Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Vibration analysis of a shear deformed anti-symmetric angle-ply conical shells with varying sinusoidal thickness

  • Javed, Saira (UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Ibnu SIna Institiute for Scientific & Industrial Research, Universiti Teknologi Malaysia) ;
  • Viswanathan, K.K. (UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Ibnu SIna Institiute for Scientific & Industrial Research, Universiti Teknologi Malaysia) ;
  • Aziz, Z.A. (UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Ibnu SIna Institiute for Scientific & Industrial Research, Universiti Teknologi Malaysia) ;
  • Lee, J.H. (Department of Naval Architecture & Oceon Engineering, Division of Mechanical Engineering, Inha University)
  • Received : 2015.04.03
  • Accepted : 2016.03.15
  • Published : 2016.06.25
⟨ Previous Next ⟩

Abstract

The study is to investigate the free vibration of antisymmetric angle-ply conical shells having non-uniform sinusoidal thickness variation. The arbitrarily varying thickness is considered in the axial direction of the shell. The vibrational behavior of shear deformable conical shells is analyzed for three different support conditions. The coupled differential equations in terms displacement and rotational functions are obtained. These displacement and rotational functions are invariantly approximated using cubic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration characteristic of the shells is examined for cone angle, aspect ratio, sinusoidal thickness variation, layer number, stacking sequence, and boundary conditions.

