29 Effects of Errors in Finite Element Models on Component Modal Tests 311 Table 29.9 MAC of exact and simulated test modes Mode number 3 modes 7 modes 1 1.00 1.00 2 0.99 0.99 3 0.94 0.94 4 0.90 0.90 5 0.91 0.91 Table 29.10 Material property errors Young’s modulus Density Case Error (%) Error (%) 1 Component 1 20 20 Component 2 10 5 2 Element 1 20 10 Others 10 5 3 Element 1 30 10 Others 20 10 Element 18 20 40 29.3.4 Effect of Different Modeling Errors on Identified Results The component mass and stiffness matrices are identified for different modeling errors as listed in Table 29.10 to confirm the effect of modeling errors on frequencies and modes obtained by component modal tests. Modeling errors of component 1 are different from those of component 2 in Case 1. In Case 2, errors in element 1 (near the fixed edge) and other elements are different. In addition, different modeling errors are contained in element 18 (near free edge) in Case 3. Identifying component mass and stiffness matrices with seven modes provides the same results as those stated in Sect. II. A three in all cases. From the above results, one can conclude that the proposed method has potential to predict the frequencies and modes. 29.4 Conclusions A component modal testing method was described to obtain the dynamic characteristics of large structures consisting of several components. In this method, to simulate the dynamic behavior of structures, the effect of untested components is considered as additional mass and stiffness attached to a tested component. Because additional mass and stiffness are calculated with mass and stiffness matrices of both structure and tested component, it is difficult to obtain the dynamic characteristics of large structures by component modal tests when finite element models have modeling errors. In this paper, the method was extended to cover the case with modeling errors. Modal tests for different tested components with additional mass and stiffness give an identical frequency, and this frequency is considered as the frequency of structures. It is shown analytically that the identical frequency cannot be obtained when there are modeling errors. Variation in predicted frequency obtained for different tested components is the basis of frequency error estimation. A numerical example shows that the proposed method has potential to be applicable to predicting the dynamic characteristics of large structures even though there are modeling errors in finite element models. References 1. Alvin KF, Peterson LD, Park KC (1995) Minimal-order experimental component mode synthesis: new results and challenges. AIAA J 33(8):1477–1485 2. Doebling SW, Peterson LD, Alvin KF (1996) Estimation of reciprocal residual flexibility from experimental modal data. AIAA J 34(8): 1678–1685 3. Morgan JA, Pierre C, Hulbert GM (1997) Forced response of coupled substructures using experimentally based component mode synthesis. AIAA J 35(2):334–339 4. Soucy Y, Humar JL (2003) Experimental verification of a test-based hybrid component mode synthesis approach. AIAA J 41(5):912–923 5. Chen WH, Cherng JS (1985) Modal synthesis via combined experimental consideration of rotational effects. J Sound Vib 103(1):1–11 6. Komatsu K, Sano M, Kai T, Tsujihata A, Mitsuma H (1991) Experimental modal analysis for dynamic models of spacecraft. J Guid Control 14(3):686–688
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