Hi Switch - Try using the thread tools for images vs links. Links will also expire in a default period. The images you linked to don't open. Interpreting a modal analysis goes like this. The structure wants to vibrate at its "natural" frequencies. This is local and global. Local free edges are the usual culprit, like brackets end of extrusions etc. Then you start getting global modes like the entire gantry wobbling. If there is a driving frequency in the machine, say at feed speed of the process the stepper pulses at a certain freq. This pulse can excite the structure if its the same freq. The tool cutting "bumps" the structure at a certain freq and this causes "chatter". Again if the Z axis has natural freq at this bump rate it will vibrate and make poor surfaces.
Is this the sort of info you need? or more along the lines of how to do it? For a modal analysis you don't need to apply loads but you do need to restrain it in the intended way as this can affect the response. A machine has to be very stiff. If its stiff enough vibration can be a secondary issue. Damping does not change the resonant freq it means the vibration instead of taking 50 cycles to stop will take 5 cycles to stop as an example... Are you going to stress relief after welding? Peter