During the correlation of vibration measurement and FE frequency response simulation data, the MAC value can be calculated in 2 ways, with and without considering the effect of phase data. These are called real and complex MAC values respectively. The real MAC value calculation is relatively simple and takes into account only the directional vector magnitudes. How can the phase data be included so as to get a more accurate correlation?
Hi Arun
The Modal Assurance Criterion is defined as
MAC = (V1*(conj(V2)))2/(abs(V1)2*abs(V2)2)
, where conj is the complex conjugate and abs is the absolute value and Vx is the modal vector x.
You may regard the MAC as a 3D version of the Coherence function.
For real valued modes (standing waves), the modal vectors V1 and V2 can contain positive and/or negative data, i.e. show a 180 degree phase shift. The MAC value then is real valued.
For complex modes (where there is a net energy flow across the system), the modal vectors contain complex (real & imaginary) data. The MAC value can then be complex.
As you can see, phase is part of both a real and a complex valued mode. The difference is that a real valued mode has a shape that stands still while the complex valued mode changes with time. This is readily seen in that node points (zero motion) stand still for the former and move for the latter.
Hope this helps
Claes
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