When a coarse set of SIMO FRF is available, the driving point is just one. But when the FRF are estimated very close to each other in spatial domain, and might be very similar and all with PI-constrained phase or one sided imaginary part (apart from little measurement errors), how can we discriminate the best/true driving point FRF?
Hi
You can and you cannot separate between the positions you describe.
Allow me to complicate your world a bit.
In vibroacoustics, the true measurement of distance is distance in meters as compared with wavelength.
So, when points are spaced within 1/10 of a wavelength they are indeed (a phase error of 5 degrees or less) at one and the same point.
When points are spaced at 1/10 of a wavelength or more you will find differences in the FRF phase and most notably at the anti-resonant frequencies.
Hope this helps
Claes
Thank you Claes for having troubled my world a bit more :-)
Indeed I find receptance FRFs so similar to each other, all potential driving point FRF from optical vibration measurements, that I was arguing if there was a criterion to assess which one might be the most close to the true one.
I am coding some algorithm based on signal strength and coherence functions, which locate the force ignition point surely in the area where the shaker is, but just within the surface of the impedance head, rarely on its geometrical center, but mostly on the border. Sure, experiments are not models, and light misalignment and low correlation might give their frequency dependent effects.
I will try to add the distance from the impedance head driving point FRF as a further metrics in the seeking algorithm. Do you think this might help?
My regards,
Alessandro
Hi Allesandro
I believe I must complicate your world a bit more. :)
You measure mobility (receptance or accelerance) rather than impedance.This is a common mistake, in fact the Impedance standardization group had to switch name to mobility standardization.
Why? Well, if you set up the impedance matrix, i.e. forced displacement input, you must block motion at all other positions and there measure blocked force. This can only be done in special test stands and with some limitations at that.
See Figures 3 & 4 here & try the same for mobility and the difference is obvious
http://qringtech.com/2014/01/28/need-to-know-about-vibration-isolation/
Next, I used to be a big fan of impedance heads until I learned that impedance heads are riddled with measurement errors. The reason lies in the force cell being situated in between your measurement object and the accelerometer.
If the measurement object stiffness is higher than that of the force cell, the accelerometer response will not move in phase with the measurement object and your FRF is in error. As most FRFs have anti.resonances, and stiffness if very high at anti-resonance, this error in your drive point FRF will be notable.
Incidentally, this is a unique way to identify the difference, ;), between the FRFs where the FRF with the accelerometer placed close to the drive point will be the correct one.
When checking things, I find that it is very useful to rely on a no-excuses-accepted case. One such is a rectangular, say 10mm thick, 40 mm wide and 1+ m long steel beam. You can simulate this case using simple Euler Bernoulli beam theory and make very accurate free-free measurements on this case. In any case, this is what Mike and I did when we were working on 6 dof mobility measurements a while back in time. https://www.researchgate.net/publication/256801180_Direct_measurement_of_moment_mobility_Part_I_A_theoretical_study?ev=prf_pub
Over2Jo
Claes
Article Direct measurement of moment mobility: Part I: A theoretical study