On March 11, 1998, about 1145 Alaska standard time, a Boeing 737-205 airplane, N733AR, had rapid, uncommanded, rudder movement while parking at the gate at Anchorage International Airport, Anchorage Alaska. The airplane was operated by Arco Alaska, Inc., under 14 CFR Part 91, between Prudhoe Bay, Alaska, and Anchorage. There were no injuries to the two pilots, three flight attendants, or the 76 passengers on board. During a telephone conversation with the NTSB investigator on March 11, the Captain indicated that while on the ground in Prudhoe Bay, the crew felt a momentary airframe vibration. The airplane then departed Prudhoe Bay for Anchorage. On arrival in Anchorage, while completing the shut down check list, the crew again felt a moderate vibration. Ground personnel outside the airplane noted a rapid movement of the rudder which vibrated the entire airframe. During maintenance troubleshooting, while on ground power, application of rudder resulted in a severe airframe vibration. Ground personnel reported the rudder was moving at a very high rate of speed. Ground tests conducted on March 14, 1998, involving the NTSB, FAA, Boeing, Honeywell, and Arco Alaska personnel, determined that the yaw damper coupler (YDC), part number 403952-906, was producing oscillatory inputs to the rudder actuator. Rudder excursions were observed to be +/- 1.5 degrees either side of centerline, at an estimated frequency of 4 to 6 cycles per second. The yaw damper mechanical authority limit is +/- 3 degrees either side of centerline. The YDC was removed and tested at Honeywell's northwest service center, Renton, Washington, on April 22, 1998. All parties were in attendance. Acceptance tests were completed as per MM-15-1141-18, Revision 1. A mechanical grinding noise was audible when the unit was operated. Tests were conducted at room temperature, after oven heating, and after cold soaking. All tests were passed with near nominal values, except for yaw rate gyro output. The yaw rate gyro, part number 2589124-902, was tested, and then disassembled for inspection at Honeywell's Phoenix, Arizona, facility on June 12, 1998, under the supervision of an NTSB investigator. The gyro failed the output oscillation tests. Disassembly revealed lack of lubrication and spalling to the spin bearings, and heavy false brinnelling to the gimbal bearings. A review of maintenance records revealed that during the previous three months, several transient, vibratory, discrepancies had been noted by flight crews, both on the ground and in-flight. No airplane control difficulties were experienced. Maintenance troubleshooting of each occurrence yielded a correctable discrepancy, unrelated to the yaw damp coupler. The YDC and the mechanical yaw rate gyro assembly had both accumulated 24,850 hours in operation. Airworthiness Directive (AD) 98-02-01 of February 17, 1998, requires the replacement of the yaw rate gyro within 3,000 hours of the effective date of this AD if the unit has accumulated more than 12,000 hours, and thereafter each 9,000 hours. Prior to AD 98-02-01, there was no life limit imposed on the yaw rate gyros installed in B-737 series airplanes. At the time of the incident, the YDC had accumulated about 150 hours since the AD became effective. Replacement of this YDC was not required for another 2,850 hours.