From the impact hammer test, I can able to obtain multiple natural frequencies of a cantilever beam. Now, to obtain the material damping coefficient of various modes of vibration, I believe that we need to decompose the signal into a multiple modes. Next, Fitting to the decaying signal over time of each mode, we can get damping coefficient of each mode.
I am not sure if it is the correct method to obtain the damping coefficient of multiple modes of beam vibration. Opinion of any expert in this field is highly appreciated.
Thanks 🙏
Damping per mode can be measured using the half power width. You find the half power value for a resonance, on each side, and compare the frequency delta with the resonance frequency df/f = eta, your loss factor.
This is a work-intensive method. It is simpler if you can do a mode fitting in a program for that and the damping values may come out of that.
A third method could be to use structural reverberation and measure in one third- or octave bands.
It depends what you are looking for, and plan to use the data for.
For FEA you need both modal and ensemble data, because the input to the model will be global. The datiled modal data is for comparson to the model output. You may have to use a frequency dependant loss factor as input. Soermthing you may extract from a set of measured modal data. Usually the loss factor will go like internal loss + x/root(f) with xes depending on the fixture, element and situation.
The boundary conditions you choose for the test will influence the measured damping. I think the best method would be to let the beam rest on something resilient, or hang in an elastic rope. It will introduce some new modes, but these should be moved as low as possible in frequency, so thy do not influence the beam modes.
I believe a curve fitting algorithm such as the Least Squares Complex Exponential method (LSCE) would be adequate for starters due to its ability to accurately model complex exponential signals, which seems to be your case. If you have the frequency response functions of your measurements, there are built-in functions such as modalfit in Matlab that compute natural frequencies, damping ratios and mode shapes of your system by using the LSCE. You may want to explore other modal estimation algorithms, such as LSCF, pLSCF or even state-space formulations,which can provide a different perspective on system modeling and analysis.
When applying modal estimation algorithms, it is important to consider certain factors such as reciprocity, which ensures that the measured responses are consistent for both excitation and response points. Additionally, assuming linearity and time-invariance of the system can simplify the analysis process and facilitate the application of these algorithms. It's crucial to verify these assumptions in your specific case to ensure the reliability of the results.
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