31. Modal Test-Analysis Correlation Using Left-Hand Eigenvectors

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]