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A PROBLEM OF BIG PRACTICAL INTEREST IN ENGINEERING IS THE ANALYSIS OF COUPLED AND UNCOUPLED FREE VIBRATION OF CYLINDRICAL SHELLS. CLOSED-FORM SOLUTIONS ARE EXTREMELY COMPLEX, SINCE THEY INVOLVE MANY TERMS AND ALGEBRAIC OPERATIONS THAT HAVE TO BE SOLVED NUMERICALLY. IN THIS WORK, A SIMPLIFIED CLOSED-FORM SOLUTION FOR THE FREE VIBRATION ANALYSIS OF AN EMPTY OR FILLED WITH AN INVISCID AND INCOMPRESSIBLE FLUID CYLINDRICAL TANK IS PRESENTED. THE PROPOSED ANALYTICAL METHOD IS DEVELOPED FOR A SIMPLY SUPPORTED SHELL, BASED ON AN ENERGY FORMULATION OBTAINED WITH VARIATIONAL CALCULUS. THE FLUID IS REPRESENTED BY AN ACOUSTIC CAVITY, MODELED BY THE WAVE EQUATION, AND THE FLUID-STRUCTURE INTERACTION (FSI) IS DONE BY CONSIDERING AN ADDED MASS OF FLUID IN THE UNCOUPLED SHELL EQUATIONS OF MOTION. A FINITE ELEMENT METHOD (FEM) NUMERICAL MODEL WAS BUILT USING THE SOFTWARE ANSYS TO VALIDATE THE CALCULATION METHODOLOGY PRESENTED HERE. THE NATURAL FREQUENCIES AND MODAL SHAPES WERE STUDIED, AND THE RESULTS OBTAINED HERE ARE CONSISTENT WITH ANALYTICAL, NUMERICAL AND EXPERIMENTAL RESULTS FOUND IN THE LITERATURE.
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