Abstract
Over many years, members of the experimental modal analysis community have been challenged over the use of modal orthogonality and cross-orthogonality criteria for validation of experimental modal vectors and for assessment of test-analysis correlation, respectively. At the heart of the challenge is the role played by the potentially inaccurate TAM mass matrix, which is derived from a mathematical model. Recent work that exploits left-hand eigenvectors, estimated by the SFD technique, provides a promising way out of the TAM mass matrix impasse. Modal orthogonality, defined as the product of left- and right-handed experimental eigenvectors (real or complex) is mathematically an identity matrix. This guarantees that SFD estimated modes are always perfectly orthogonal. Modal cross-orthogonality, defined by product of analytical left-hand eigenvectors and experimental right-hand eigenvectors (after consistent “mass” normalization of both sets) does not possess the desired “unit maximum coefficient magnitude” property. Therefore, an alternative cross-orthogonality definition, based on weighted complex linear least-squares analysis, is evaluated and found to possess the desired property. Employment of (1) the left- and right-handed experimental eigenvector based orthogonality matrix and (2) the weighted complex linear least-squares based cross-orthogonality matrix represents a “game changer” that potentially frees the experimental modal analysis community from the potentially inaccurate TAM mass matrix.
[Test FEM Correlation Left Eigenvectors]
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Coppolino, R.N. (2020). Modal Test-Analysis Correlation Using Left-Hand Eigenvectors. In: Mains, M.L., Dilworth, B.J. (eds) Topics in Modal Analysis & Testing, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12684-1_31
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DOI: https://doi.org/10.1007/978-3-030-12684-1_31
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