A Comparison of Some Thin Shell Theories Used for the Dynamic Analysis of Stiffened Cylinders

Free-Vibration Analysis of Ring-Stiffened Branched Composite Shells of Revolution

“…A ij = extensional stiffness coefficients (i; j 1, 2, 6) As ij = transverse shear stiffness coefficients (i; j 4, 5) B ij = bending-stretching coupling stiffness coefficients (i, j 1, 2, 6) D ij = bending stiffness coefficients (i; j 1, 2, 6) E 1 = Young's modulus in the fiber direction E 2 = Young's modulus transverse to fiber G 12 = in-plane shear modulus G 23 , G 13 = transverse shear moduli h = thickness of the shell wall During the filament-winding process, filaments are usually placed in arbitrary orientation with respect to the geometric axis of the shell of revolution. In the present state of the art, the filament-winding process is usually applied by using geodesic paths.…”

“…Most of the other work on the ringstiffened composite shells of revolution has been primarily on shells without any branch and on cylindrical shells of revolution. Ruotolo [13] studied the dynamics of shells of revolution reinforced with ring stiffeners and compared the Donnell, Love, Sanders, and Flügge thin-shell theories in the evaluation of natural frequencies of cylinders stiffened with rings. In [13] results were obtained for isotropic and specially orthotropic cylinders that were simply supported at the edges.…”

“…Ruotolo [13] studied the dynamics of shells of revolution reinforced with ring stiffeners and compared the Donnell, Love, Sanders, and Flügge thin-shell theories in the evaluation of natural frequencies of cylinders stiffened with rings. In [13] results were obtained for isotropic and specially orthotropic cylinders that were simply supported at the edges. Xiang et al [14] presented an analytical method based on the state-space technique and domain-decomposition approach to determine the natural frequencies of isotropic cylindrical shells having multiple intermediate ring supports and various combinations of end-support conditions.…”

“…In the following, to keep the uniformity of the notation used for the partitioned fundamental variable vector, the boundary conditions are also represented by the same vector notation defined by Eqs. (13) and (14). Therefore, the boundary condition at the ends of the branched shell of revolution is expressed by…”

Free vibration and dynamic response analysis of stiffened parabolic shells using equivalent orthotropic shell parameters

“…A comprehensive review has recently been given by Xu et al [4] about vibration of stiffened plates. Replacement of stiffened structures with the equivalent unstiffened orthotropic structures has been performed only in the case of stiffened plates [1][2][3][4][5][6][7] and curved stiffened shells with constant radius of curvature [8][9][10][11][12][13][14][15][16][17]. Srinivasan [16] studied dynamic analysis of stiffened conical shell panels wherein the smearing technique is used for closely spaced stiffeners and the time domain analysis has been done using the mode superposition method.…”