42 Robust Expansion of Experimental Mode Shapes Under Epistemic Uncertainties 423 Fig. 42.1 FEmodel Fig. 42.2 Sensor locations Table 42.1 Discrepancy real/model Name: Zone Real Model Error YoungMod. E1 (Pa): 1 3.109 2,5.109 6% YoungMod. E5 (Pa): 5 3.109 2,2.109 13% YoungMod. E2 (Pa): 2 2.109 2,4.109 C20% YoungMod. E4 (Pa): 4 2,5.109 2,7.109 C8% Fig. 42.3 MAC between model and test u D E1 E5 p D E2 E4 : (42.14) The mode shapes we seek to expand are composed of four local modes and one global mode as indicated in Fig. 42.4. In practice, the resolution of the ECRE-based system (Eq. (42.7)) is performed directly in two main steps by using MD Nastran®language (DMAP language): decomposition coupled with a forward-backward substitution. However, solving such linear system yields to prohibitive CPU-time because of the decomposition process of ŒA . The decomposition algorithms available in MD Nastran® are suitable for large, sparse, hermitian matrices with a small bandwidth of non-zero terms around the diagonal. However, ECRE equations lead to matrices with large bandwidth of non-zero terms around the diagonal (cf. Fig. 42.5), which precisely makes the decomposition operation prohibitive. Though renumbering techniques are evidently used in this work,3 the decomposition operation is always the heavier one in the process. 3In the case of large number of dofs, Metis renumbering method available in MD Nastran® permits to minimize the decomposition CPU-time.
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