Structural Engineering and Mechanics

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Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness under shear deformation theory

  • Viswanathan, K.K. (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia) ;
  • Javed, Saira (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia) ;
  • Aziz, Zainal Abdul (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia)
  • Received : 2012.05.27
  • Accepted : 2012.11.30
  • Published : 2013.01.25
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Abstract

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five-layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.

Keywords

References

  1. Ghosh, A.K. and Dey, S.S. (1994), "Free vibration of laminated composite plates-a simple finite element based on higher order theory", Computers & Struct., 52, 397-404. https://doi.org/10.1016/0045-7949(94)90225-9
  2. Girgin, K. (2006), "Free vibration analysis of non-cylindrical helices with variable cross-section by using mixed fem", J. Sound and Vib., 297, 931-945. https://doi.org/10.1016/j.jsv.2006.05.001
  3. Hua, L. and Lam, K.Y. (2001), "Orthotropic influence on frequency characteristics of a rotating composite laminated conical shells by the generalized differential quadrature method", Int. J. Solid and Struct., B, 3995-4015.
  4. Kabir, H.R.H., Al-Khaleefi, A.M. and Chaudhuri, R.A. (2001), "Free vibration analysis of thin arbitrarily laminated anisotropic plates using boundary-continuous displacement fourier approach", Compos. Struct., 53, 469-476. https://doi.org/10.1016/S0263-8223(01)00059-9
  5. Kayran, A. and Vinson, J.R. (1990), "Free vibration analysis of laminated composite truncated circular conical shells", J. AIAA., 28, 1259-1269. https://doi.org/10.2514/3.25203
  6. Mizusawa, T. and Kito, H. (1995), "Vibration of cross-ply laminated cylindrical panels by the spline strip method", Computers and Struct., 57, 253-265. https://doi.org/10.1016/0045-7949(94)00613-8
  7. Reddy, J.N. (1978), "Free vibration of antisymmetric angle-ply laminated plates including transverse shear deformation by the finite element method", J. Sound and Vib., 66, 565-576.
  8. Shu, C. (1996), "Free vibration analysis of composite laminated conical shells by generalized differential quadrature", J. Sound and Vib., 194, 587-604. https://doi.org/10.1006/jsvi.1996.0379
  9. Sivadas, K.R. and Ganesan, N. (1991), " Free vibration of circular cylindrical shells with axially varying thickness", J. Sound Vib., 147, 73-85. https://doi.org/10.1016/0022-460X(91)90684-C
  10. Tong, L. (1994), "Free vibration of laminated conical shells including transverse shear deformation", Int. J. Solids Struct., 31, 443-456. https://doi.org/10.1016/0020-7683(94)90085-X
  11. Toorani, M.H. and Lakis, A.A. (2000), "General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects", J. Sound Vib., 237, 561-615. https://doi.org/10.1006/jsvi.2000.3073
  12. Viswanathan, K.K., and Lee, S.K. (2007), "Free vibration of laminated dross-ply plates including shear deformation by spline method", Int. J. Mech. Sci., 49, 352-363. https://doi.org/10.1016/j.ijmecsci.2006.08.016
  13. Viswanathan, K.K. and Kim, K.S. (2008), "Free vibration of antisymmetric angle-ply laminated plates including shear deformation: spline method", Int. J. Mech. Sci., 50, 1476-1485. https://doi.org/10.1016/j.ijmecsci.2008.08.009
  14. Viswanathan, K.K., Kim, K.S., Lee, J.H., Lee, C.H and Lee, J.B. (2008), "Axisymmetric vibration of layered cylindrical shells of variable thickness using spline function approximation", Struct. Eng. Mech., 28, 749-765. https://doi.org/10.12989/sem.2008.28.6.749
  15. Viswanathan, K.K., Saira, J., Zanial, A.A. and Hossain, I. (2011), "Free vibration of symmetric angle-ply laminated cylindrical shells of variable thickness including shear deformation theory", Int. J. Phy. Sci., 6, 6098-6109.
  16. Viswanathan, K.K., Lee, J.H., Zainal, A.A., Hossain. I., Wang, R. and Abdullah, H.Y. (2012), "Vibration analysis of cross-ply laminated truncated conical shells using spline method", J. Eng. Math., 76, 139-156 https://doi.org/10.1007/s10665-011-9525-x
  17. Wang, X.H., Xu, B. and Redekop, D. (2006), "FEM free vibration and buckling analysis of stiffened toroidal shells", Thin Wall. Struct., 44, 2-6. https://doi.org/10.1016/j.tws.2005.11.002
  18. Wu, C.P. and Lee, C.Y. (2001), "Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness", Int. J. Mech. Sci., 43, 1853-1869. https://doi.org/10.1016/S0020-7403(01)00010-8
  19. Wu, C.P., and Wu, C.H. (2000), "Asymptotic differential quadrature solutions for the free vibration of laminated conical shells", Comput. Mech., 25, 346-357. https://doi.org/10.1007/s004660050482

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