Hi all!
I have a complicated composite specimen vibration velocity response due to shaker excitation. The excitation signal consists of 3 predominant short impulses with small time separation followed by a low amplitude burst near the end of the record. The response comprises free vibration decay at the start followed by a few localized bursts. I was thinking of time-frequency analysis, since the ordinary Fourier Transform is not applicable here due to transients in the response. Modulus of continuous wavelet transform revealed that frequency components are not stationary but rather changing with time. The question is how to proceed with the analysis if I want to extract the modal frequencies and damping from time-frequency analysis, since it appears that they are changing with time. Or maybe I should use a different method to extract the modal parameters in this case? The response was measured at 43 points along the carbon composite hollow tube specimens.
Another question related to this one - can I maybe divide the response into several blocks and analyze these blocks separately instead of analyzing the whole response? For example, block 1 contains the free vibration decay at the star, block 2 - the 1st burst, block 3 - the 2nd burst and so on. Or is this approach flawed for some reason connected with signal processing rules?
Thanks!
How deep have you already looked into the theory of "modal analysis" and "operational deflection shapes"? These are maybe keywords to extensive theory about how to derive the vibration modes of the structure from the measured motion under excitation.
Dear Rims, your case is truly complex! I am from the old school and would prefer to start with a direct multi-scale (from a time perspective, from seconds down to milliseconds) observation of the raw time signals memorized sequentially with a trigger on the first burst of the sequence; you can already visualize the similarity from a sequence to the next and the dominant components of the frequency response. Then, to investigate the causality with the excitation signal, I would continue with true correlation (as defined in a signal processing math's book) in the unfiltered time series between your output and your input, and display the successive sequences of correlations in a waterfall mode to see if the behaviour is repeatable (= periodic) or fluctuating. As long as you remain in the unfiltered/unaveraged time signals, you remain on the safe side of physics! If the periodicity is clear then you have access to the full range of transient signals analysis toolbox, including the frequency domain analysis. If not, you have first to understand what makes things non repeatable ! Don't forget with such complex excitation signal that non-linearities might arise from the way you drive the shaker (no one is perfect), its interface with your structure and the other boundary conditions of your test sample, and the assemblies, possible de-laminations etc of the sample itself...
The signals are likely to be dispersive. Maybe a room acoustic approach can be used by filtering the data in one third octave bands and backwards integrate them making so called Schroeder curves. Presented in a logaritmic scale you should see different decay times and incidents directly given straight lines in the data. This is essentially looking at impulse responses.
For analysis of fast varying signals I have learnt that wavelets are useful.
I would also point out that shakers do infleunce the object they excite quite a bit. Adding mass, damping, changing the conditions in activity and at rest. The conmtact point of ectiation is not on the object but inside the exciter between the electromagnet and the rod. The rod from the exciter is part of the vibrating unity. So if that mass is substatial in comparison to the tested object it will mass load and move the mode frequencies and affect the modal effective masses and amplitudes.
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