FREQUENCY RESPONSE NONPARAMETRIC ANALYSIS
9.4 QR decomposition of the CFRF matrices
9.4.6 Concluding remarks
Mode indicator functions locate the observable modes in the test data and their natural frequencies, sometimes used together with interference diagrams and singular value ratio plots. Their performance is determined by the selection of input and output locations for the adequate definition of all modes of interest.
Eigenvalue based MIFs and the CMIF use rectangular FRF matrices calculated in turn at each excitation frequency. Their plots have as many curves as the number of references. The number of input points should be equal to the multiplicity of modal frequencies.
Other MIFs do the simultaneous analysis of all FRF information organized in a compound FRF matrix. They have a different physical basis and outperform the eigenvalue based MIFs developed to locate frequencies where the response is closest to the monophase condition.
The left singular vectors (U-vectors) or the Q-vectors obtained from the pivoted QLP decomposition of the CFRF matrix contain the frequency information and are used to construct MIFs. They are based on projections onto an orthogonal base of the subspace of measured FRFs. These orthogonal response functions are calculated as linear combinations of the measured FRFs and represent a response dominated by a single mode with a major contribution to the dynamics of the test structure in the given frequency band.
The number of curves in a CoMIF or QCoMIF plot is equal to the effective rank of the CFRF matrix. If this is lower than the number of response coordinates, a single point excitation can locate even double modes. The condition to use as many input points as the multiplicity of modal frequencies is no more imposed.
They have been used with good results for complex structures with high modal density.
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