A seal assembly for a turbomachine includes a plurality of compliant plate members attached to an interior surface of a stationary housing. The compliant plate members define a sealing ring between the stationary housing and a rotor. Each of the compliant plate members comprises at least one slot therein. The seal assembly further includes at least one arcuate static ring attached to the interior surface of the stationary housing and extending radially into the at least one slot in the compliant plate members. Each of the at least one static ring extends circumferentially through and between a plurality of the compliant plate members. Finally, the seal assembly includes a vibration damper disposed adjacent to or provided on the plurality of compliant plate members. The vibration damper is configured to dampen vibration of the plurality of compliant plate members.