The answer to your question will be dependent on the situation.
Exhaust systems are usually left until the end of the design process.
The engine will be attached to the chassis through flexible mounts.
The exhaust system bridges those flexible mounts. Something has to give.
A critical point will be the coupling between the exhaust manifold and the engine pipe.
Dampers that prevent movement are different to flexible mounts that allow movement.
Fitting dampers to the engine pipe may hold the exhaust system steady while the engine is vibrating. That may focus energy onto the manifold coupling resulting in failure.
Mechanical vibration energy from the engine flows along the exhaust system like a transmission line. Destructive vibration can be reduced by preventing the reflection of energy from the mountings or from the open end of the system.
The exhaust pipe should have sufficient bends near the manifold to isolate the longitudinal mode of vibration. It should also be made from the smallest diameter tube with the lightest wall. Unfortunately, bends are expensive and make fitting difficult, small tubes have poor flow capacity and thin walls rust out quickly.
You are designing a compromise. Cost, mass and reliability will be your design constraints.