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To add to Jonathan and Robin's comments, this is not the right type of analysis.

Resonances of the bed in that condition don't tell you much as they will completely change when the mass and...

Have you seen evidence that a laser will cut through that thickness of material. I would imagine the power needed to slice through that much fabric would charr the edges and set the material on fire....

I think you are worrying about the wrong part.

You can always add dead weight to the bed if you have a vibration problem.

Suggest you worry about connecting the bed to the tool tip. That is...

This thesis should help you. The sources which excite resonance in the system are the tool and motor, so you can consider the spindle speed and number of flutes for the former. The latter is less...

Co2 laser machine parts including laser head mirror mounts tube support belt fixutre speed reducer gears-in Laser Equipment Parts from Industry & Business on Aliexpress.com

have a look at...