NON AXISYMMETRIC FREE VIBRATION ANALYSIS OF LINEARLY VARYING THICKNESS
AbstractA BI-HIERARCHICAL FOUR NODES QUADRILATERAL ELEMENT WITH THREE DISPLACEMENTS AS DEGREES OF FREEDOM BY NODE IS DEVELOPED TO ANALYZE THE FREE VIBRATION OF ISOTROPIC SHELLS OF REVOLUTIONWITH LINEARLY VARYING THICKNESS. THE ELEMENT IS BI-HIERARCHICAL BECAUSE OF THE DOUBLE INCREASE OF THE HIERARCHICAL MODE NUMBER INDEPENDENTLY ACCORDING TO BOTH AXIAL AND RADIAL DIRECTIONS. THE ACCURACY OF SOLUTION IS FOR HIGH RATIO DIMENSIONS AS WELL FLATTENED AXISYMMETRIC (PLATES) SHELLS THAT SLIM ONES (HIGH CYLINDRICAL SHELLS) WITH DIFFERENT SHAPES AND BOUNDARY CONDITIONS. THE SECOND ADVANTAGE IS THE POSSIBILITY OF USING ONLY ONE ELEMENT TO IDEALIZE COMPOSED SHELLS OF LINEARLY VARYING THICKNESS. THROUGH THE APPLICATION OF THIS ELEMENT TO SOME NUMERICAL EXAMPLES, THE COMPARISONS WITH OTHER STUDIES SHOW CLEARLY THAT THIS ELEMENT GIVES GOOD RESULTS ACCURACY WITH SIMPLE IDEALIZATION FOR AXISYMMETRIC AND NON-AXISYMMETRIC SHELLS VIBRATION (THICK AND THIN).
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