# Orbit Analysis (particle accelerators) [short article]

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The following sections review the relevant theoretical concepts and equations required for discussing the estimation of final, scaled modal vectors. The final scaled modal vectors are often presented as the residues of the partial fraction model of the MIMO FRF data matrix [1]. MAr /. / D N X Apqr j! rD1 C r Apqr j! / D N X rD1 ŒAr  j! C r Ar j! /NL NS D ŒLNL NL D ŒLNS 2N 2N r 2N X rD1 1 j! 4) 2N 2N 1 j! ŒAr  j! 1 0 Mode Frequency, Hz Fig. 5) M Ar In the above equations, and particularly in Eq.

In: Proceedings of international modal analysis conference, pp. 397–405 6. Allemang RJ (2003) The modal assurance criterion (MAC): twenty years of use and abuse. Sound Vib Mag 37(8):14–23 7. Allemang RJ, Phillips AW (2014) Un-weighted and weighted versions of the modal assurance criterion (MAC) for evaluation of modal vector contamination. In: Proceedings of international modal analysis conference (IMAC), 8 pp 8. Deblauwe F, Allemang RJ (1986) A possible origin of complex modal vectors. In: Proceedings of 11th international seminar on modal analysis (ISMA), Katholieke Universiteit Leuven, Belgium, 10 pp 9.

Given that the FE model used to generate the test plan is not validated, it is unsurprising that the modal analysis may fail to adequately describe the dynamics of the structure, and so a new test plan and further experimental analysis may be required. Once an acceptable modal solution is believed to have been found the FE model can be correlated against the EMA and attempts can be made to update the model. Again, the model updating process can fail if the model cannot be reconciled with the experimental data, requiring revisions to be made to the model structure, which in turn may show some deficiency in the EMA.