Dovetail seals are quickly and inexpensively applied to turbine buckets or rotor disks by ultrasonically welding a piece of material onto the dovetail portion of the bucket or the disk slot of the rotor disk. The method includes placing the piece of material into contact with the appropriate turbine structure and applying a compressive force so as to press the piece of material against the turbine structure. Ultrasonic energy is then applied to the piece of material so as to ultrasonically weld it to the turbine structure.