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Effects of anisotropy and curvature on free vibration characteristics of laminated composite cylindrical shallow shells

  • Dogan, Ali (Department of Civil Engineering, Cukurova University) ;
  • Arslan, H. Murat (Department of Civil Engineering, Cukurova University) ;
  • Yerli, Huseyin R. (Department of Civil Engineering, Cukurova University)
  • Received : 2008.07.24
  • Accepted : 2010.02.18
  • Published : 2010.07.10

Abstract

This paper presents effects of anisotropy and curvature on free vibration characteristics of cross-ply laminated composite cylindrical shallow shells. Shallow shells have been considered for different lamination thickness, radius of curvature and elasticity ratio. First, kinematic relations of strains and deformation have been showed. Then, using Hamilton's principle, governing differential equations have been obtained for a general curved shell. In the next step, stress-strain relation for laminated, cross-ply composite shells has been given. By using some simplifications and assuming Fourier series as a displacement field, differential equations are solved by matrix algebra for shallow shells. The results obtained by this solution have been given tables and graphs. The comparisons made with the literature and finite element program (ANSYS).

Keywords

References

  1. Amabili, M. (2003), "A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach", J. Sound Vib., 264, 1091-1125. https://doi.org/10.1016/S0022-460X(02)01385-8
  2. ANSYS Inc. (1996), User manual Version: 5.3.
  3. Djoudi, M.S. and Bahai, H. (2003), "A shallow shell finite element for the linear and non-linear analysis of cylindrical shells", Eng. Struct., 25(6), 769-778. https://doi.org/10.1016/S0141-0296(03)00002-6
  4. Gautham, B.P. and Ganesan, N. (1997), "Free vibration characteristics of isotropic and laminated orthotropic spherical caps", J. Sound Vib., 204(1), 17-40. https://doi.org/10.1006/jsvi.1997.0904
  5. Grigorenko, A.Y. and Yaremchenko, N.P. (2007), "Stress-strain state of shallow shells with rectangular planform and varying thickness: Refined formulation", Int. Appl. Mech., 43(10), 1132-1141. https://doi.org/10.1007/s10778-007-0113-8
  6. Gurdal, Z., Haftka, R.T. and Hajela, P. (1998), Design and Optimization of Laminated Composite Materials, John Wiley & Sons Inc., USA.
  7. Hyer, M.W. (1997), Stress Analysis of Fiber-reinforced Composite Materials, McGraw-Hill Book Company, Singapore.
  8. Jones, R.M. (1984), Mechanics of Composite Materials, Taylor & Francis, USA.
  9. Latifa, S.K. and Sinha, P.K. (2005), "Improved finite element analysis of multilayered doubly curved composite shells", J. Reinf. Plast. Comp., 24, 385-404. https://doi.org/10.1177/0731684405044899
  10. Liew, K.M., Peng, L.X. and Ng, T.Y. (2002), "Three dimensional vibration analysis of spherical shell panels subjected to different boundary conditions", Int. J. Mech. Sci., 44, 2103-2117. https://doi.org/10.1016/S0020-7403(02)00167-4
  11. Qatu, M.S. (1991), "Free vibration of laminated composite rectangular plates", Int. J. Solids Struct., 28, 941-954. https://doi.org/10.1016/0020-7683(91)90122-V
  12. Qatu, M.S. (1992a), "Mode shape analysis of laminated composite shallow shells", J. Acoust. Soc. Am., 92, 1509-1520. https://doi.org/10.1121/1.403943
  13. Qatu, M.S. (1992b), "Review of shallow shell vibration research", Shock Vib. Digest, 24, 3-15.
  14. Qatu, M.S. (1993a), "Theories and analysis of thin and moderately thick laminated composite curved beams", Int. J. Solids Struct., 30(20), 2743-2756. https://doi.org/10.1016/0020-7683(93)90152-W
  15. Qatu, M.S. (1993b), "Vibration of doubly cantilevered laminated composite thin shallow shells", Thin Wall. Struct., 15, 235-248. https://doi.org/10.1016/0263-8231(93)90028-9
  16. Qatu, M.S. (2004), Vibration of Laminated Shells and Plates, Elsevier, Netherlands.
  17. Reddy, J.N. (1993), An Introduction to the Finite Element Method, McGraw Hill, USA.
  18. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press, USA.
  19. Reddy, J.N. and Miravete, A. (1995), Practical Analysis of Composite Laminates, CRC Press, USA.

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