Steel and Composite Structures

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Free vibration analysis of uniform and stepped functionally graded circular cylindrical shells

  • Li, Haichao (College of Shipbuilding Engineering, Harbin Engineering University) ;
  • Pang, Fuzhen (College of Shipbuilding Engineering, Harbin Engineering University) ;
  • Du, Yuan (College of Shipbuilding Engineering, Harbin Engineering University) ;
  • Gao, Cong (College of Shipbuilding Engineering, Harbin Engineering University)
  • Received : 2018.08.20
  • Accepted : 2019.10.13
  • Published : 2019.10.25
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Abstract

A semi analytical method is employed to analyze free vibration characteristics of uniform and stepped functionally graded circular cylindrical shells under complex boundary conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy complex boundary conditions, the penalty method about spring technique is adopted. The solutions about free vibration behavior of functionally graded circular cylindrical shells were obtained by approach of Rayleigh-Ritz. To confirm the dependability and validity of present approach, numerical verifications and convergence studies are conducted on functionally graded cylindrical shells under various influencing factors such as boundaries, spring parameters et al. The present method apparently has rapid convergence ability and excellent stability, and the results of the paper are closely agreed with those obtained by FEM and published literatures.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, Central University, China Postdoctoral Science Foundation

References

  1. Bambill, D.V., Rossit, C.A. and Felix, D.H. (2015), "Free vibrations of stepped axially functionally graded Timoshenko beams", Meccanica, 50(4), 1073-1087. https://doi.org/10.1007/s11012-014-0053-4
  2. Beni, Y.T., Mehralian, F. and Razavi, H. (2015), "Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory", Compos. Struct., 120, 65-78. https://doi.org/10.1016/j.compstruct.2014.09.065
  3. Bhrawy, A.H., Taha, T.M. and Machado, J.A.T. (2015), "A review of operational matrices and spectral techniques for fractional calculus", Nonlinear Dyn., 81(3), 1023-1052. https://doi.org/10.1007/s11071-015-2087-0
  4. Bidgoli, M.R., Karimi, M.S. and Arani, A.G. (2015), "Viscous fluid induced vibration and instability of FG-CNT-reinforced cylindrical shells integrated with piezoelectric layers", Steel Compos. Struct., Int. J., 19(3), 713-733. https://doi.org/10.12989/scs.2015.19.3.713
  5. Bodaghi, M. and Shakeri, M. (2012), "An analytical approach for free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to impulsive loads", Compos. Struct., 94(5), 1721-1735. https://doi.org/10.1016/j.compstruct.2012.01.009
  6. Brischetto, S., Tornabene, F., Fantuzzi, N. and Viola, E. (2016), "3D exact and 2D generalized differential quadrature models for free vibration analysis of functionally graded plates and cylinders", Meccanica, 51(9), 2059-2098. https://doi.org/10.1007/s11012-016-0361-y
  7. Cao, Z.Y. and Tang, S.G. (2012), "Natural Vibration of Functionally Graded Cylindrical Shells With Infinite and Finite Lengths", J. Vib. Acoust., 134(1), 011013. https://doi.org/10.1115/1.4004900
  8. Fantuzzi, N., Brischetto, S., Tornabene, F. and Viola, E. (2016), "2D and 3D shell models for the free vibration investigation of functionally graded cylindrical and spherical panels", Compos. Struct., 154, 573-590. https://doi.org/10.1016/j.compstruct.2016.07.076
  9. Guo, J., Shi, D., Wang, Q., Tang, J. and Shuai, C. (2018), "Dynamic analysis of laminated doubly-curved shells with general boundary conditions by means of a domain decomposition method", Int. J. Mech. Sci., 138, 159-186. https://doi.org/10.1016/j.ijmecsci.2018.02.004
  10. Hosseini-Hashemi, S., Ilkhani, M.R. and Fadaee, M. (2012), "Identification of the validity range of Donnell and Sanders shell theories using an exact vibration analysis of functionally graded thick cylindrical shell panel", Acta Mechanica, 223(5), 1101-1118. https://doi.org/10.1007/s00707-011-0601-0
  11. Hosseini-Hashemi, S., Derakhshani, M. and Fadaee, M. (2013), "An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates", Appl. Math. Model., 37(6), 4147-4164. https://doi.org/10.1007/s00707-011-0601-0
  12. Javed, S., Viswanathan, K.K. and Aziz, Z.A. (2016), "Free vibration analysis of composite cylindrical shells with nonuniform thickness walls", Steel Compos. Struct., Int. J., 20(5), 1087-1102. https://doi.org/10.12989/scs.2016.20.5.1087
  13. Jin, G.Y., Xie, X. and Liu, Z.G. (2014), "The Haar wavelet method for free vibration analysis of functionally graded cylindrical shells based on the shear deformation theory", Compos. Struct., 108, 435-448. https://doi.org/10.1016/j.compstruct.2013.09.044
  14. Kamarian, S., Sadighi, M., Shakeri, M. and Yas, M.H. (2014), "Free vibration response of sandwich cylindrical shells with functionally graded material face sheets resting on Pasternak foundation", J. Sandw. Struct. Mater., 16(5), 511-533. https://doi.org/10.1177/1099636214541573
