NATURAL FREQUENCIES AND CRITICAL VELOCITIES OF FIXED-FIXED LAMINATED CIRCULAR CYLINDRICAL-SHELLS CONVEYING FLUIDS

The natural frequencies and critical velocities of laminated circular cylindrical shells with fixed-fixed ends conveying fluids are studied. Equations of motion are derived by the Hamilton principle under the s cope of the Mindlin-type first-order transverse shear deformable cylin drical shell theory. Fluid pressure acting on the wall is obtained thr ough the nonpenetration condition and the assumption of ideal flow. Dy namic characteristic equations are then obtained under the assumption of harmonic motion. Using linear superposition, the natural frequencie s corresponding to each flow velocity are found by satisfying dynamic characteristic equation and boundary conditions. Critical velocities a re those where the natural frequencies vanish, wherein the static dive rgence, i.e. buckling, occurs. Numerical examples are presented, in wh ich the parameter studies include stacking angle, length-to-thickness and radius-to-thickness ratios.