29 Effects of Errors in Finite Element Models on Component Modal Tests 305 calculations. Comparing additional mass Mid and stiffness Kid with original additional mass Mo and stiffness Ko, one can confirm how system identification reduces modeling errors. The measured frequencies and modes of structures are obtained by component modal tests with identified additional mass Mid and stiffness Kid. The final step is to predict frequencies and modes of structures. Note that modeling errors affect only additional mass and stiffness because the tested component subjected to the modal test has no errors in mass and stiffness distributions. If there is no modeling error in the analytical model, frequencies fs,id and fs,test are identical. Therefore, "1 defined by the following equation gives an indication showing the frequency error of structures. "1 D ˇ ˇ ˇ ˇ fs;id fs;test fs;id ˇ ˇ ˇ ˇ 100.%/ (29.18) If frequency error "1 is small, the test frequency may be structure frequency. The other indication is defined by the measured frequencies. As stated in Sect. 29.2.1, predicted frequencies obtained by using different tested components are identical if there is no modeling error. Therefore, it is reasonable to use an indication defined by Eq. (29.19) to predict structure frequencies. "2 Dmax ˇ ˇ ˇ ˇ fs;testi fs;testj fs;testi ˇ ˇ ˇ ˇ 100.%/ .i D1;2; : : : ;nI j Di C1; i C2; : : : ;n/ (29.19) Though the exact frequencies of structures are unknown, structure frequency can be predicted within some error. It is important to confirm how additional mass and stiffness vary with the different number of modes used in system identification. If identified frequencies fs,id vary with the increasing number of modes, those frequencies must approach structure frequencies. 29.3 Numerical Examples Figure 29.2 shows an analytical model consisting of two components. Arabic numbers denote the location number. Location 9 is the boundary location of two components. Each element length is 100 mm. Figure 29.2 also shows the test configuration of the tested components with an additional mass Mand an additional stiffness K. The subscript of Mand Kshows Component 2 DM2 DK2 Component 1 DK1 DM1 800mm Component 1 Height = 3mm Width = 10mm (1) Cantilever beam Cross section Density = 1.6 × -6 10 Material properties Young' s modulus = 7.6 ×104 kg/mm3 N/mm2 1000mm Component 2 123456789 11 13 15 17 19 (2) Component test configuration X Z Y Fig. 29.2 Analytical model and component test configuration
RkJQdWJsaXNoZXIy MTMzNzEzMQ==