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Abstract
In this paper the free vibration behaviours of thick laminated composite non-circular cylindrical shells are investigated using higher-order theory. The formulation accounts for the variation of the in-plane and transverse displacements through the thickness, abrupt discontinuity in slope of the in-plane displacements at the interfaces, and includes in-plane, rotary inertia terms, and also the inertia contributions due to the coupling between the different order displacement terms. The strain-displacement relations are accurately accounted for in the formulation without neglecting/approximating the (I +z/R) terms. The solutions are obtained employing finite element procedure. Detailed study is made to highlight the influences of length and thickness ratios, eccentricity parameter, ply-angles and number of layers on the free vibration characteristics of non-circular shells.
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References
- Leissa, A.W., "Vibration of Shells", NASA SP-288, 1973.
- Noor, A.K., "Bibliography of Monographs and Surveys on Shells", Applied Mechanics Review, Vol.43, 1990, pp.223-234.
- Noor, A.K. and Burton, W.S., "Assessment of Computational Models for Multilayered Composite Shells", Applied Mechanics Review, Vol.43, 1990, pp.67-97.
- Qatu, M.S., "Review of Shallow Shell Vibration Research", Shock Vibration Digest, Yol.24, 1992, pp.3- 15.
- Soldatos, K.P., "Mechanics of Cylindrical Shells with Non-circular Cross Section : A Survey", Applied Mechanics Review, Vol.52, 1999, pp.237 -274.
- Soldatos, K.P. and Tzivanidis, G.J., "Buckling and Vibration of Cross-ply Laminated Non-Circular Cylindrical Shells", Journal of Sound and Vibration, Vol.82, 1982, pp.425-434.
- Soldatos, K.P., ' A Flugge-type Theory for the Analysis of Anisotropic Laminated Non-circular Cylindrical Shells", Int. J. Solids Structures, Vol.20, 1984, pp.l07-120.
- Hui, D. and Du, H.Y., "Effects of Axial Imperfections on Vibrations of Anti-symmetric Cross-ply, Oval Cylindrical Shells", Journal of Applied Mechanics, Vol.53, 1986, pp.675-680.
- Suzuki, K., Shikanai, G. and Leissa, A.W., "Free Vibrations of Laminated Composite thin Non-Circular Cylindrical Shell", Journal of Applied Mechanics, Vol.61, 1994, pp.861-871.
- Noor, A.K., "Noncircular Cylinder Vibration by Multilocal Method", Engineering Mechanics Division, Proc. ASCE, Vol.99, 1973, pp.389-407 .
- Kumar, V. and Singh, A.V., "Vibrations of Composite Noncircular Cylindrical Shells", J. Vibration and Acoustics, Vol. 117, 1995, pp.471-476.
- Suzuki, K., Shikanai, G. and Leissa, A.W., "Free Vibrations of Laminates Composite Thick Noncircular Cylindrical Shell", Int. J. Solids Struct., Vol.33, 1996, pp.4079-4100.
- Soldatos, K.P., "Free Vibration Analysis of Thickness Shear Deformable Cross-ply Laminated Oval Shells, in Refined Dynamical Theories of Beams, Plates and Shells", Lect. Notes Eng2S, L Elishakoff et.al (eds) Springer, Berlin, 1987 , pp.324-332.
- Kumar, V. and Singh, A.V., "Vibrations of Fibre-Reinforced Deep Shells", J. Pressure Vessel Technology, VoI.118, 1996, pp.407-414.
- Bhimaraddi, A., 'A Higher-Order Theory for Free Vibration Analysis of Circular Cylindrical Shells", Int. J. Solids Structures, Vol.20, 1984, pp. 623-630.
- Bhaskar, K. and Varadan, T.K., "A Higher-order Theory for Bending Analysis of Laminated Shells of Revolution", Computers and Structures, Vol.40, 1991, pp.815-819.
- He, L.H., "A Linear Theory of Laminated Shells Accounting for Continuity of Displacement and Transverse Shear Stresses at Layer Interfaces", International Journal of Solids Structures, Vol.31; 1994, pp.613-627
- Makhecha, D.P., Ganapathi, M. and Patel, B.P., Dynamic Analysis of Laminated Composite Plates Subjected to Thermal/Mechanical Loads using an Accurate Theory", Composite Structures, Vol.51, 2001,pp.221-236.
- Murakami, H., "Laminated Composite Plate Theory with Improved In - plane Responses", ASME Journal of Applied Mechanics, Vol.53, 1986, pp.661-666.
- Kraus, H., "Thin Elastic Shells", John Wiley, New York, 1967.
- Rao, S.R. and Ganesan, N., "Interlaminar Stresses rn Shells of Revolution", Mechanics of Composite Materials and Structures, Vol.3, 1996, pp.321-339.
- Herakovich, C.T., Mechanics of Fibrous Composites, John Wiley and Sons, Inc, New York, 1998.
- Zienkiewicz, O.C., Finite Element Methods in Engineering Science, McGraw Hill, London , 197l .
- Prathap, G., "A Co Continuous 4-Noded Cylindrical Shell Element", Computers and Structures, Vol.21, 1985, pp.995-999.
- Ganapathi, M. and Makhecha, D.P., "Free Vibration Analysis of Multi-layered Composite Laminates Based on an Accurate Higher-Order Theory", Composites, Part B, Engineering, Yo1.32,2001, pp.535-543.
- Makhecha, D.P., Ganapathi, M. and Patel, B.P., 'A Shear Flexible Shell Element Based on Higher-order Realistic Theory for Dynamic Analysis", Proceedings of International Conference on Theoretical, Applied, computational and Experimental Mechanics, December 27-30, Kharagpur, India, 2001.
