I looked it up. A rapier loom lacks a shuttle, but instead transfers fill thread across the width of the machine by means of one or two rapiers, or swordlike probes. I'd guess there's a fair amount of reciprocating mass.
I'm guessing that mounting the machines on mounts that are very loose in the transverse direction, even on rollers or something like a porch glider, would allow the entire machine to move and react to the excitation from the rapiers.
The traditional solution, for arrays of looms, is to drive them all at slightly different speeds, e.g. by lineshafts with pulleys of differing diameters or with specially wound electric motors that are not all synchronous at the same line frequency, so that destructive reinforcement of vibration forces among the looms is made less likely.
Mike Halloran
Pembroke Pines, FL, USA