WRONG ARPT RWY APCH. UNAUTH PENETRATION OF AIRSPACE; PROX OF D AIRSPACE.

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UPON ARRIVING IN THE BNA TERMINAL AREA; WINDS WERE RPTED 310 DEGS AT 33 KTS GUSTING 43 KTS. RWYS 2L/R IN USE. AS WE NEARED; ACFT WERE EXECUTING MISSED APCHS DUE TO THE WIND CONDITIONS. RWY 31 WAS CLOSED DUE TO TXWY CONSTRUCTION. AS THE ARPT WAS EFFECTIVELY CLOSED; WE WERE INFORMED RWY 31 WAS GOING TO BE OPENED IN 10-15 MINS. WE WERE THEN GIVEN A 'RADAR VECTOR HOLDING PATTERN' SW OF THE ARPT APPROX 15-25 DME AT 7000 FT MSL; FOR APPROX 25 MINS. AS RWY 31 WAS OPENED WE WERE STEPPED DOWN TO 6000 FT MSL; THEN 3000 FT MSL. AT APPROX 20 DME AND 3000 FT WE WERE CLRED FOR THE VISUAL APCH ON A HDG OF 310 DEGS. THIS PLACED SMYRNA ARPT RWY 32 AT 1200 FT AND APPROX 10 MI. WE CALLED THE ARPT IN SIGHT THINKING SMYRNA ARPT RWY 32 WAS ACTUALLY BNA RWY 31. NO LOC WAS OPERATING FOR BNA RWY 31; BUT DME OFF BNA WAS IN USE. DSCNT FOR LNDG WAS INITIATED AT APPROX 5 MI FINAL FOR SMYRNA RWY 32. DME READ 15 ME AND OM FLASHED ON EADI. I EVEN MADE A COMMENT 'OM AT 15 OUT?' BUT STILL CALLED FOR GEAR DOWN; AND ADDITIONAL BEFORE LNDG CHKLIST ITEMS NOT LOOKING TO SEE IF DME ON FIELD. AS THE CAPT WAS CALLING THE BEFORE LNDG CHKLIST; BNA TWR CALLED US TO GAR AND INFORMED US WE WERE LINED UP WITH SMYRNA RWY 32. GAR WAS EXECUTED ON A 2 MI FINAL AT APPROX 1200 FT MSL. WE CLBED STRAIGHT AHEAD TO 2500 FT MSL AND LANDED BNA RWY 31 UNEVENTFULLY WITH NO COMMENTS FROM PAX. CONTRIBUTING FACTORS WERE: RELATIVELY SIMILAR RWY LENGTH AND WIDTH. DELAY IN APCH AND LNDG. WX CONDITIONS (MODERATE TURB). CONCERN OVER POSSIBLE XWIND LNDG. CONCERN WITH NUMEROUS ACFT VFR HOLDING IN CLOSE PROX. NO OPERATING EXPERIENCE APCHING FOR RWY 31 BNA. NO LOC GS. I SHOULD HAVE CAUGHT MISTAKE WHEN DME READ 15 AND OM; BUT DID NOT LOOK TO SEE IF DME WAS LOCATED ON FIELD. I SAW WHAT I THOUGHT WAS CORRECT RWY AND FIXATED ON IT. SUPPLEMENTAL INFO FROM ACN 266356: DUE TO OUR LOW ALT 3000 FT AND LONG DISTANCE 20 DME FROM BNA; WE COULD NOT SEE BNA ON THE HORIZON. BOTH OF US ASSUMED DME DISCREPANCY DUE TO VOR BEING OFF ARPT (ERRONEOUSLY); BUT WE DIDN'T CONFIRM THIS DUE TO MODERATE TURB AND VISUAL ON RWY. BNA NEVER TURNED ON ILS/DME TO RWY 31 (COULD HAVE BEEN INOP DUE TO CONSTRUCTION). OUR ALT OF 3000 FT AT 26 MI OUT HAD US TOO LOW TO DETECT THE CORRECT ARPT ON THE HORIZON. I THANK THE BNA TWR CTLR FOR NOTING OUR ERROR IN TIME; BUT PERHAPS THE ERROR COULD HAVE BEEN DETECTED EARLIER; WHEN WE CALLED 5 MI OUT AND WE WERE 10 MI INSTEAD. THIS WAS A BUSY ARR TIME FOR BNA AND HE MAY HAVE NOT HEARD OUR CALLOUT DUE TO A POSSIBLE BLOCKED XMISSION.