This Article Abstract Free Full Text (Free PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Shao, Z.S. Articles by Ma, G.W. Search for Related Content Social Bookmarking                         What's this?

Free Vibration Analysis of Laminated Cylindrical Shells by Using Fourier Series Expansion Method

School of Civil & Environmental Engineering, Nanyang Technological University, Singapore 639798, Singapore

G.W. Ma

School of Civil & Environmental Engineering, Nanyang Technological University, Singapore 639798, Singapore, cgwma{at}ntu.edu.sg

Free vibration analysis of laminated cylindrical shells with arbitrary classical boundary conditions is presented in this article. Strain-displacement relations from Love's shell theory are employed in the analysis. Using Fourier series expansion and Stokes' transformation, frequency determinant of laminated cylindrical shells is derived. Comparisons between the results of the present method and previous studies are performed. Excellent agreement is obtained when enough terms of the infinite Fourier series are considered. As a numerical example, an antisymmetric angle-ply laminated cylindrical shell is considered. The effects of boundary conditions, length-to-radius ratio, thickness-to-radius ratio, and fiber orientation on the natural frequencies are analyzed and graphically presented.

Key Words: laminated cylindrical shell • free vibration • Fourier series expansion method • Stokes' transformation.

References

• Arnold, R. and Warburton, G.B. (1949). Flexural Vibrations of the Walls of Thin Cylindrical Shells have Freely Supported Ends, Proceedings of the Royal Society London A, 197: 238—256.[Abstract/Free Full Text]
• Reddy, J.N. (1978). Free Vibration of Antisymmetric Angle-ply Laminated Plates Including Transverse Shear Deformation by the Finite Element Method, Journal of Sound and Vibration, 66: 565—576.[CrossRef][Web of Science]
• Sinha, P.K. and Rath, A.K. (1975). Free Vibration and Buckling of Cross-ply Laminated Circular Cylindrical Panels, Aeronautical Quarterly, 26: 211—218.[Web of Science]
• Noor, A.K. (1973). Free Vibration of Multilayered Composite Plates, AIAA Journal, 11: 1038—1039.[CrossRef][Web of Science]
• Kapania, R.K. (1989). A Review on the Analysis of Laminated Shells, Journal of Pressure Vessel Technology, 111: 88—96.[Web of Science]
• Reddy, J.N. (1989). On Refined Computational Models of Composite Laminated, International Journal of Numerical Methods in Engineering, 27: 361—382.[CrossRef]
• Lam, K.Y. and Loy, C.T. (1998). Influence of Boundary Conditions for a Thin Laminated Rotating Cylindrical Shell, Composite Structures, 41: 215—228.[CrossRef][Web of Science]
• Lam, K.Y. and Loy, C.T. (1995). Influence of Boundary Conditions and Fiber Orientation on the Natural Frequencies of Thin Orthotropic Cylindrical Shells, Composite Structures, 31: 21—30.[CrossRef][Web of Science]
• Lee, Y.S., Yang, M.S., Kim, H.S. and Kim, J.H. (2002). A Study on the Free Vibration of the Joined Cylindrical-spherical Shell Structures, Computers & Structures, 80: 2405—2414.[CrossRef][Web of Science]
• Viswanathan, K.K. and Lee, S.K. (2007). Free Vibration of Laminated Cross-ply Plates Including Shear Deformation by Spline Method, International Journal of Mechanical Sciences, 49: 352—363.[CrossRef][Web of Science]
• Viswanathan, K.K. and Navaneethakrishnan, P.V. (2005). Free Vibration of Layered Truncated Conical Shell Frusta of Differently Varying Thickness by the Method of Collocation with Cubic and Quintic Splines, International Journal of Solids and Structures, 42: 1129—1150.[CrossRef][Web of Science]
• Haftchenari, H., Darizeh, M., Darizeh, A., Ansari, R. and Sharma, C.B. (2007). Dynamic Analysis of Composite Shells Using Differential Quadrature Method (DQM), Composite Structures, 78: 292—298.[CrossRef][Web of Science]
• Sharma, C.B., Darvizeh, M. and Darvizeh, A. (1997). Free Vibration Behaviour of Helically Wound Cylindrical Shells, Composite Structures, 44: 55—62.[CrossRef]
• Shu, C. and Du, H. (1997). Free Vibration Analysis of Laminated Composite Cylindrical Shell by DQM, Composite Technology Part B, 28: 267—274.[CrossRef]
• Bert, C.W. and Malik, M. (1997). Differential Quadrature Method: A Powerful New Technique for Analysis of Composite Structures, Composite Structures, 39: 179—189.[CrossRef][Web of Science]
• Chung, H. (1981). Free Vibration Analysis of Circular Cylindrical Shells, Journal of Sound and Vibration, 74 (3): 331—335[CrossRef][Web of Science]
• Kabir, H.R.H. and Al-Khaleefi, R.A. (2001). Free Vibration Analysis of Thin Arbitrary Laminated Anisotropic Plates Using Boundary-continuous Displacement Fourier Approach, Composite Structures, 53: 469—476.[CrossRef][Web of Science]
• Jeong, K.H. and Lee, S.C. (1995). Fourier Series Expansion Method for Free Vibration Analysis of Either a Partially Liquid-filled or a Partially Liquid-Surrounded Circular Cylindrical Shell, Computers & structures, 58 (5): 937—946.[Web of Science]
• Jeong, K.H. and Lee, S.C. (1998). Hydroelastic Vibration of a Liquid-filled Circular Cylindrical Shell, Computers & Structures, 66(2-3): 173—185.[CrossRef][Web of Science]
• Whitney, J.M. and Leissa, W. (1969). Analysis of Heterogeneous Anisotropic Plates, Journal of Applied Mechanics, 36: 261—266.[Web of Science]
• Whitney, J.M. and Paganao, N.J. (1970). Shear Deformation in Heterogeneous Plates, Journal of Applied Mechanics, 37: 1031—1036.

Journal of Thermoplastic Composite Materials, Vol. 20, No. 6, 551-573 (2007)
DOI: 10.1177/0892705707084542


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?

This Article Abstract Free Full Text (Free PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Shao, Z.S. Articles by Ma, G.W. Search for Related Content Social Bookmarking                         What's this?