measure of the mathematical orthogonality and linear independence of a set of mode shapes (analytical or measured) using the mass matrix of the mathematical model (FEM or TAM) as a weighting factor
NOTE 1 The following are common definitions of the orthogonality check
a. Auto orthogonality check (AOC)
Measure of the mathematical orthogonality of mode shapes Fr and Fs taken from the same set j of analytical or measured mode shapes.
Where 0 £ AOCrs £1.
b. Cross orthogonality check (COC)
Measure of the mathematical orthogonality of mode shapes Fr and Fs taken from two different sets, j and k, of mode shapes (analytical and measured, respectively).
Where 0 £ COCrs £1.
NOTE 2 The degree of orthogonality is usually assessed by the magnitude of the off-diagonal elements AOCrs and COCrs of the orthogonality matrices [AOC] and [COC], respectively.
NOTE 3 The auto orthogonality check is an indicator of the accuracy of the assumed mass matrix and the acquired data. Ideally:
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