MD-11 Captain reported Engine 3 Lubrication System malfunction during cruise resulting in airframe vibration. After troubleshooting the issue; the flight crew shutdown the engine and requested priority handling to a diversion airport.

Narrative

Experienced airframe vibration while at FL350. Engine parameters normal. No abnormal indications on any system display pages. Vibration seemed to be coming from the right side of the airplane. Decreased #3 throttle to troubleshoot. The vibration decreased but we received a Level 2; ENG 3 OIL FILTER Alert. Consulted QRH. Alert did not clear with throttle at idle. Shutdown engine as directed by referring to Abnormal Non-Alert Procedure - ENGINE SHUTDOWN IN FLIGHT. Received clearance to descend FL310. Contacted Dispatch to inform them of our situation and get their input on our options. We decided to divert to ZZZZ. Dispatch provided us with their preferred routing and fuel burn numbers. Requested priority handling and routing to ZZZZ received from ZZZZ control. Landed Runway XXL. Priority handling terminated upon clearing runway.Cause: #3 engine making metal and clogging the oil filter triggering an ENG 3 OIL FILTER Alert & QRH Directed Action of Engine shutdown inflight with subsequent diversion to ZZZZ.