and ANSYS were applied to perform Optimization and FEA and text files were used as media of the Fig. 44.1 Measurement grid for fin
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