Abstract
The present work deals with the determination of the newly discovered conditions necessary for model updating with the eigensensitivity approach. The treatment concerns the maximum number of identifiable parameters regarding the structure of the eigenvectors derivatives. A mathematical demonstration is based on the evaluation of the rank of the least-squares matrix and produces the algebraic limiting conditions. Numerical application to a lumped parameter structure is employed to validate the mathematical limits taking into account different subsets of mode shapes. The demonstration is extended to the calculation of the eigenvector derivatives with both the Fox and Kapoor, and Nelson methods. III conditioning of the least-squares sensitivity matrix is revealed through the covariance jump.
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