Performance of Various Mode Indicator Functions

摘要

Mode Indicator Functions (MIFs) are real-valued frequency-dependent scalars that exhibit local minima or maxima at the modal frequencies of the system. This paper presents an overview of the currently used and some recently developed MIFs, revealing their features and limitations. Eigenvalue or singular value based MIFs use rectangular frequency response function (FRF) matrices calculated in turn at each excitation frequency. Their plots have as many curves as the number of references. Recently developed MIFs do the simultaneous analysis of all FRF information organized in a compound FRF (CFRF) matrix. The left singular vectors or the Q-vectors obtained from the pivoted QLP decomposition of this matrix contain the frequency information and are used to construct MIFs. The number of curves in such a MIF plot is equal to the effective rank of the CFRF matrix. If the number of response coordinates is larger than this rank, 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.