Natural frequency characteristics of thin-walled homogeneous and manifold layered cylindrical shells under pressure using energy method

Abstract

Energy method for the vibration of two types of cylindrical shells, namely thin-walled homogeneous isotropic and manifold layered isotropic cylindrical shells under uniform external lateral pressure is presented. The study is carried out based on strain-displacement relationship from Love’s shell theory with beam functions as axial modal function. A manifold layered cylindrical shell configuration is formed by three layers of isotropic material where the inner and outer layers are stainless steel and the middle layer is aluminum. The homogeneous cylindrical shell is made-up of isotropic one layer with stainless steel. The governing equations with uniform external lateral pressure for homogeneous isotropic and manifold layered isotropic cylindrical shells are obtained using energy functional by the Lagrangian function with Rayleigh-Ritz method. The boundary conditions that are presented at the end conditions of the cylindrical shell are simply supported-simply supported, clamped-clamped and free-free. The influences of uniform external lateral pressure and symmetrical boundary conditions on the natural frequency characteristics for both homogeneous and manifold layered isotropic cylindrical shells are examined. For all boundary conditions considered, the natural frequency of both cylindrical shells with symmetric uniform lateral pressure increases as h/R ratio increases and those considering natural frequency of the both cylindrical shells with symmetric uniform lateral pressure decrease as L/R ratio increases.

Keywords

cylindrical shell / manifold layered / pressure / energy method

References

[1] LoveA E HA treatise on the mathematical theory of elasticity [M], 1944, New York, Dover Publication: 643-644

[2] LiuY, ChuF. Nonlinear vibrations of rotating thin circular cylindrical shell [J]. Nonlinear Dynamics, 2012, 67(2): 1467-1479

[3] ShenH. Boundary layer theory for the nonlinear vibration of anisotropic laminated cylindrical shells [J]. Composite Structures, 2013, 97: 338-352

[4] LiuaB, XingaY F, QatubM S, FerreiraA J M. Exact characteristic equations for free vibrations of thin orthotropic circular cylindrical shells [J]. Composite Structures, 2012, 94(2): 484-493

[5] ChenY, JinG, LiuZ. Free vibration analysis of circular cylindrical shell with non-uniform elastic boundary constraints [J]. International Journal of Mechanical Sciences, 2013, 74: 120-132

[6] LamK Y, LoyC T. On vibration of thin rotating laminated composite cylindrical shell [J]. International Journal Solid Structures, 1994, 4(11): 1153-1167

[7] ShenH. Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium [J]. Composite Structures, 2012, 3: 1144-1154

[8] LiD, QingG, LiuY. A layerwise/solid-element method for the composite stiffened laminated cylindrical shell structures [J]. Composite Structures, 2013, 98: 215-227

[9] PrabuB, RaviprakashA V, VenkatramanA. Parametric study on buckling behaviour of dented short carbon steel cylindrical shell subjected to uniform axial compression [J]. Thin-Walled Structures, 2010, 48(8): 639-649

[10] HuangH, HanQ. Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to time-dependent axial load [J]. Composite Structures, 2010, 92(2): 593-598

[11] MorozovE V, LopatinA V, NesterovV A. Finite-element modelling and buckling analysis of anisogrid composite lattice cylindrical shells [J]. Composite Structures, 2011, 93(2): 308-323

[12] LiZ, WangL, GuoZ, ShuH. Elastic buckling of cylindrical pipe linings with variable thickness encased in rigid host pipes [J]. Thin-Walled Structures, 2012, 51: 10-19

[13] NajafizadehM M, IsvandzibaeiM R. Vibration of functionally graded cylindrical shells based on different shear deformation shell theories with ring support under various boundary conditions [J]. Journal of Mechanical Science and Technology, 2009, 23(8): 2072-2084

[14] MalekzadehK, KhaliliS M R, DavarA, MahajanP. Transient dynamic response of clamped-free hybrid composite circular cylindrical shells [J]. Application Composite Materials, 2010, 17(2): 243-57

[15] ArshadS H, NaeemM N, SultanaN, ShahG A, IqbalZ. Vibration analysis of bi-layered FGM cylindrical shells [J]. Archive of Applied Mechanics, 2011, 81(3): 319-343

[16] LoveA E HA treatise on the mathematical theory of elasticity [M], 19524th edCambridge, Cambridge University Press: 662-663

[17] LamK Y, LoyC T. Effects of boundary conditions on frequencies characteristics for a multi-layered cylindrical shell [J]. Journal Sound and Vibration, 1995, 188(3): 365-384

[18] MoonF C, ShawS W. Chaotic vibrations of a beam with non-linear boundary conditions [J]. International Journal of Non-Linear Mechanics, 1983, 18(6): 465-477

[19] WarburtonB. Vibration of thin cylindrical shells [J]. Journal of Mechanical Engineering Science, 1965, 7(4): 399-407

[20] LoyC T, LamK Y. Vibration of cylindrical shells with ring support [J]. International Journal of Mechanical Sciences, 1997, 39(4): 455-471

[21] BlevinsR DFormulas for natural frequency and mode shapes [M], 1979, New York, Van Nostrand Reinhold