Vibration Analysis of Shear Deformable Cylindrical Shells Made ‎of Heterogeneous Anisotropic Material with Clamped Edges

Document Type : Research Paper


Department of Civil Engineering, Istanbul Medeniyet University, Uskudar, Istanbul, 34700, Türkiye‎


The vibration behavior of moderately-thick inhomogeneous orthotropic cylindrical shells under clamped boundary conditions based on first-order shear deformation theory (FOSDT) is investigated using an analytical approach. The basic relationships for cylindrical shells composed of inhomogeneous orthotropic materials are established, and then partial differential equations of motion are derived in the framework of FOSDT. The analytical expression for frequency is found for the first time using the special approach for clamped boundary conditions. After checking the accuracy of obtained expressions, the effects of shear stress, orthotropy ratio and inhomogeneity on frequency values are examined in detail.


Main Subjects

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[1] Lomakin, V.A., Theory of Elasticity of Inhomogeneous Bodies, Publishing House of Moscow State University, Moscow, 1976.
[2] Lekhnitsky, S.G., Anisotropic Plates, Gostekhizdat, Moscow, 1957.
[3] Ambartsumyan, S.A., Theory of Anisotropic Shells, NASA, TT F–118, 1964.
[4] Kravchuk, A.S., Mayboroda, V.V., Urzhumtsev, Yu.S., Mechanics of Polymeric and Composite Materials, Nauka, Moscow, 1985.
[5] Babich, D.V., Khoroshun, L.P., Stability and Natural Vibrations of Shells with Variable Geometric and Mechanical Parameters, International Applied Mechanics, 37, 2001, 837–869.
[6] Pan, E., Exact Solution for Functionally Graded Anisotropic Composite Laminates, Journal of Composite Materials, 37, 2003, 1903-1920.
[7] Awrejcewicz, J., Krysko A.V., Mitskevich, S.A., Zhigalov, M.V., Krysko, V.A., Nonlinear Dynamics of Heterogeneous Shells Part 1. Statics and Dynamics of Heterogeneous Variable Stiffness Shells, International Journal of Non-Linear Mechanics, 130, 2021, 103669.
[8] Krysko, A.V., Awrejcewicz, J., Bodyagina, K.S., Krysko, V.A., Mathematical Modeling of Planar Physically Nonlinear Inhomogeneous Plates with Rectangular Cuts in the Three-Dimensional Formulation, Acta Mechanica, 232, 2021, 4933–4950.
[9] Sofiyev, A.H., Kuruoglu, N., Halilov, H.M., The Vibration and Stability of Non-Homogeneous Orthotropic Conical Shells with Clamped Edges Subjected to Uniform External Pressures, Applied Mathematical Modeling, 34(7), 2010, 1807-1822.
[10] Sofiyev, A.H., On the Vibration and Stability of Clamped FGM Conical Shells under External Load, Journal of Composite Materials, 45(7), 2011, 771-788.
[11] Shen, H.S., Noda, N., Postbuckling of Pressure-Loaded FGM Hybrid Cylindrical Shells in Thermal Environments, Composite Structures, 77(4), 2007, 546-560.
[12] Brunetti, M., Vincenti, A., Vidoli, S., A Class of Morphing Shell Structures Satisfying Clamped Boundary Conditions, International Journal of Solids and Structures, 82, 2016, 47-55.
[13] Babaei, H., Kiani, Y., Eslami, M.R., Thermal Buckling and Post-Buckling Analysis of Geometrically Imperfect FGM Clamped Tubes on Nonlinear Elastic Foundation, Applied Mathematical Modeling, 71, 2019, 12-30.
[14] Akhmedov, N.K., Sofiyev, A.H., Asymptotic Analysis of Three-Dimensional Problem of Elasticity Theory for Radially Inhomogeneous Transversally-Isotropic Thin Hollow Spheres, Thin-Walled Structures, 139, 2019, 232–241.
[15] Akhmedov, N., Akbarova, S., Ismailova, J., Analysis of axisymmetric problem from the theory of elasticity for an isotropic cylinder of small thickness with alternating elasticity modules, Eastern-European Journal of Enterprise Technologies, 2(7 (98)), 2019, 13-19.