- Ye, J.Q. and Soldatos, K.P., "Three-Dimensional Vibrations of Cross-ply Laminated Hollow Cylinders with Clamped Edge Boundaries, ASME Journal of Vibration and Acoustics, Vol.119, 1997, pp.317-323.
- ANSYS, ANSYS 5.6 User's Manual, Swanson Analysis Systems Inc, 1997.
References
Leissa, A.W., "Vibration of Shells", NASA SP-288, 1973.
Noor, A.K., "Bibliography of Monographs and Surveys on Shells", Applied Mechanics Review, Vol.43, 1990, pp.223-234.
Noor, A.K. and Burton, W.S., "Assessment of Computational Models for Multilayered Composite Shells", Applied Mechanics Review, Vol.43, 1990, pp.67-97.
Qatu, M.S., "Review of Shallow Shell Vibration Research", Shock Vibration Digest, Yol.24, 1992, pp.3- 15.
Soldatos, K.P., "Mechanics of Cylindrical Shells with Non-circular Cross Section : A Survey", Applied Mechanics Review, Vol.52, 1999, pp.237 -274.
Soldatos, K.P. and Tzivanidis, G.J., "Buckling and Vibration of Cross-ply Laminated Non-Circular Cylindrical Shells", Journal of Sound and Vibration, Vol.82, 1982, pp.425-434.
Soldatos, K.P., ' A Flugge-type Theory for the Analysis of Anisotropic Laminated Non-circular Cylindrical Shells", Int. J. Solids Structures, Vol.20, 1984, pp.l07-120.
Hui, D. and Du, H.Y., "Effects of Axial Imperfections on Vibrations of Anti-symmetric Cross-ply, Oval Cylindrical Shells", Journal of Applied Mechanics, Vol.53, 1986, pp.675-680.
Suzuki, K., Shikanai, G. and Leissa, A.W., "Free Vibrations of Laminated Composite thin Non-Circular Cylindrical Shell", Journal of Applied Mechanics, Vol.61, 1994, pp.861-871.
Noor, A.K., "Noncircular Cylinder Vibration by Multilocal Method", Engineering Mechanics Division, Proc. ASCE, Vol.99, 1973, pp.389-407 .
Kumar, V. and Singh, A.V., "Vibrations of Composite Noncircular Cylindrical Shells", J. Vibration and Acoustics, Vol. 117, 1995, pp.471-476.
Suzuki, K., Shikanai, G. and Leissa, A.W., "Free Vibrations of Laminates Composite Thick Noncircular Cylindrical Shell", Int. J. Solids Struct., Vol.33, 1996, pp.4079-4100.
Soldatos, K.P., "Free Vibration Analysis of Thickness Shear Deformable Cross-ply Laminated Oval Shells, in Refined Dynamical Theories of Beams, Plates and Shells", Lect. Notes Eng2S, L Elishakoff et.al (eds) Springer, Berlin, 1987 , pp.324-332.
Kumar, V. and Singh, A.V., "Vibrations of Fibre-Reinforced Deep Shells", J. Pressure Vessel Technology, VoI.118, 1996, pp.407-414.
Bhimaraddi, A., 'A Higher-Order Theory for Free Vibration Analysis of Circular Cylindrical Shells", Int. J. Solids Structures, Vol.20, 1984, pp. 623-630.
Bhaskar, K. and Varadan, T.K., "A Higher-order Theory for Bending Analysis of Laminated Shells of Revolution", Computers and Structures, Vol.40, 1991, pp.815-819.
He, L.H., "A Linear Theory of Laminated Shells Accounting for Continuity of Displacement and Transverse Shear Stresses at Layer Interfaces", International Journal of Solids Structures, Vol.31; 1994, pp.613-627
Makhecha, D.P., Ganapathi, M. and Patel, B.P., Dynamic Analysis of Laminated Composite Plates Subjected to Thermal/Mechanical Loads using an Accurate Theory", Composite Structures, Vol.51, 2001,pp.221-236.
Murakami, H., "Laminated Composite Plate Theory with Improved In - plane Responses", ASME Journal of Applied Mechanics, Vol.53, 1986, pp.661-666.
Kraus, H., "Thin Elastic Shells", John Wiley, New York, 1967.
Rao, S.R. and Ganesan, N., "Interlaminar Stresses rn Shells of Revolution", Mechanics of Composite Materials and Structures, Vol.3, 1996, pp.321-339.
Herakovich, C.T., Mechanics of Fibrous Composites, John Wiley and Sons, Inc, New York, 1998.
Zienkiewicz, O.C., Finite Element Methods in Engineering Science, McGraw Hill, London , 197l .
Prathap, G., "A Co Continuous 4-Noded Cylindrical Shell Element", Computers and Structures, Vol.21, 1985, pp.995-999.
Ganapathi, M. and Makhecha, D.P., "Free Vibration Analysis of Multi-layered Composite Laminates Based on an Accurate Higher-Order Theory", Composites, Part B, Engineering, Yo1.32,2001, pp.535-543.
Makhecha, D.P., Ganapathi, M. and Patel, B.P., 'A Shear Flexible Shell Element Based on Higher-order Realistic Theory for Dynamic Analysis", Proceedings of International Conference on Theoretical, Applied, computational and Experimental Mechanics, December 27-30, Kharagpur, India, 2001.
Ye, J.Q. and Soldatos, K.P., "Three-Dimensional Vibrations of Cross-ply Laminated Hollow Cylinders with Clamped Edge Boundaries, ASME Journal of Vibration and Acoustics, Vol.119, 1997, pp.317-323.
ANSYS, ANSYS 5.6 User's Manual, Swanson Analysis Systems Inc, 1997.