>>How does the frame base connect to the ground?  Are there four mount points that are fixed to ground? 

Yes, the base is firmly fixed to the ground

>>A Modal analysis will show the free vibrations of that structure. You should add a Distributed Mass on the pipe elements to represent the weight of the liquid in the pipe.

Just to check free vibrations? And all?

If there are free vibrations, then there is vibration; if there are no free vibrations, then there is no vibration. Right?