Frequency & Damping Methods

Polynomial Method

The Polynomial method is Multi-Degree-Of-Freedom (MDOF) method that simultaneously estimates the modal parameters of one or more modes.
This method uses the complex (real & imaginary) FRF An FRF (Frequency Response Function) is a cross-channel frequency domain function that defines the dynamic properties of a structure between an excitation Force and the Response caused by that force. An FRF is defined as the ratio (Response DFT / Force DFT). The FRF is a special case of a Transfer Function, where the response is the numerator (Output) and the force is the denominator (Input). data in the cursor band for curve fitting.

A least squared error curve fit is performed on the FRF data to obtain estimates of the coefficients of the FRF denominator polynomial, called the characteristic polynomial.  Modal frequency & damping estimates are then extracted as the roots of the characteristic polynomial, or poles of the FRF.

Curve Fitting Assumptions

1. Modal frequency & damping are global properties of a structure.

2. Each resonance peak in an FRF is evidence of at least one mode.

3. All FRF measurements taken from the same structure should have a resonance peak at the same frequency for each resonance.

4. If multiple FRFs are overlaid on one another, each resonance peak should appear at the same frequency in all FRFs.

Non-Stationary Data

If a set of FRFs is acquired under non-stationary conditions (such as different mass loading due to roving accelerometers, temperature changes, etc.), resonance peaks may not be at the same frequency for each resonance.

Global Versus Local Curve Fitting

Global curve fitting can be used when resonance peaks "line up" in a set of overlaid FRFs.
Local curve fitting should be used when resonance peaks "do not line up" in a set of overlaid FRFs.