Is it "Work Related" ?

"The Control of Vibration at Work Regulations 2005" as a title is a pretty good give away

So for the General Public in a gymnasium these regs are not directly applicable.

If you want to be scared to let Joe Public on the machines ask the insurer for advice - your instructors as part of their duties should be considering the issues presented by the equipment during the "induction" nearly every gym seems to demand you sign off before getting on any equipment.

https://bjsm.bmj.com/content/39/9/585 is a link to an old BMJ paper on Whole Body Vibration, which discussed the possible health benefits of this treatment while recognising the possible ill health consequences of vibration as well. It looks like for it to be beneficial it needs to be of a particular frequency and or amplitude which is different to that you might encounter while working with vibrating work equipment.  If you are concerned about the health risks from this or any other piece of gym equipment, just ban it.