A Parametric Study of Higher-Mode Natural Frequencies of Composite Stiffened Cylindrical Shell With Cut-Out
A finite element-based dynamic study of cut-out borne composite cylindrical shells reinforced with stiffeners is conducted. Isoparametric shell element with eight nodes and beam element with three nodes are used to study the mode-frequency behavior of shells with varied edge conditions. Anti-symmetric angle-ply laminates of two, four and ten layers with varying lamination angles are considered. Ten-layer laminates are investigated further as they exhibit better performance in fundamental frequency than two and four-layer laminates. The reduced integration method is adopted to find the shell element’s stiffness and mass matrices and the subspace iteration method is used for the eigenvalue solution of free vibration formulation. Natural frequencies for the first five modes are considered. The effects of fiber orientation angle (θ), degree of orthotropy (E11/E22), and width/thickness ratio (b/h) on the natural frequency are determined through numerical studies. It is revealed that vibration behavior strongly depends on both the number and arrangement of boundary constraints.
Liew K.M., Lim C.W., Vibration of perforated doubly-curved shallow shells with rounded corners, International Journal of Solids and Structures, 31(11): 1519–1536, 1994, doi: 10.1016/0020-7683(94)90012-4.
Liew K.M., Lim C.W., A global continuum Ritz formulation for flexural vibration of pretwisted trapezoidal plates with one edge built in, Computer Methods in Applied Mechanics and Engineering, 114(3–4): 233–247, 1994, doi: 10.1016/0045-7825(94)90173-2.
Lim C.W., Liew K.M., A pb-2 Ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform, Journal of Sound and Vibration, 173(3): 343–375, 1994, doi: 10.1006/jsvi.1994.1235.
Liew K.M., Lim C.W., Vibratory characteristics of cantilevered rectangular shallow shells of variable thickness, AIAA Journal, 32(2): 387–396, 1994, doi: 10.2514/3.59996.
Lim C.W., Liew K.M., Vibration of pretwisted cantilever trapezoidal symmetric laminates, Acta Mechanica, 111(3): 193–208, 1995, doi: 10.1007/BF01376930.
Liew K.M., Lim C.W., Kitipornchai S., Vibration of shallow shells: a review with bibliography, Applied Mechanics Reviews, 50(8): 431–444, 1997, doi: 10.1115/1.3101731.
Sivasubramonian B., Kulkarni A.M., Rao G.V., Krishnan A., Free vibration of curved panels with cutouts, Journal of Sound and Vibration, 200(2): 227–234, 1997, doi: 10.1006/jsvi.1996.0637.
Sivasubramonian B., Rao G.V., Krishnan A., Free vibration of longitudinally stiffened curved panels with cutout, Journal of Sound and Vibration, 226(1): 41–55, 1999, doi: 0.1006/jsvi.1999.2281.
Sai Ram K.S., Sreedhar Babu T., Free vibration of composite spherical shell cap with and without a cutout, Computers & Structures, 80(23): 1749–1756, 2002, doi: 10.1006/S0045-7949(02)00210-9.
Hota S.S., Chakravorty D., Free vibration of stiffened conoidal shell roofs with cutouts, Journal of Vibration and Control, 13(3): 221–240, 2007, doi: 10.1177/1077546307072353.
Hota S.S., Padhi P., Vibration of plates with arbitrary shapes of cutouts, Journal of Sound and Vibration, 302(4–5): 1030–1036, 2007, doi: 10.1016/j.jsv.2007.01.003.
Nanda N., Bandyopadhyay J.N., Nonlinear free vibration analysis of laminated composite cylindrical shells with cutouts, Journal of Reinforced Plastics and Composites, 26(14): 1413–1427, 2007, doi: 10.1177/0731684407079776.
Sahoo S., Free vibration of laminated composite hypar shell roofs with cutouts, Advances in Acoustics and Vibration, 2011, Article ID 403684, 13 pp, doi: 10.1155/2011/403684.
