FRFs in Terms of Modal Parameters

FRF -based curve fitting assumes that any FRF calculated between two DOFs of a vibrating structure can be completely represented in terms of modal parameters.

Partial Fraction Expansion of the FRF Matrix

The following parametric model is used to estimate experimental modal parameters by curve fitting FRF data.

Local versus Global Curve Fitting

Local curve fitting is necessary when physical changes such as mass loading, temperature changes, or other effects cause the resonant frequencies & damping to change during the course of a modal test.

Generally speaking, modes are global properties of a structure.  Therefore, each mode has only one frequency & damping value, and one mode shape.

Residue Matrix

A Residue represents the "strength" of a resonance.  That is, the stronger a resonance is relative to other resonances, the larger its residue will be.  In general, residues are complex numbers with magnitude & phase.

Residue units = ( FRF units ) x ( radians / second )
When one row or column of FRFs in the MIMO model is curve fit, the residues from the same row or column of the Residue matrix are estimated.

Parameter Estimation (Curve Fitting)

During curve fitting, four modal parameters are estimated for each mode (k),
Frequency & damping, or the pole location p(k) = -s(k) + jw(k).
Magnitude & phase of the complex Residue R(k).