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Hi Sean,
thank you so much for this lecture, as usual. I have a question though:
on the first course, we discussed that c = (4mk)^0,5 for SDoF Systems and in here, you mentioned that damping has to do with the internal friction within the structure. It seems to me then that damping is strucure-dependent. Why is it then that different modes may have different damping?
This is a good question @josbarort1
If we think about each mode of vibration, it’s not just an oscillation in time, the oscillation maps to the real structure via the mode shape. In other words, the mode shape tells us the parts of the structure that oscillate with a particular modal frequency. And as such, these specific parts of the structure will contribute towards damping in that mode. This is why the damping may vary slightly in different modes - different parts of the structure are contributing to the damping in each mode.
In truth, it will be very difficult, if not impossible, to determine a priori the appropriate damping levels per mode. However, if you have experimental data that suggests individual levels of damping, then we can use this to back into an orthogonal damping matrix, should we need this for simulation.
Hope that helps.
S
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