Abstract
NATURAL FREQUENCIES ARE IMPORTANT DYNAMIC CHARACTERISTICS OF A STRUCTURE THAT THESE ARE REQUIRED FOR THE FORCED VIBRATION ANALYSIS AND SOLUTION OF RESONANT RESPONSE. THEREFORE, THE EXACT SOLUTION TO FREE VIBRATION OF ELASTICALLY RESTRAINED TIMOSHENKO BEAM ON AN ARBITRARY VARIABLE ELASTIC FOUNDATION USING GREEN FUNCTION PRESENTS IN THIS PAPER. AN EXACT AND DIRECT MODELING TECHNIQUE IS INTRODUCED FOR MODELING UNIFORM TIMOSHENKO BEAM WITH ARBITRARY BOUNDARY CONDITIONS. THE APPLIED METHOD IS BASED ON THE GREEN FUNCTION. THE EFFECT OF THE TRANSLATIONAL AND ROTATIONAL SUPPORT FLEXIBILITIES, THE ELASTIC COEFFICIENT OF WINKLER FOUNDATION AND OTHER PARAMETERS IS ASSESSED. FINALLY, SOME NUMERICAL EXAMPLES ARE SHOWN TO PRESENT THE EFFICIENCY AND SIMPLICITY OF THE GREEN FUNCTION IN THE NEW FORMULATION.
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