AT 0729 CDT THE PLT FILED A FLIGHT PLAN AND OBTAINED A WX BRIEF FORECASTING MOIST UNSTABLE AIR WITH SEVERAL SCATTERED AND BROKEN CLOUD LAYERS BEGINNING AT 1,500 FT. THE BRIEFER FURTHER ADVISED THE PLT OF THUNDERSTORM ACTIVITY AT VARIOUS LOCATIONS ALONG THE PROPOSED ROUTE OF FLIGHT. AT 0855, THE ACFT DEPARTED AND CLIMBED TO 8,000 FT. ACCORDING TO THE PLT, ABOUT 1/2 HR INTO THE FLIGHT A 'HEAVY LAYER OF CLOUDS' WERE SEEN AHEAD, AT AND BELOW HIS CRUISING ACT. A DESCENT TO 4,000 FT WAS REQUESTED AND GRANTED BY ARTCC. AT0926 THE PLT ASKED LAFAYETTE APCH CONTROL WHICH WAY THE WX WAS MOVING AND THAT THEY WERE IN SOME 'ROUGH STUFF'. FOR APRX THE NEXT 23 MIN THE ACFT REPEATEDLY ENCOUNTERED AREAS OF TURBULENCE VIOLENT ENOUGH TO CAUSE SUBSTANTIAL AIRFRAME DAMAGE AND RENDER SOME OF THE FLT INSTRUMENTS INOP. THE ACFT WAS VECTORED OUT OF THE WX AND TO AN ALTERNATE ARPT. AT 0957 A WX ADVISORY WAS ISSUED WHICH WARNED OF A LINE OF LEVEL 3 TO 5 THUNDERSTORMS ALONG THE ACFT'S ROUTE. HOWEVER, THE PLT TOOK OF AT 0900 & WAS NOT AWARE OF THE ADVISORY.