On the basis of the thin-shell theory and on the use of the transfer matrix approach, this paper presents the vibrational response and buckling analysis of three-lobed cross-section cylindrical shells, with circumferentially varying thickness, subjected to uniform axial membrane loads. A Fourier approach is used to separate the variables, and the governing equations of the shell are formulated in terms of eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations are written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells with variable thickness by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The natural frequencies and critical loads beside the mode shapes are calculated numerically in terms of the transfer matrix elements for the symmetrical and antisymmetrical vibration modes. The influences of the thickness variation of cross- section and radius v
J. B. Greenberg and Y. Stavsky, “Vibrations of Axially Compressed Laminated Orthotropic Cylindrical Shells, Including Transverse Shear Deformation,” Acta Mechanica, Vol. 37, No. 1-2, 1980, pp. 13-28. doi:10.1007/BF01441240
J. B. Greenberg and Y. Stavsky, “Stability and Vibrations of Compressed Aeolotropic Composite Cylindrical Shells,” Journal of Applied Mechanics, Vol. 49, No. 4, 1982, pp. 843-848. doi:10.1115/1.3162625
J. B. Greenberg and Y. Stavsky, “Vibrations and Buckling of Composite Orthotropic Cylindrical Shells with Nonuniform Axial Loads,” Composites Part B: Engineering, Vol. 29, No. 6, 1998, pp. 695-702. doi:10.1016/S1359-8368(98)00029-8
G. Yamada, T. Irie and M. Tsushima, “Vibration and Stability of Orthotropic Circular Cylindrical Shells Subjected to Axial Load,” Journal of Acoustical Society of America, Vol. 75, No. 3, 1984, pp. 842-848. doi:10.1121/1.390594
G. Yamada, T. Irie and Y. Tagawa, “Free Vibration of Non-Circular Cylindrical Shells with Variable Circumferential Profile,” Journal of Sound and Vibration, Vol. 95, No. 1, 1984, pp. 117-126. doi:10.1016/0022-460X(84)90264-5
K. Suzuki and A. W. Leissa, “Free Vibrations of Noncircular Cylindrical Shells Having Circumferentially Varying Thickness,” Journal of Applied Mechanics, Vol. 52, No. 1, 1985, pp. 149-154. doi:10.1115/1.3168986
R. M. Bergman, S. A. Sidorin and P. E. Tovstik, “Construction of Solutions of the Equations for Free Vibration of a Cylindrical Shell of Variable Thickness along the Directrix,” Mechanics of Solids, Vol. 14, No. 4, 1979, pp. 127-134.
W. I. Koiter, I. Elishakoff, Y. W. Li and J. H. Starness, “Buckling of an Axially Compressed Cylindrical Shell of Variable Thickness,” International Journal of Solids and Structures, Vol. 31, No. 6, 1994, pp. 797-805. doi:10.1016/0020-7683(94)90078-7
H. Abdullah and H. Erdem, “The Stability of Non-Homogenous Elastic Cylindrical Thin Shells with Variable Thickness under a Dynamic External Pressure,” Turkish Journal of Engineering and Environmental Sciences, In Turkish, Vol. 26, No. 2, 2002, pp. 155-164.
S. B. Filippov, D. N. Ivanov and N. V. Naumova, “Free Vibrations and Buckling of a Thin Cylindrical Shell of Variable Thickness with Curelinear Edge,” Technische Mechanik, Vol. 25, No. 1, 2005, pp. 1-8.