DYNAMIC ANALYSIS AND CRITICAL SPEED OF ROTATING LAMINATED CONICAL SHELLS WITH ORTHOGONAL STIFFENERS USING GENERALIZED DIFFERENTIAL QUADRATURE METHOD

Abstract

THIS PAPER PRESENTS BOUNDARY CONDITIONS AND AXIAL LOAD INFLUENCES ON FREQUENCY CHARACTERISTICS OF A ROTATING LAMINATED CONICAL SHELLS WITH MERIDIONAL AND CIRCUMFERENTIAL STIFFENERS, I.E., STRINGERS AND RINGS, BY USING GENERALIZED DIFFERENTIAL QUADRATURE METHOD (GDQM). HAMILTON’S PRINCIPLE IS APPLIED WHILE THE STIFFENERS ARE TREATED AS DISCRETE ELEMENTS. THE CONICAL SHELLS ARE STIFFENED WITH UNIFORM INTERVAL AND IT IS ASSUMED THAT THE STIFFENERS HAVE THE SAME MATERIAL AND GEOMETRIC PROPERTIES. THE EQUATIONS OF MOTION AS WELL AS THE BOUNDARY CONDITION EQUATIONS ARE TRANSFORMED INTO A SET OF ALGEBRAIC EQUATIONS BY APPLYING THE GDQM. THE RESULTS DISCUSS THE EFFECTS OF PARAMETERS SUCH AS ROTATING VELOCITIES, DEPTH TO WIDTH RATIOS OF THE STIFFENERS, NUMBER OF STIFFENERS, CONE ANGLES, AND BOUNDARY CONDITIONS ON NATURAL FREQUENCY OF THE SHELL. THE PRESENT RESULTS ARE COMPARED WITH THOSE OF OTHER PUBLISHED WORKS PARTICULARLY WITH A NON-STIFFENED CONICAL SHELL AND A SPECIAL CASE WHERE THE ANGLE OF THE STIFFENED CONICAL SHELL APPROACHES ZERO, I.E. A STIFFENED CYLINDRICAL SHELL. IN ADDITION ANOTHER COMPARISON IS MADE WITH PRESENT FE METHOD FOR A NON-ROTATING STIFFENED CONICAL SHELL. THESE COMPARISONS CONFIRM THE RELIABILITY OF THE PRESENT WORK AS A BENCHMARK TO APPROXIMATE SOLUTIONS TO THE PROBLEM OF ROTATING STIFFENED CONICAL SHELLS.