Hello, Naresh Kali!

1. Estimating modal properties from all measured FRFs at once is usually referred to as a global method. However, the global methods rarely use one "synthesised" FRF and employ more sophisticated procedures. You can start reading this excellent paper by Mark H. Richardson:

http://papers.vibetech.com/Paper06-GlobalFrequencyAndDampingFromFRFMeasurements.pdf

If you really need to visualise one "global" FRF, the good idea is to compute the mean of absolute values at each spectral line. You lose information about phases, but positive and negative values of imaginary parts of FRF (i.e. resonances if you measure acceleration) do not cancel each other.

2. Yes, in theory. But this means that any mode shape has the same magnitude and phase in both locations! In practice, it can happen if you measure only a handful of natural frequencies (say 2 or 3) on symmetrical systems.

From the top of my head, this situation can happen in a case of an isolated beam (with symmetric supports with very low friction) whose response is measured at both ends and which is excited in the middle. FRFs between the reference (excitation) point and both endpoints should be very similar around the first few resonances.

3. FRF measures the transmissibility between a reference point and a measurement point. You can measure as many FRFs as there are combinations of reference points and measurement points.

Hi Kali Naresh,

You can find my final thesis in my page. It may help to you since i perform my thesis with hammer test.

Dear Meysam, It is only at resonances that the mode shape is independent of the location of the test point but only depend to the boundary conditions. Modal analysis is required to create from your collection of location-dependent FRFs a global descriptor of your structural response now independent from the measurement points! This requires dedicated software as post-processing of the FRFs... There is a very abundant literature on modal analysis, but in practice it requires special expertise. The modal base is a complete descriptor of the structural behaviour which substitute to your collection of FRFs

thank you all for your good suggestions

Hello, Luboš Smolík

I am performing roving accelerometer method to find out FRF and natural frequencies for my composite plate (total 5 points : 4 points for response, 1 point is reference point made on cantilever plate). But here 1 FRF  and 3 first natural frequencies are getting by taking the response at each points by impacting at reference point using impact hammer like that total 4 FRFs and 12 natural frequencies are obtained. how do I use these 4 FRFs and 12 natural frequencies to get first 3 natural frequencies and single FRF of my composite plate.

1. can I take average of 4 FRFS to get single FRF of a composite plate

2. how can I show first three natural frequencies of composite plate out of these 12 frequencies ?? should I take average of these frequencies??

Dear Kali,

NO this has no meaning to average FRFs from different locations (unless you just switch the excitation and response locations, as the FRF is the same due to reciprocity; exact symmetry should also provide identical FRFs that can theoretically be averaged, but it remains unlikely in practice).

YES the resonance frequencies are independent from the excitation and response locations and are the same, so you can average the frequency values for increasing the accuracy. Resonances are easier to detect on the FRF phase plot than on the amplitude plot, it is the point of inflexion at +/-90° of the sudden 180° phase shift associated to any resonance, more precise than the peak of the response amplitude. If these resonance frequencies differ measurably in your FRF collection, this means your set-up is inappropriate (e.g. too heavy accelerometers) as they are by essence independent from the sensors and hammer location (however, at some locations too close to a modal line, you might miss some in a particular FRF)...

Once again, you have to perform modal analysis from your FRF collection to get generalized dynamic properties of your plate (modal frequencies, modal masses, damping etc)

Thank you, Bernard Garnier

I will take the average of first three natural frequencies at 4 points on a cantilever beam but which point FRF should I take from four points.

I am adding some remarks to the excellent answer by Bernard Garnier

Remark to question 1: You can, but do not do that! More on that later.

FRFs are averaged in practice only for a handful of reasons. These reasons include:

Remark to question 2: Sort of. However, most contemporary methods use the least squared error equations to mitigate the influence of outliers. Let's say that you analyse one FRF at a time and you estimate the first natural frequency to be 54,9 Hz, 55,1 Hz, 55 Hz and 57,5 Hz. If you compute the mean of these values, your result will have high uncertainty. Using all your FRFs at once, you can estimate the first natural frequency more accurately.

Some more information about this process is in these papers:

http://papers.vibetech.com/Paper05-GlobalCurveFittingUsingTheRationalFractionPolynomialMethod.pdf

http://papers.vibetech.com/Paper06-GlobalFrequencyAndDampingFromFRFMeasurements.pdf

http://papers.vibetech.com/Paper07-ParameterEstimationUsingRationalFractionPolynomials.pdf

Nothing to add to the very clear guidance provided by Lubos, just proceed as suggested...

BTW no one answered yet your question 3, the answer is simply an infinity because your structure is continuous and every couple of points will provide a distinct FRF (a 2D infinity of possible excitation points x a 2D infinity of possible response points, divided by 2 for factoring reciprocity, possibly further reduced by symmetry, that makes infinity anyway)

Thank you, Luboš Smolík

Thank you, Bernard Garnier