DC9-10 FLC HAS MASTER CAUTION WARNING LIGHT ACTIVATE AT CRUISE. THE R OIL STRAINER CLOGGING ANNUNCIATOR LIGHT ACTIVATES. FOLLOWING CHKLIST PROCS; AN INFLT ENG SHUTDOWN IS EXECUTED ALONG WITH DIVERTING TO NEARBY ARPT. UNABLE TO CONTACT DISPATCH UNTIL AFTER LNDG.

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SCHEDULED PAX FLT ENRTE FROM MEM TO MSP AT FL350; CLR AND SMOOTH. JUST PASSED OVER IOW VOR; APPROX 10 MI N HDG DIRECT ALO VOR; CAPT PF; FO PNF. BOTH PLTS SIMULTANEOUSLY NOTICED AMBER ANNUNCIATOR LIGHT FLICKERING; ALONG WITH AMBER MASTER CAUTION WARNING LIGHT COMING ON. AMBER ANNUNCIATOR WAS THE 'R OIL STRAINER CLOGGING.' CAPT CONTINUED FLYING AND WORKING RADIOS WHILE FO COMPLETED ABNORMAL CHKLIST. WITHIN SECONDS OF THAT CHKLIST COMPLETION; THE AMBER ANNUNCIATOR 'R OIL PRESSURE LOW' ILLUMINATED. R OIL STRAINER CLOGGING LIGHT HAD REMAINED ILLUMINATED ALONG WITH MASTER CAUTION LIGHT. CAPT CONTINUED FLYING AND RADIOS WHILE FO COMPLETED ABNORMAL CHKLIST. OIL PRESSURE ON R ENG HAD DROPPED BELOW 35 PSI; WHICH IS THE MINIMUM ACCEPTABLE PER THAT ABNORMAL CHKLIST. PROCEEDED WITH PRECAUTIONARY ENG SHUTDOWN CHKLIST FOR R ENG. CAPT DECLARED EMER AND REQUESTED DIVERSION TO NEAREST SUITABLE ARPT. ATC VECTORED ACFT TO DSM. FLT ATTENDANTS AND PAX WERE BRIEFED ACCORDINGLY. CAPT REQUESTED EQUIP STANDING BY IN DSM. VECTORED FOR VISUAL APCH TO RWY 31R DSM. A FLAWLESS APCH BY CAPT AND SMOOTH LNDG AND ROLLOUT WITHOUT INCIDENT. TAXIED TO GATE AS NORMAL; AND PAX DEPLANED VIA JETWAY. THE MOST DISTRACTING AND FRUSTRATING ASPECT OF THIS EVENT WAS OUR INABILITY TO RAISE OUR DISPATCHER VIA RADIO. BOTH CAPT AND FO TRIED SEVERAL TIMES ON NUMEROUS COMPANY FREQS; WITH NO SUCCESS. ULTIMATELY; FO SENT NOTICE OF SHUTDOWN AND DIVERSION BY ACARS 30 MINS AFTER SHUTDOWN AND COMPLETION OF ALL CHKLISTS AND BRIEFINGS. ALSO; ACFT PREFLT INSPECTION BY FO IN MEM REVEALED NO UNUSUAL CONDITIONS OR OIL LEAK ASSOCIATED WITH R ENG. CALLBACK CONVERSATION WITH RPTR ACN 371363 REVEALED THE FOLLOWING INFO: ACFT WAS A DC9-10 WITH JT8D-7 ENGS. MAINT HAS NOT RPTED THE CAUSE OR CORRECTIVE ACTION TAKEN FOR THIS ENG. WHEN THE FLT CREW WERE ON THE GND IN DSM; THEY LEFT A TRAIL OF OIL FROM THE RWY TO THE GATE. AFTER PARKING; THE REMAINING ENG OIL FORMED A LARGE POOL UNDER #2 ENG. NO PREVIOUS MAINT ACTION WAS INDICATED IN THE LOGBOOK REGARDING THE ENG OIL SYS. THE RPTR WAS NOT CONTACTED BY THE FAA.