By H.G. Natke
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Additional resources for Identification of Vibrating Structures
60)"1 Q~ =L"~ .. i-1 Uo1-U Relations between system parameter matrices and modal magnitudes 37 Multi-degree-of-freedom Systems ~ VISCOUS DAMPED SYSTEM SPEC 1FICATION MATRIX EIGEN- ( ~I t:1 + ~I § + IS )YBI = Q VALUE PRO- '=1(1) 2n, J\BQ~ MOB+Q~MQe6g+ BLEM +U~ BUs= I INERTIA MATRIX A .. 2 ~ a-t:1UB~Q~ t:1 r 2 .. G. 3 HYSTERETIC DAMPED SYSTEM 2 . ). :lOi =Q i =l(l)n, Mo =! s+jQ~- ~06h - n ~ Q1 u· ~. 01 _0, r(jw) a(. +6o)"1 Ql; ~ Yo; UBi -leI AQj-Sl Relations between system parameter matrices and modal magnitudes 39 Multi-degree-of-freedom Systems It can be seen that the relationships for active systems can be derived in the same way, Lancaster: 5 -1 ~2 ~1 (49 ) -1 ~ The above-mentioned relationships are not useful for calculating the system parameter matrices from the identified eigenmagnitudes, because the latter are generally incomplete and inaccurate, and all errors will enter into the computation.
However, they will never achieve the importance of the above-mentioned methods, because these are simple and robust in application. 1. g. The broad scope of application spectrum is contained in the proceedings of the IFAC symposia on 'Identification and System parameter Estimation' edited by Eykhoff (1973), Rajbman (1976), and Isermann (1979). Another research direction in this phase of development was the comparison of different estimation methods in order to select an optim~l identification method for the type of application (Saridis (1974) , Gehring (1973), Unbehauen (1973b), Isermann (1973».
G. Natke o The eigenvalues are, moreover, non-negative o There are n eigenvalues Aoi' i = 1 (1 ) n, counted according to their multiplicities (det 0 is the coefficient of' ~ ~ An of the characteristic polynominal) o Right and left eigenvectors are equal (symmetry of matrices) o 1\ For each eigenvalue Aoi one eigenvector ~i ~ Q exists, " which can be normalized in such a manner that ~i is real (homogeneous system of equations with real coefficients and singular system matrix) o The eigenvectors fulfil the generalized orthogonality relations "T ~i ,..