Hi Jimbob,
You will have an inboard diaphragm pump, and these like a car engine have reciprocating components, hence the vibration. Some times it can be damped by mounting it in a resilient pad or squashy washers, or even relocating it to a more solid part of the caravan structure, but when it runs it will always vibrate.
Chrissylissie's solution to ad a surge damper, may help reduce the number of times the pump runs, but when it does it will run for a bit longer.
If the noise is too much for you, then the only real alternative is to remove your pump, replace it s with a pressure switch and none return valve (Usually built into the pressure switch), and fit an external pump connection unit and use a submersible centrifugal pump which is almost silent inside the caravan.