Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Free vibration analysis of functionally graded cylindrical shells with different shell theories using semi-analytical method

  • Received : 2017.10.23
  • Accepted : 2018.07.07
  • Published : 2018.09.25
⟨ Previous Next ⟩

Abstract

In this study, the semi-analytical finite strip method is adopted to examine the free vibration of cylindrical shells made up of functionally graded material. The properties of functionally graded shells are assumed to be temperature-dependent and vary continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of ceramic and metal. The material properties of the shells and stiffeners are assumed to be continuously graded in the thickness direction. Theoretical formulations based on the smeared stiffeners technique and the classical shell theory with first-order shear deformation theory which accounts for through thickness shear flexibility are employed. The finite strip method is applied to five different shell theories, namely, Donnell, Reissner, Sanders, Novozhilov, and Teng. The approximate procedure is compared favorably with three-dimensional finite elements. Finally, a detailed numerical study is carried out to bring out the effects of power-law index of the functional graded material, stiffeners, and geometry of the shells on the difference between various shell theories. Finally, the importance of choosing the shell theory in simulating the functionally graded cylindrical shells is addressed.

Keywords

References

  1. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A. and Mahmoud, S.R. (2015), "Ending and buckling analyses of functionallyw graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  2. Cinefra, M., Belouettar, S., Soave, M. and Carrera, E. (2010), "Variable kinematic models applied to free-vibration analysis of functionally graded material shells", Eur. J. Mech.- A/Solids, 29(6), 1078-1087. https://doi.org/10.1016/j.euromechsol.2010.06.001
  3. Civalek, O. (2017), "Vibration of laminated composite panels and curved plates with different types of FGM composite constituent", Compos. Part B, 122, 89-108. https://doi.org/10.1016/j.compositesb.2017.04.012
  4. Damnjanovic, E., Marjanovic, M. and Danilovic, M.N. (2017), "Free vibration analysis of stiffened and cracked laminated composite plate assemblies using shear-deformable dynamic stiffness elements", Compos. Struct., 180, 723-740. https://doi.org/10.1016/j.compstruct.2017.08.038
  5. Donnell, L.H. (1934), Stability Of Thin-walled Tubes Under Torsion, NACA Report; CA, United States.
  6. Duc, D.D. (2016), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech.- A/Solids, 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004
  7. Farid, M., Zahedinejad, P. and Malekzadeh, P. (2010), "Threedimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on twoparameter elastic foundation using a hybrid semi-analytic, differential quadrature method", Mater. Des., 31(1), 2-13. https://doi.org/10.1016/j.matdes.2009.07.025
  8. Frikha, A., Wali, M., Hajlaoui, A. and Dammak, F. (2016), "Dynamic response of functionally graded material shells with a discrete double directors shell element", Compos. Struct., 154, 385-395. https://doi.org/10.1016/j.compstruct.2016.07.021
  9. Ganapathi, M. (2007), "Dynamic stability characteristics of functionally graded materials shallow spherical shells", Compos. Struct., 79(3), 338-343. https://doi.org/10.1016/j.compstruct.2006.01.012
  10. Jagtap, K.R., Lal, A. and Singh, B.N. (2011), "Stochastic nonlinear free vibration analysis of elastically supported functionally graded materials plate with system randomness in thermal environment", Compos. Struct., 93(12), 3185-3199. https://doi.org/10.1016/j.compstruct.2011.06.010
  11. Jin, G., Shi, S., Su, Z., Li, S. and Liu, Z. (2015), "A modified Fourier-Ritzapproach for free vibration analysis of laminated functionally graded shallow shells with general boundary conditions", Int. J. Mech. Sci., 93, 256-269. https://doi.org/10.1016/j.ijmecsci.2015.02.006
  12. Khalili, S.M.R. and Mohammadi, Y. (2012), "Free vibration analysis of sandwich plates with functionally graded face sheets and temperature-dependent material properties: A new approach", Eur. J. Mech.- A/Solids, 35, 61-74. https://doi.org/10.1016/j.euromechsol.2012.01.003
  13. Khayat, M., Poorvies, D. and Moradi, S. (2016a), "Buckling of Thick Deep Laminated Composite Shell of Revolution under Follower Forces", Struct. Eng. Mech., Int. J., 58(1), 59-91. https://doi.org/10.12989/sem.2016.58.1.059
  14. Khayat, M., Poorvies, D., Moradi, S. and Hemmati, M. (2016b), "Buckling analysis of laminated composite cylindrical shell subjected to lateral displacement-dependent pressure using semi-analytical finite strip method", Steel Compos. Struct., Int. J., 22(2), 301-321. https://doi.org/10.12989/scs.2016.22.2.301
  15. Khayat, M., Poorvies, D. and Moradi, S. (2017a), "Buckling analysis of functionally graded truncated conical shells under external displacement-dependent pressure", Steel Compos. Struct., Int. J., 23(1), 1-16. https://doi.org/10.12989/scs.2017.23.1.001