Chaubey A.K., Kumar A., Chakrabarti A., Vibration of laminated composite shells with cutouts and concentrated mass, AIAA Journal, 56(4): 1662–1678, 2018, doi: 10.2514/1.J056320.
Kulikov G.M., Plotnikova S.V., Advanced formulation for laminated composite shells: 3D stress analysis and rigid-body motions, Composite Structures, 95: 236–246, 2013, doi: 10.1016/j.compstruct.2012.07.020.
Talebitooti R., Zarastvand M.R., Gheibi M.R., Acoustic transmission through laminated composite cylindrical shell employing third order shear deformation theory in the presence of subsonic flow, Composite Structures, 157: 95–110, 2016, doi: 10.1016/j.compstruct.2016.08.008.
Tornabene F., Fantuzzi N., Bacciocchi M., The local GDQ method for the natural frequencies of doubly-curved shells with variable thickness: a general formulation, Composites Part B: Engineering, 92: 265–289, 2016, doi: 10.1016/j.compositesb.2016.02.010.
Tornabene F., Fantuzzi N., Bacciocchi M., The GDQ method for the free vibration analysis of arbitrarily shaped laminated composite shells using a NURBS-based isogeometric approach, Composite Structures, 154: 190–218, 2016, doi: 10.1016/j.compstruct.2016.07.041.
Wang Q., Shi D., Liang Q., Pang F., Free vibrations of composite laminated doubly-curved shells and panels of revolution with general elastic restraints, Applied Mathematical Modelling, 46: 227–262, 2017, doi: 10.1016/j.apm.2017.01.070.
Tornabene F., Fantuzzi N., Bacciocchi M., Reddy J.N., An equivalent layer-wise approach for the free vibration analysis of thick and thin laminated and sandwich shells, Applied Sciences, 7(1): 17, 2016, doi: 10.3390/app7010017.
Chaudhuri P.B., Mitra A., Sahoo S., Mode frequency analysis of antisymmetric angle-ply laminated composite stiffened hypar shell with cutout, Mechanics and Mechanical Engineering, 23(1): 162–171, 2019, doi: 10.2478/mme-2019-0022.
Reddy J.N., Energy and Variational Methods in Applied Mechanics: with an Introduction to the Finite Element Method, John Wiley, New York, 1986.
Chandrashekhara K., Free vibrations of anisotropic laminated doubly curved shells, Computers & Structures, 33(2): 435–440, 1989, doi: 10.1016/0045-7949(89)90015-1.
Leissa A.W., Qatu M.S., Equations of elastic deformation of laminated composite shallow shells, Journal of Applied Mechanics, 58(1): 181–188, 1991, doi: 10.1115/1.2897146.
Vasiliev V.V., Jones R.M., Man L.I., Mechanics of Composite Structures, Taylor & Francis, USA, 1993.
Qatu M.S., Vibration of Laminated Shells and Plates, Elsevier, UK, 2004.
Sahoo S., Laminated composite stiffened cylindrical shell panels with cutouts under free vibration, International Journal of Manufacturing, Materials, and Mechanical Engineering (IJMMME), 5(3): 37–63, 2015, doi: 10.4018/IJMMME.2015070103.
Mukherjee A., Mukhopadhyay M., Finite element free vibration of eccentrically stiffened plates, Computers & Structures, 30(6): 1303–1317, 1998. doi: 10.1016/0045-7949(88)90195-2.
Nayak A.N., Bandyopadhyay J.N., On the free vibration of stiffened shallow shells, Journal of Sound and Vibration, 255(2): 357–382, 2002, doi: 10.1006/jsvi.2001.4159.
Chakravorty D., Sinha P.K., Bandyopadhyay J.N., Applications of FEM on free and forced vibration of laminated shells, Journal of Engineering Mechanics, 124(1): 1–8, 1998, doi: 10.1061/(ASCE)0733-9399(1998)124:1(1).