  15. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  16. Li, H., Pang, F., Gong, Q. and Teng, Y. (2019), "Free vibration analysis of axisymmetric functionally graded doubly-curved shells with un-uniform thickness distribution based on Ritz method", Compos. Struct., 225, 111145. https://doi.org/10.1016/j.compstruct.2019.111145
  17. Liu, D.Y., Kitipornchai, S., Chen, W.Q. and Yang, J. (2018), "Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell", Compos. Struct., 189, 560-569. https://doi.org/10.1016/j.compstruct.2018.01.106
  18. Pang, F., Li, H., Chen, H. and Shan, Y. (2019a), "Free vibration analysis of combined composite laminated cylindrical and spherical shells with arbitrary boundary conditions", Mech. Adv. Mater. Struct., 1-18. https://doi.org/10.1080/15376494.2018.1553258
  19. Pang, F., Li, H., Cui, J., Du, Y. and Gao, C. (2019b), "Application of flugge thin shell theory to the solution of free vibration behaviors for spherical-cylindrical-spherical shell: A unified formulation", Eur. J. Mech. - A/Solids, 74, 381-393. https://doi.org/10.1016/j.euromechsol.2018.12.003
  20. Pang, F.Z., Li, H.C., Jing, F.M. and Du, Y. (2019c), "Application of first-order shear deformation theory on vibration analysis of stepped functionally graded paraboloidal shell with general edge constraints", Materials, 12(1), 69. https://doi.org/10.3390/ma12010069
  21. Qu, Y., Chen, Y., Long, X., Hua, H. and Meng, G. (2013a), "Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method", Appl. Acoust., 74(3), 425-439. https://doi.org/10.1016/j.apacoust.2012.09.002
  22. Qu, Y.G., Long, X.H., Yuan, G.Q. and Meng, G. (2013b), "A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions", Compos. Part B-Eng., 50, 381-402. https://doi.org/10.1016/j.compositesb.2013.02.028
  23. Razavi, H., Babadi, A.F. and Beni, Y.T. (2017), "Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory", Compos. Struct., 160, 1299-1309. https://doi.org/10.1016/j.compstruct.2016.10.056
  24. Su, Z., Jin, G.Y., Shi, S.X., Ye, T.G. and Jia, X.Z. (2014), "A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions", Int. J. Mech. Sci., 80, 62-80. https://doi.org/10.1016/j.ijmecsci.2014.01.002
  25. Tang, D., Yao, X.L., Wu, G.X. and Peng, Y. (2017), "Free and forced vibration analysis of multi-stepped circular cylindrical shells with arbitrary boundary conditions by the method of reverberation-ray matrix", Thin-Wall. Struct., 116, 154-168. https://doi.org/10.1016/j.tws.2017.03.023
  26. 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(37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011
  27. 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
  28. Wang, Y.W. and Wu, D.F. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aerosp. Sci. Technol., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003
  29. Wang, Q., Cui, X., Qin, B. and Liang, Q. (2017a), "Vibration analysis of the functionally graded carbon nanotube reinforced composite shallow shells with arbitrary boundary conditions", Compos. Struct., 182, 364-379. https://doi.org/10.1016/j.compstruct.2017.09.043
  30. Wang, Q.S., Shi, D.Y., Liang, Q. and Pang, F.Z. (2017b), "Free vibration of moderately thick functionally graded parabolic and circular panels and shells of revolution with general boundary conditions", Eng. Computat., 34(5), 1598-1641. https://doi.org/10.1108/EC-06-2016-0218
  31. Yas, M.H. and Aragh, B.S. (2011), "Elasticity solution for free vibration analysis of four-parameter functionally graded fiber orientation cylindrical panels using differential quadrature method", Eur. J. Mech. A-Solids, 30(5), 631-638. https://doi.org/10.1016/j.euromechsol.2010.12.009
  32. Yas, M.H., Pourasghar, A., Kamarian, S. and Heshmati, M. (2013), "Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube", Mater. Des., 49, 583-590. https://doi.org/10.1016/j.matdes.2013.01.001
  33. Ye, T.G., Jin, G.Y. and Su, Z. (2016), "Three-dimensional vibration analysis of functionally graded sandwich deep open spherical and cylindrical shells with general restraints", J. Vib. Control, 22(15), 3326-3354. https://doi.org/10.1177/1077546314553608
  34. Zeighampour, H. and Shojaeian, M. (2017), "Size-dependent vibration of sandwich cylindrical nanoshells with functionally graded material based on the couple stress theory", J. Brazil. Soc. Mech. Sci. Eng., 39(7), 2789-2800. https://doi.org/10.1007/s40430-017-0770-4
  35. 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
  36. Zhang, B., He, Y.M., Liu, D.B., Shen, L. and Lei, J.A. (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
  37. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Thermoelastic and vibration analysis of functionally graded cylindrical shells", Int. J. Mech. Sci., 51(9-10), 694-707. https://doi.org/10.1016/j.ijmecsci.2009.08.001

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