[16] Akhmedov, N., Akbarova, S., Behavior of Solution of the Elasticity Problem for a Radial Inhomogeneous Cylinder with Small Thickness, Eastern-European Journal of Enterprise Technologies, 6(7 (114)), 2021, 29-42.
[17] Akhmedov, N.K., Axisymmetric Problem of the Elasticity Theory for the Radially Inhomogeneous Cylinder with a Fixed Lateral Surface, Journal of Applied and Computational Mechanics, 7(2), 2021, 598-610.
[18] Li, W., Hao, Y.X., Zhang, W., Yang, H., Resonance Response of Clamped Functionally Graded Cylindrical Shells with Initial Imperfection in Thermal Environments, Composite Structures, 259, 2021, 113245.
[19] Sofiyev, A., Fantuzi, N., Analytical Solution of Stability and Vibration Problem of Clamped Cylindrical Shells Containing Functionally Graded Layers Within Shear Deformation Theory, Alexandria Engineering Journal, 64, 2023, 141-154.
[20] Sofiyev, A.H., Fantuzzi, N., Ipek, C., Tekin, G., Buckling Behavior of Sandwich Cylindrical Shells Covered by Functionally Graded Coatings with Clamped Boundary Conditions Under Hydrostatic Pressure, Materials, 15(23), 2022, 8680.
[21] Sofiyev, A.H., A New Approach to Solution of Stability Problem of Heterogeneous Orthotropic Truncated Cones with Clamped Edges within Shear Deformation Theory, Composite Structures, 301, 2023, 116209.
[22] Phu, K.V., Bich, D.H., Doan, L.X., Nonlinear Forced Vibration and Dynamic Buckling Analysis for Functionally Graded Cylindrical Shells with Variable Thickness Subjected to Mechanical Load, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 46(3), 2022, 649-65.
[23] Phung, M.V., Nguyen, D.T., Doan, L.T., Nguyen, D.V., Duong, T.V., Numerical İnvestigation on Static Bending and Free Vibration Responses of Two-Layer Variable Thickness Plates with Shear Connectors, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 46(4), 2022, 1047-1065.
[24] Nguyen, V.L., Tran, M.T., Limkatanyu, S., Sedighi, M.H., Rungamornrat J., Reddy’s Third-Order Shear Deformation Shell Theory for Free Vibration Analysis of Rotating Stiffened Advanced Nanocomposite Toroidal Shell Segments in Thermal Environments, Acta Mechanica, 233(11), 2022, 4659-84.
[25] Kucharski, D.M., Pinto, V.T., Rocha, L.A., Dos Santos, E.D., Fragassa, C., Isoldi, L.A., Geometric Analysis by Constructal Design of Stiffened Steel Plates Under Bending with Transverse I-Shaped or T-Shaped Stiffeners, Facta Universitatis, Series: Mechanical Engineering, 20(3), 2022, 617-32.
[26] Nadeem, M., He, J.H., He, C.H., Sedighi, H.M., Shirazi, A., A Numerical Solution of Nonlinear Fractional Newell-Whitehead-Segel Equation Using Natural Transform, TWMS Journal of Pure and Applied Mathematics, 13(2), 2022, 168-82.
[27] Santiago, J.M., Wisniewski, H.L., Convergence of Finite Element Frequency Prediction for a Thin Walled Cylinder, Computers and Structures, 32(3/4), 1989, 745–759.
[28] Xuebin, L., Study on Free Vibration Analysis of Circular Cylindrical Shells Using Wave Propagation, Journal of Sound and Vibration, 311, 2008, 667–682.
[29] Volmir, A.S., The Nonlinear Dynamics of Plates and Shells, Nauka, Moscow, 1972.
[30] Reddy, J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, New York, 2004.
[31] Eslami, M.R., Buckling and Postbuckling of Beams, Plates and Shells, Springer, Switzerland, 2018.
[32] Semenov, A., Buckling of Shell Panels Made of Fiberglass and Reinforced with an Orthogonal Grid of Stiffeners, Journal of Applied and Computational Mechanics, 7(3), 2021, 1856-1861.