  16. Khayat, M., Poorvies, D. and Moradi, S. (2017b), "Semi-Analytical Approach in Buckling Analysis of Functionally Graded Shells of Revolution Subjected to Displacement Dependent Pressure", J. Press. Vessel Technol., 139.
  17. Lee, H.W. and Kwak, M.K. (2015), "Free vibration analysis of a circular cylindrical shell using the Rayleigh-Ritz method and comparison of different shell theories", J. Sound Vib., 353(29), 344-377. https://doi.org/10.1016/j.jsv.2015.05.028
  18. Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally gradedcylindrical shells", Int. J. Mech. Sci., 41, 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X
  19. Mahamood, R.M. and Akinlabi, E.T. (2012), "Functionally Graded Material: An Overview", Proceedings of the World Congress on Engineering, London, UK.
  20. Mahmoud, S.R. and Tounsi, A. (2017), "A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 24(5), 569-578.
  21. Naghsh, A., Saadatpour, M.M. and Azhari, M. (2015), "Free vibration analysis of stringer stiffened general shells of revolution using a meridional finite strip method", Thin-Wall. Struct., 94, 651-662. https://doi.org/10.1016/j.tws.2015.05.015
  22. Nanda, N. and Sahu, S.K. (2012), "Free vibration analysis of delaminated composite shells using different shell theories", Int. J. Press. Vessels Piping, 98, 111-118. https://doi.org/10.1016/j.ijpvp.2012.07.008
  23. Novozhilov, V.V. (1964), The Theory Of Thin Elastic Shells, P. Noordhoff, Ltd., Groningen, The Netherlands.
  24. Patel, B.P., Gupta, S.S., Loknath, M.S. and Kadu, C.P. (2005), "Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory", Compos. Struct., 69, 259-270. https://doi.org/10.1016/j.compstruct.2004.07.002
  25. Qin, X.C., Dong, C.Y., Wang, F. and Qu, X.Y. (2017), "Static and dynamic analyses of isogeometric curvilinearly stiffened plates", Appl. Math. Model., 45, 336-364. https://doi.org/10.1016/j.apm.2016.12.035
  26. Rajasekaran, S. (2013), "Free vibration of centrifugally stiffened axially functionally graded tapered Timoshenko beams using differential transformation and quadrature methods", Appl. Math. Model., 37(6), 4440-4463. https://doi.org/10.1016/j.apm.2012.09.024
  27. Reissner, E. (1941), "A new derivation of the equations for the deformation of elastic shells", Am. J. Math, 63,177-188. https://doi.org/10.2307/2371288
  28. Sanders, J.L. (1959), An Improved First-approximation Theory For Thin Shells; NACA Report, CA, United States.
  29. Shahba, A. and Rajasekaran, S. (2012), "Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials", Appl. Math. Model., 36(7), 3094-3111. https://doi.org/10.1016/j.apm.2011.09.073
  30. Shahba, A., Attarnejad, R., Marvi, M.T. and Hajilar, S. (2011), "Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and nonclassical boundary conditions", Compos. Part B, 42(4), 801-808. https://doi.org/10.1016/j.compositesb.2011.01.017
  31. Sofiyev, A.H. (2010), "The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure'', Compos. Struct., 92, 488-498. https://doi.org/10.1016/j.compstruct.2009.08.033
  32. Su, Z., Jin, G. and Ye, T. (2014), "Free vibration analysis of moderately thick functionally graded open shells with general boundary conditions'', Compos. Struct., 117, 169-186. https://doi.org/10.1016/j.compstruct.2014.06.026
  33. Teng, J.G. and Hong, T. (1998), "Nonlinear thin shell theories for numerical buckling predictions", Thin-Wall. Struct., 31, 89-115. https://doi.org/10.1016/S0263-8231(98)00014-7
  34. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Methods Appl. Mech. Eng., 198, 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011
  35. Tornabene, F. and Viola, E. (2009), "Free vibration analysis of functionally graded panels and shells of revolution", Meccanica, 44(3), 255-281. https://doi.org/10.1007/s11012-008-9167-x
  36. 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
  37. Tornabene, F., Brischetto, S., Fantuzzi, N. and Viola, E. (2015), "Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels", Compos. Part B, 81, 231-250. https://doi.org/10.1016/j.compositesb.2015.07.015
  38. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2016), "The GDQ method for the free vibration analysis of arbitrarily shaped laminated composite shells using a NURBS-based isogeometric approach", Compos. Struct., 15, 190-218.
  39. Torki, M.E., Kazemi, M.T., Haddadpour, H. and Mahmoudkhani, S. (2014), "Dynamic stability of cantilevered functionally graded cylindrical shells under axial follower forces", Thin-Wall. Structures, 79, 138-146. https://doi.org/10.1016/j.tws.2013.12.005
  40. Wali, M., Hentati, T. and Dammak, F. (2015), "Free vibration analysis of FGM shell structures with a discrete double directors shell element", Compos. Struct., 125, 295-303. https://doi.org/10.1016/j.compstruct.2015.02.032
  41. Zghal, S., Frikha, A. and Dammak, F. (2018), "Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures'', Appl. Math. Model., 53, 132-155. https://doi.org/10.1016/j.apm.2017.08.021

Cited by

  1. The influence of graphene platelet with different dispersions on the vibrational behavior of nanocomposite truncated conical shells vol.38, pp.1, 2021, https://doi.org/10.12989/scs.2021.38.1.047
  2. An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells vol.40, pp.2, 2018, https://doi.org/10.12989/scs.2021.40.2.307