The following was written by Adrian Lincoln in response to a customer asking about averaging Frequency Response Functions (FRFs)
Further to your reply it should be noted that there is no such mathematical or physical quantity corresponding to an averaged structural FRF except in those special cases where you are testing a symmetric structure comprised of nominally identical components (such as turbine blades). For symmetric structures, where you can impact at a similar position on each component and measure the corresponding acceleration at a similar response position, then the individual FRF’s should have the same characteristics and therefore can be averaged.
For structures that don’t have multiple symmetric components then you should not perform any sort of averaging because the FRF’s will not have the same characteristics. For example, if you have beam-like structure and are measuring the FRF’s between different locations along the beam, then these FRF’s should only be averaged as moduli and not with respect to phase and coherence.