Basically, I am trying to detect damage on beam structures for a cantilever support. Suppose, I am measuring first natural frequencies from the experiments at several times of undamaged state of structure. I will get different first natural frequencies value in each trial with slight variation. Now how do I take single value of natural frequency ? Which method should I use to get mean value?
It is unclear how you measure frequency. If your are using a bump test without an instrumented hammer, then you are just estimating the frequency from the time record (waveform). If you have the FFT of the signal, then you can confirm the measurement. More accurately, if you have an instructed impact hammer, and using a 2-channel signal analyzer; then you can obtain more accurate estimates by measuring the FRF and observing the coherence. In either case, care must be given to locations of excitation and locations of measurements. Also, the selection of hammer weight and type of head is related to the structural inertia and frequency range.
If you are using Bayesian method to obtain the frequency from each test, you will also obtain the variance of each estimate. Then, you can do a weighted average with the weighting being the reciprocal of the variance.
Otherwise, assuming that each test is associated with same duration, same sampling rate and similar noise level, then you can approximate it using the simple average.
1. Transform the measured data into frequency domain.
2. Compute the FRF (Frequency Respone Function) for each measurement. (do not change the location of force and responce signal)
3. Average the FRF functions.
4. Estimate the natural frequencies on averaged FRF.
5. If you have different location for FRF measurements, use the SVD decomposition of FRF matrix. Use my method:
http://papai.modal.hu/papaiarticles/papai%20article%20111.pdf
If you do your modal test properly (right hammer tip and mass, right impact, right sensor location), the value of the frequency measured from different tests should be very very close. You take the average value. Whne you pile the FRF curves from different tests, you will see the quality of your tests.
By the way, the first frequency is very insensitive to damage features unless they are big. Other quatities had better be considered.
The so called "sensitivity analysis" expresses the effect of structure modification on the eigen properties (natural frequencies and damping and mode shapes).
Equations are the link below.
Br
http://papai.modal.hu/sensitivity/sensitivity.html
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