A laundry appliance includes a cabinet. A rotating drum is positioned within the cabinet. A blower directs process air through an airflow path. The airflow path includes the drum. A motor is coupled to the cabinet via a retaining bracket. The motor includes a drive shaft operably coupled to one of the drum and the blower. A damping ring is positioned about the drive shaft and between the motor and the retaining bracket. Damping apertures are defined within a body of the damping ring. The damping apertures define respective voids that absorb operational vibrations generated by the motor in an activated state.