Inertance vs Transmissibility

[amanuensis]

Hi
Inertance and Transmissibility are both two FRF's.
Is there a relationship between these two functions?
I was wondering whether the following equation was right
Y12/Y11=T12 where Y is the inertance and T is transmissibility.
Regards
Amanuensis

 

[electricpete]

For starters, lets look at the definitions:

According to forum member Tom Irvine at

http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/intro_freq_resp_functions.pdf

Inertance = Acceleration / Force


According to Shock and Vib Handbook:
Transmissibility is the nondimensional ratio of the response amplitude of a system in steady-state forced vibration to the excitation amplitude. The ratio may be one of forces, displacements, velocities, or accelerations.

Y12/Y11=T12... I guess you are talking about a matrix form?

Let's say
Y12 = A2/F1 where A is accel and F is force
Y11 = A1/F1

Y12/Y11 = (A2/F1) / (A1/F1) = A2/A1

Yes, that looks to be the transmissibility to me
The units work out also (it is dimensionless like transmissibility)


=====================================
(2B)+(2B)' ?

 

[electricpete]

I think there needs to be an assumption that force is only applied at location 1 in above analysis.
Otherwise we would get a different transmissibility I think.

=====================================
(2B)+(2B)' ?

 

[amanuensis]

Thanks Electricpete for your answers.
I can briefly describe my issue. I have to find the transmissibility between two points of a structure (T12=A2/A1). For this, I have a model from which I have modes, that is resonance frequencies and modal displacements at the points 1 and 2.

From these data (plus a damping loss factor), I can carry out a modal synthesis. It allows me to get merely inertance, either direct inertance (Y11) or transfer inertance (Y12).

So, it is the reason why I would like to know if transmissibility can be deduce from the two inertances Y11 and Y12.