Keywords

References

  1. Akbari, M., Kiani, Y., Aghdam, M.M. and Eslami, M.R. (2014), "Free vibration of FGM Levy conical panels", Compos. Struct., 116, 732-746. https://doi.org/10.1016/j.compstruct.2014.05.052
  2. Alibeigloo, A. (2009), "Static and vibration analysis of axi-symmetric angle-ply laminated cylindrical shell using state space differential quadrature method", Int. J. Press. Ves. Pip., 86, 738-747. https://doi.org/10.1016/j.ijpvp.2009.07.002
  3. Ansari, R., Faghih Shojaei, M., Rouhi, H. and Hosseinzadeh, M. (2015), "A novel variational numerical method for analyzing the free vibration of composite conical shells", Appl. Math. Model., 39(10), 2849-2860. https://doi.org/10.1016/j.apm.2014.11.012
  4. Chernobryvko, M.V., Avramov, K.V., Romanenko, V.N., Batutina, T.J. and Tonkonogenko, A.M. (2014), "Free linear vibrations of thin axisymmetric parabolic shells", Meccanica, 49(12), 2839-2845. https://doi.org/10.1007/s11012-014-0027-6
  5. Dey, S. and Karmakar, A. (2012), "Natural frequencies of delaminated composite rotating conical shells-A finite element approach", Finite Elem. Anal. Des., 56, 41-51. https://doi.org/10.1016/j.finel.2012.02.007
  6. Firouz-Abadi, R.D., Rahmanian, M. and Amabili, M. (2014), "Free vibration of moderately thick conical shells using a higher order shear deformable theory", J. Vib. Acoust., 136(5), 051001. https://doi.org/10.1115/1.4027862
  7. George, H.S. (1999), Laminar Composites, Butterworth-Heinemann publications, USA.
  8. Gibson, R.F. (1994), Principles of Composite Material Mechanics, McGraw-Hill, Singapore.
  9. Jin, G., Ma, X., Shi, S., Ye, T. and Liu, Z. (2014), "A modified Fourier series solution for vibration analysis of truncated iconical shells with general boundary conditions", Appl. Acoust., 85, 82-96. https://doi.org/10.1016/j.apacoust.2014.04.007
  10. Khare, R.K., Kant, T. and Garg, A.K. (2004), "Free vibration of composite and sandwich laminates with a higher-order facet shell element", Compos. Struct., 65(3-4), 405-418. https://doi.org/10.1016/j.compstruct.2003.12.003
  11. Kang, J.H. (2014), "Vibration analysis of complete conical shells with variable thickness", Int. J. Struct. Stab. Dyn., 14(4), 1450001. https://doi.org/10.1142/S0219455414500011
  12. Lal, R. and Rani, R. (2014), "Mode shapes and frequencies of radially symmetric vibrations of annular sandwich plates of variable thickness", Acta Mechanica, 225(6), 1565-1580. https://doi.org/10.1007/s00707-013-1018-8
  13. Liu, M., Liu, J. and Cheng, Y. (2014), "Free vibration of a fluid loaded ring-stiffened conical shell with variable thickness", J. Vib. Acoust., 136, 051003-1-051003-10. https://doi.org/10.1115/1.4027457
  14. Ma, X., Jin, G., Xiong, Y. and Liu, Z. (2014), "Free and forced vibration analysis of coupled conical-cylindrical shells with arbitrary boundary conditions", Int. J. Mech. Sci., 88, 122-137. https://doi.org/10.1016/j.ijmecsci.2014.08.002
  15. Madabhusi-Raman, P. and Davalos, J.F. (1996), "Static shear correction factor for laminated rectangular beams", Compos. Part B: Eng., 27(3-4), 285-293. https://doi.org/10.1016/1359-8368(95)00014-3
  16. Pai, P.F. and Schulz, M.J. (1999), "Shear correction factors and an energy-consistent beam theory", Int. J. Solid. Struct., 36, 1523-1540. https://doi.org/10.1016/S0020-7683(98)00050-X
  17. Patel, B.P., Singh, S. and Nath, Y. (2008), "Postbuckling characteristics of angle-ply laminated truncated circular conical shells", Commun. Nonlin. Sci. Numer. Simul., 13(7), 1411-1430. https://doi.org/10.1016/j.cnsns.2007.01.001
  18. Reddy, J.N. (1997), Mechanics of Laminated Composite Plates, CRC Press, New York.
  19. Selahi, E., Setoodeh, A.R. and Tahani, M. (2014), "Three-dimensional transient analysis of functionally graded truncated conical shells with variable thickness subjected to an asymmetric dynamic pressure", Int. J. Press. Ves. Pip., 119, 29-38. https://doi.org/10.1016/j.ijpvp.2014.02.003
  20. Shakouri, M. and Kouchakzadeh, M.A. (2014), "Free vibration analysis of joined conical shells: Analytical and experimental study", Thin Wall. Struct., 85, 350-358. https://doi.org/10.1016/j.tws.2014.08.022
  21. Sofiyev, A.H., Omurtag, M.H. and Schnack, E. (2009), "The vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure", J. Sound Vib., 319, 963-983. https://doi.org/10.1016/j.jsv.2008.06.033
  22. Sofiyev, A.H. (2014), "Large-amplitude vibration of non-homogeneous orthotropic composite truncated conical shell", Compos. Part B: Eng., 61, 365-374. https://doi.org/10.1016/j.compositesb.2013.06.040
  23. Sofiyev, A.H. and Kuruoglu, N. (2014), "Combined influences of shear deformation, rotary inertia and heterogeneity on the frequencies of cross-ply laminated orthotropic cylindrical shells", Compos. Part B: Eng., 66, 500-510. https://doi.org/10.1016/j.compositesb.2014.06.015
  24. Sofiyev, A.H. (2016), "Buckling of heterogeneous orthotropic composite conical shells under external pressures within the shear deformation theory", Compos. Part B: Eng., 84, 175-187.
  25. Su, Z., Jin, G. and Ye, T. (2014), "Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints", Compos. Struct., 118, 432-447. https://doi.org/10.1016/j.compstruct.2014.07.049
  26. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories", Compos. Part B: Eng., 67, 490-509. https://doi.org/10.1016/j.compositesb.2014.08.012
  27. Tornabene, F., Fantuzzi, N., Viola, E. and Batra, R.C. (2015), "Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory", Compos. Struct., 119, 67-89. https://doi.org/10.1016/j.compstruct.2014.08.005
  28. Viswanathan, K.K., Saira, J., Izliana, A.B. and Zainal, A.A. (2015), "Free vibration of anti-symmetric angleply laminated conical shells", Compos. Struct., 122, 488-495. https://doi.org/10.1016/j.compstruct.2014.11.075
  29. 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
  30. Wu, S., Qu, Y. and Hua, H. (2015), "Free vibration of laminated orthotropic conical shell on Pasternak foundation by a domain decomposition method", J. Compos. Mater., 49(1), 35-52. https://doi.org/10.1177/0021998313514259
  31. Xie, X., Jin, G., Ye, T. and Liu, Z. (2014), "Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method", Appl. Acoust., 85, 130-142. https://doi.org/10.1016/j.apacoust.2014.04.006
  32. Zarouni, E., Jalilian Rad, M. and Tohidi, H. (2014), "Free vibration analysis of fiber reinforced composite conical shells resting on Pasternak-type elastic foundation using Ritz and Galerkin methods", Int. J. Mech. Mater. Des., 10(4), 421-438. https://doi.org/10.1007/s10999-014-9254-1
  33. Zhang, B., He, Y., Liu, D., Shen, L. and Lei, J. (2015), "Free vibration analysis of four-unknown shear deformable functionally graded cylindrical microshells based on the strain gradient elasticity theory", Compos. Struct., 119, 578-597. https://doi.org/10.1016/j.compstruct.2014.09.032

Cited by

  1. The GDQ method for the free vibration analysis of arbitrarily shaped laminated composite shells using a NURBS-based isogeometric approach vol.154, 2016, https://doi.org/10.1016/j.compstruct.2016.07.041
  2. Dynamic behaviour of orthotropic elliptic paraboloid shells with openings vol.63, pp.2, 2016, https://doi.org/10.12989/sem.2017.63.2.225
  3. Free Vibration Analysis of Composite Conical Shells with Variable Thickness vol.2020, pp.None, 2020, https://doi.org/10.1155/2020/4028607
  4. Free vibration of FG-GPLRC conical panel on elastic foundation vol.75, pp.1, 2020, https://doi.org/10.12989/sem.2020.75.1.001
  5. Natural vibrations of truncated conical shells of variable thickness vol.13, pp.4, 2016, https://doi.org/10.7242/1999-6691/2020.13.4.31
  6. Geometrical Influences on the Vibration of Layered Plates vol.2021, pp.None, 2016, https://doi.org/10.1155/2021/8843358
  7. Vibration of two types of porous FG sandwich conical shell with different boundary conditions vol.79, pp.4, 2016, https://doi.org/10.12989/sem.2021.79.4.401