Recording vibration is difficult. It is not a problem to record movements over a short period of time. You can use an accelerometer connected to a recorder. From these recordings you are able to integrate movement speed and displacement. But the problem is you very soon just get to many data.
You have following options. You can measure your trucks over a short period of time and analyse the data. But then you have to be aware of that both speed and loads on the truck give a lot of change in the vibration. Another problem is you can expect a lot of different trucks to be used. So you have to design to all kind of different trucks, superstructure design, and loads, and speeds, and road structure.
You either have to ask your supplier what to expect or trust institutes measurements. Do not trust transport suppliers promising vibration free transport.
Vibration free transport does not exist.