Exhaust systems are meant to move some on every car. However, if you’re moving it enough for it to make contact with other components such as the uni-body or chassis/suspension components, that'* a sign the hangers themselves (the little rubber things) are probably stretched out and/or loose.
I noticed this in the rear of mine this morning coming to work but it may just be some of the loose stuff I have in my trunk.
If it is something in the suspension, you should be able to note it when driving repeatedly over the part of the road causing the noise as to whether or not it'* a suspension clunk or something clunking in reaction to the vehicle'* composure. Chassis problems can sometimes be difficult to diagnose as when you're checking them out in the driveway, what to yo physically may be tight, may not be when 3,600 pounds of car are on it. Unless you somehow magically can hang under the car while someone else drives.