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FREE VIBRATION OF BIMATERIAL&NBSP;CIRCULAR NANO-TUBE&NBSP;IS INVESTIGATED.&NBSP;THE TUBE IS FORMED BY BONDING TOGETHER A SI3N4/SUS304 FUNCTIONALLY GRADED UPPER SEMI TUBE AND A ZRO2/TI-6AL-4V FUNCTIONALLY GRADED LOWER SEMI TUBE. THE MATERIAL PROPERTIES OF THE TUBE ARE ASSUMED TO VARY ALONG THE RADIUS ACCORDING TO POWER LAW WITH THE POWER INDEX OF UPPER SEMI TUBE DIFFERING FROM THAT OF LOWER SEMI TUBE. BASED ON NON-LOCAL ELASTICITY THEORY AND HAMILTON’S PRINCIPLE, A REFINED BEAM MODEL TAKING&NBSP;INTO ACCOUNT THE EFFECT OF TRANSVERSE SHEAR DEFORMATION IS USED TO DERIVE THE GOVERNING EQUATIONS,&NBSP;THEN ANALYTICAL SOLUTION IS OBTAINED BY USING A TWO-STEPS PERTURBATION METHOD. COMPARISON OF EXISTING RESULTS WITH OURS IS PERFORMED TO VALIDATE THE PRESENT ANALYSIS.&NBSP;THE EFFECTS&NBSP;ON TUBE’S LINEAR AND NON-LINEAR FREQUENCY ARE ANALYZED OF THE FACTORS, INCLUDING SMALL SCALE PARAMETER, TEMPERATURE, THE DOUBLE VOLUME FRACTION INDEXES, SLENDERNESS RATIO AND DIFFERENT TYPES OF BEAM MODEL. A NEW APPROACH IS FOUND IN THIS ARTICLE&NBSP;TO CHANGE THE NATURAL FREQUENCY OF THE TUBES BY ADJUSTING CONSTITUENT&NBSP;MATERIALS. IN CONTRAST TO CONVENTIONAL APPROACH, THE PRESENT ONE CAN RESULT IN MORE ACCURATE FREQUENCY CONTROL IN THE SAME&NBSP;DIMENSIONLESS SIZE OF TUBES.
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