Structural Engineering and Mechanics

  • 제61권5호
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  • Pages.563-576
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  • 2017
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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Three-dimensional analysis of the natural vibration of the three-layered hollow sphere with middle layer made of FGM

  • Akbarov, Surkay D. (Department of Mechanical Engineering, Yildiz Technical University) ;
  • Guliyev, Hatam H. (Institute of Geology and Geophysics of the National Academy of Sciences of Azerbaijan) ;
  • Yahnioglu, Nazmiye (Department of Mathematical Engineering, Yildiz Technical University)
  • 투고 : 2016.04.24
  • 심사 : 2016.10.19
  • 발행 : 2017.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper is a continuation of the investigations started in the paper by Akbarov, S.D., Guliyev, H.H and Yahnioglu, N. (2016) "Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach", Structural Engineering and Mechanics, 57(2), 239-263, to the case where the three-layered sphere is a hollow one. Three-dimensional exact field equations of elastodynamics are employed for investigation and the discrete-analytical method is employed for solution of the corresponding eigenvalue problem. The FGM is modelled as inhomogeneous for which the modulus of elasticity, Poison's ratio and density vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies are presented and discussed. These results are also compared with the corresponding ones obtained in the previous paper by the authors. In particular, it is established that for certain harmonics and for roots of certain order, the values of the natural frequency obtained for the hollow sphere can be greater (or less) than those obtained for the solid sphere.

키워드

과제정보

연구 과제번호 : Complex of theoretical and experimental investigations related to the study of the interdisciplinary problems of the Geomechanics

