Wow that's impressive and also quite informative
It appears the entire skid base is moving relative to the foundation. There is also relative motion at the welded frame members likely due to "fatigue?" cracks (you should check and confirm).
Others will chime in I'm sure but I would not be recommending any type of damping to fix this problem. I would look to be repairing the entire skid and have it re-installed and grouted by a competent contractor