when doing structural dynamic analysis, many people refer to "modal density" and "modal overlap factor", could anyone tell me what do the two parameters mean and how to calculate them?
Hi
If you calculate the number of modes, N, versus frequency, f, then modal density n = dN/df, is the gradient of this function. Modal density can be shown to be independent of boundary conditions and shape at large values of N, i.e. modal density is the asymptotic trend of the modal count N.
The structural loss factor, eta = df/fj, where df is the half power bandwidth of the resonance fj. The Q-factor has the relation that Q = 1/eta.
https://en.wikipedia.org/wiki/Q_factor
Modal Overlap Factor = n*eta*f, which should be viewed as the average number of resonances that fall within the half power bandwidth of a single resonance.
High Modal Overlap signifies that summation of modes becomes pointless, i.e. amplitude-phase becomes meaningless while power-energy converges.
This is why acousticians get away with summing squared quantities, why experimental modal analysis does not work at high modal overlap and explains some cases of why you get product variation.
More in detail, amplitude-phase is sensitive due to the 180 degree phase flip that occurs above/below resonance when there are many resonances nearby.
The enclosed presentation that was made by Gärdhagen and Plunt at a SAE conference provides a good explanation as to why this is so.
Hope this helps
Claes
Hi
If you calculate the number of modes, N, versus frequency, f, then modal density n = dN/df, is the gradient of this function. Modal density can be shown to be independent of boundary conditions and shape at large values of N, i.e. modal density is the asymptotic trend of the modal count N.
The structural loss factor, eta = df/fj, where df is the half power bandwidth of the resonance fj. The Q-factor has the relation that Q = 1/eta.
https://en.wikipedia.org/wiki/Q_factor
Modal Overlap Factor = n*eta*f, which should be viewed as the average number of resonances that fall within the half power bandwidth of a single resonance.
High Modal Overlap signifies that summation of modes becomes pointless, i.e. amplitude-phase becomes meaningless while power-energy converges.
This is why acousticians get away with summing squared quantities, why experimental modal analysis does not work at high modal overlap and explains some cases of why you get product variation.
More in detail, amplitude-phase is sensitive due to the 180 degree phase flip that occurs above/below resonance when there are many resonances nearby.
The enclosed presentation that was made by Gärdhagen and Plunt at a SAE conference provides a good explanation as to why this is so.
Hope this helps
Claes
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