Ventilation Problem: Centrifugal Exhaust Fan

Place flat or hemi-spherical rubber washers under the attachment points of the grill terminal. This will isolate the grill from the surface that is vibrating. The rubber washers that are used in water faucets work great for this type of aplication and are inexpensive and durable.

If the problem is air noise through the grille ,then line the duct with a suitable

accoustic duct liner.Increase size of duct and use bigger terminal to slow down air velocity would also suggest flexible connection between fan and and duct.

If the problem is noise from the ceiling area then wrap the system with an accoustic

material. would also ensure fan is mounted on A/vs (isolated from structure)

In order:

Nothing with a motor (the fan) should have hard/direct contact to the structure supporting it. This means that you need to "hang it" with a spring or elastomeric isolation, or mount it on top of the same kind of isolation elements, sitting on a structural member.

Make sure that final connections to grille and fan are flexible. This is taken care of if you use a flexible duct (spiral-wound, usually) for the entire run.

Use the largest reasonable duct size.
- Airflow noise: 6" is quieter than 4" duct which is quieter than the 3" that often comes packed with a toilet fan (never use anything smaller, and know they packed it with the fan because it's the cheapest).
- Impregnated fabric duct is quieter than plastic
- Insulated duct is quieter than non-insulated.

Fan noise: Every change of direction >90 deg cuts the noise, but raises the static pressure (reduces the fans throughput), so if you put in a couple of S-bends, use a larger duct.