연구 과제 주관 기관 : National Academy of Sciences of Azerbaijan

참고문헌

  1. Akbarov, A.D., Guliyev, H.H. and Yahnioglu, N. (2016), "Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach", Struct. Eng. Mech., 57, 239-263. https://doi.org/10.12989/sem.2016.57.2.239
  2. Akbarov, S.D. (2006), "Frequency response of the axisymmetrically finite pre-stretched slab from incompressible functionally graded material on a rigid foundation", Int. J. Eng. Sci., 44, 484-500. https://doi.org/10.1016/j.ijengsci.2006.04.004
  3. Akbarov, S.D. (2015), Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized Three-Dimensional Approach, Springer-Heidelberg, New York, NY, USA.
  4. Anderson, D.L. (2007), New Theory of the Earth, Cambridge University Press, Cambridge, UK.
  5. Asemi, K., Salehi, M. and Sadighi, M. (2014), "Three dimensional static and dynamic analysis of two dimensional functionally graded annular sector plates", Struct. Eng. Mech., 51, 1067-1089. https://doi.org/10.12989/sem.2014.51.6.1067
  6. Asgari, M. and Akhlagi, M. (2011), "Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations", Eur. J. Mech. A Solid, 30, 72-81. https://doi.org/10.1016/j.euromechsol.2010.10.002
  7. Chen, W.Q. and Ding, H.J. (2001), "Free vibration of multi-layered spherically isotropic hollow spheres", Int. J. Mech. Sci., 43, 667-680. https://doi.org/10.1016/S0020-7403(00)00044-8
  8. Chree, C. (1889), "The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solution and applications", Trans. Cambridge Philos. Soc., 14, 250-309.
  9. Eringen, A.C. and Suhubi, E.S. (1975), Elastodynamics. Vol I. Finite Motion; Vol II. Linear Theory, Academic Press, New York, NY, USA.
  10. Grigorenko, Y.M. and Kilina, T.N. (1989), "Analysis of the frequencies and modes of natural vibration of laminated hollow spheres in three- and two-dimensional formulations", Int. Appl. Mech., 25, 1165-1171.
  11. Guz, A.N. (1985a), "Dynamics of an elastic isotropic sphere of an incompressible material subjected to initial uniform volumetric loading", Int. Appl. Mech., 21, 738-746.
  12. Guz, A.N. (1985b), "Dynamics of an elastic isotropic sphere of a compressible material under cubic initial loading", Int. App. Mech., 21, 1153-1159.
  13. Hasheminejad, S.M. and Mirzaei, Y. (2011), "Exact 3D elasticity solution for free vibrations of an eccentric hollow sphere", J. Sound Vib., 330, 229-244. https://doi.org/10.1016/j.jsv.2010.08.011
  14. Ilhan, N. and Koc N. (2015), "Influence of polled direction on the stress distribution in piezoelectric materials", Struct. Eng. Mech., 54, 955-971. https://doi.org/10.12989/sem.2015.54.5.955
  15. Ipek, C. (2015), "The dispersion of the flexural waves in a compound hollow cylinder under imperfect contact between layers", Struct. Eng. Mech., 55, 338-348.
  16. Jiang, H., Young, P.G. and Dickinson, S.M. (1996), "Natural frequencies of vibration of layered hollow spheres using exact three-dimensional elasticity equations", J. Sound Vib., 195, 155-162. https://doi.org/10.1006/jsvi.1996.0412
  17. Jin, G., Su, Z., Shi, S., Ye, T. and Gao, S. (2014a), "Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions", Compos. Struct., 108, 565-577. https://doi.org/10.1016/j.compstruct.2013.09.051
  18. Jin, G., Su, Z., Shi, S., Ye, T. and Jia, X. (2014b), "Three-dimensional vibration analysis of isotropic and orthotropic conical shells with elastic boundary restraints", Int. J. Mech. Sci., 89, 207-221. https://doi.org/10.1016/j.ijmecsci.2014.09.005
  19. Jin, G., Su, Z., Ye, T. and Gao, S. (2015), "Three-dimensional free vibration analysis of functionally graded annular sector plates with general boundary conditions", Compos. Part B, 83, 352-366. https://doi.org/10.1016/j.compositesb.2015.08.032
  20. Lamb, H. (1882), "On the vibrations of an elastic sphere", Proc. London Math. Soc., 13, 189-212.
  21. Lapwood, E.R. and Usami, T. (1981), Free Oscillations of the Earth, Cambridge University Press, Cambridge, UK.
  22. Love, A.E.H. (1944), A treatise on the Mathematical Theory of Elasticity, Dover, New York, NY, USA.
  23. Sato, Y. and Usami, T. (1962a), "Basic study on the oscillation of a homogeneous elastic sphere; part I, frequency of the free oscillations", Geophys. Mag., 31, 15-24.
  24. Sato, Y. and Usami, T. (1962b), "Basic study on the oscillation of a homogeneous elastic sphere; part II, distribution of displacement", Geophys. Mag., 31, 25-47.
  25. Sato, Y., Usami, T. and Ewing, M. (1962), "Basic study on the oscillation of a homogeneous elastic sphere, IV. Propagation of disturbances on the sphere", Geophys. Mag., 31, 237-242.
  26. Shah, A.H., Ramakrishnan, C.V. and Datta, S.K. (1969a), "Three dimensional and shell theory analysis of elastic waves in a hollow sphere, Part I. Analytical foundation", J. Appl. Mech., 36, 431-439. https://doi.org/10.1115/1.3564698
  27. Shah, A.H., Ramakrishnan, C.V. and Datta, S.K. (1969b), "Three dimensional and shell theory analysis of elastic waves in a hollow sphere, Part II. Numerical results", J. Appl. Mech., 36, 440-444. https://doi.org/10.1115/1.3564699
  28. Sharma, J.N., Sharma, D.K. and Dhaliwai, S.S. (2012), "Free vibration analysis of a viscothermoelastic solid sphere", Int. J. Appl. Math. Mech., 8, 45-68.
  29. Ye, T., Jin, G. and Su, Z. (2014), "Three-dimensional vibration analysis of laminated functionally graded spherical shells with general boundary conditions", Compos. Struct., 116, 571-588. https://doi.org/10.1016/j.compstruct.2014.05.046
  30. Ye, T., Jin, G. 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, 3326-3354. https://doi.org/10.1177/1077546314553608
  31. Yun, W., Rongqiao, X. and Haojiang, D. (2010), "Three-dimensional solution of axisymmetric bending of functionally graded circular plates", Compos. Struct., 92, 1683-1693. https://doi.org/10.1016/j.compstruct.2009.12.002

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