Performance of Various Mode Indicator Functions

M Radeş

doi:10.1155/2010/546802

Abstract

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.

Highlights

Mode Indicator Functions (MIFs) are real-valued frequency-dependent scalars that exhibit local minima or maxima at the modal frequencies of the system
Mode Indicator Functions (MIFs) are calculated using frequency response function (FRF) measured at N o response coordinates, Ni input coordinates (Ni No) and Nf frequencies
MIFs based on the singular value decomposition (SVD) of the compound FRF (CFRF) matrix are plots of its left singular vectors versus frequency

Summary

MIF basic approaches

Mode Indicator Functions (MIFs) are calculated using FRFs measured at N o response coordinates, Ni input coordinates (Ni No) and Nf frequencies. Such data are obtained from either multiple-excitation measurements or multi-reference impact tests. MIFs based on the SVD of the CFRF matrix are plots of its left singular vectors (or combinations of these) versus frequency. The Complex Mode Indicator Function (CMIF) is defined [3] by the singular values plotted as a function of frequency on a logarithmic magnitude scale. The CMIF performance declines for structures with very close frequencies and high damping levels In such cases, two different curves exhibit flat peaks at very close frequencies which have to be located by cursors. Each curve has local minima at the DNFs, with the deepest trough at the natural frequency of the corresponding dominant mode

QCoMIF

Numerical simulation examples

Test data example