When Is Multi-Reference Modal Analysis Necessary?

The term Multi-Reference Modal Analysis means that FRFs are acquired using two or more references (fixed input or output sensors) and are curve fit using Multi-Reference curve fitting methods.

Multi-Reference Modal Analysis is required when a structure has resonances that occur under one of the following conditions;

  1. Closely Coupled modes:  One resonance peak represents two or more modes.

  2. Repeated Roots:  Two or more modes having the same natural frequency but different mode shapes.

  3. Local modes:  Different resonance peaks occur in FRFs from different references.

In each of the above cases, multiple reference curve fitting is required in order to properly extract all modal parameters from a set of FRFs.  Multiple reference FRFs correspond to multiple rows or columns of the FRF matrix in the MIMO model .

Single Reference versus Multi-Reference FRFs

A single reference set of FRFs is,

A multi-reference set of FRFs is,