Structural Engineering and Mechanics

  • 제59권1호
  • /
  • Pages.153-186
  • /
  • 2016
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  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear higher order Reddy theory for temperature-dependent vibration and instability of embedded functionally graded pipes conveying fluid-nanoparticle mixture

  • Raminnea, M. (Faculty of Mechanical Engineering, University of Tabriz) ;
  • Biglari, H. (Faculty of Mechanical Engineering, University of Tabriz) ;
  • Tahami, F. Vakili (Faculty of Mechanical Engineering, University of Tabriz)
  • 투고 : 2015.07.22
  • 심사 : 2016.04.15
  • 발행 : 2016.07.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper addresses temperature-dependent nonlinear vibration and instability of embedded functionally graded (FG) pipes conveying viscous fluid-nanoparticle mixture. The surrounding elastic medium is modeled by temperature-dependent orthotropic Pasternak medium. Reddy third-order shear deformation theory (RSDT) of cylindrical shells are developed using the strain-displacement relations of Donnell theory. The well known Navier-Stokes equation is used for obtaining the applied force of fluid to pipe. Based on energy method and Hamilton's principal, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the frequency and critical fluid velocity of system. The effects of different parameters such as mode numbers, nonlinearity, fluid velocity, volume percent of nanoparticle in fluid, gradient index, elastic medium, boundary condition and temperature gradient are discussed. Numerical results indicate that with increasing the stiffness of elastic medium and decreasing volume percent of nanoparticle in fluid, the frequency and critical fluid velocity increase. The presented results indicate that the material in-homogeneity has a significant influence on the vibration and instability behaviors of the FG pipes and should therefore be considered in its optimum design. In addition, fluid velocity leads to divergence and flutter instabilities.

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참고문헌

  1. Abdollahian, M., Ghorbanpour Arani, A., Mosallaie Barzoki, A.A., Kolahchi, R. and Loghman, (2013), "A. Non-local wave propagation in embedded armchair TWBNNTs conveying viscous fluid using DQM", Physica B, 418, 1-15. https://doi.org/10.1016/j.physb.2013.02.037
  2. Amabili, M., Pellicano, F. and Paidoussis, M.P. (2002), "Non-linear dynamics and stability of circular cylindrical shells conveying flowing fluid", Comput. Struct., 80, 899-906. https://doi.org/10.1016/S0045-7949(02)00055-X
  3. Amabili, M. (2003), "A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach", J. Sound Vib., 264, 1091-1125. https://doi.org/10.1016/S0022-460X(02)01385-8
  4. Amabili, M., Karagiozis, K. and Paidoussis, M.P. (2009), "Effect of geometric imperfections on non-linear stability of circular cylindrical shells conveying fluid", Int. J. Nonlin. Mech., 44, 276- 289. https://doi.org/10.1016/j.ijnonlinmec.2008.11.006
  5. Fazzolari, F.A. and Carrera, E. (2014), "Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core", J. Sound. Vib., 333,1485-1508. https://doi.org/10.1016/j.jsv.2013.10.030
  6. Ghorbanpour Arani, A., Karimi, M.S. and Rabani Bidgoli, M. (2016), "Nonlinear vibration and instability of rotating piezoelectric nanocomposite sandwich cylindrical shells containing axially flowing and rotating fluid-particle mixture", Polym. Compos., doi: 10.1002/pc.23949. (in Press)
  7. Jansen, E.L. (2008), "A perturbation method for nonlinear vibrations of imperfect structures: Application to cylindrical shell vibrations", Int. J. Solid. Struct., 45, 1124-1145. https://doi.org/10.1016/j.ijsolstr.2007.07.007
  8. Jung, W.Y., Park, W.T. and Han, S.C. (2014), "Bending and vibration analysis of S-FGM microplates embedded in Pasternak elastic medium using the modified couple stress theory", Int. J. Mech. Sci., 87, 150-162. https://doi.org/10.1016/j.ijmecsci.2014.05.025
  9. Karagiozis, K.N., Amabili, M., Paidoussis, M.P. and Misra, A.K. (2005), "Nonlinear vibrations of fluidfilled clamped circular cylindrical shells", J. Fluid. Struct., 21, 579-595. https://doi.org/10.1016/j.jfluidstructs.2005.07.020
  10. Khadimallaha, M.A., Casimir, J.B., Chafra, M. and Smaoui, H. (2011), "Dynamic stiffness matrix of an axisymmetric shell and response to harmonic distributed loads", Comput. Struct., 89, 467-475. https://doi.org/10.1016/j.compstruc.2010.11.017
  11. Khalili, S.M.R., Davar, A. and Malekzadeh Fard, K. (2012), "Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional refined higher-order theory", Int. J. Mech. Sci., 56, 1-25. https://doi.org/10.1016/j.ijmecsci.2011.11.002
  12. Kim, Y.W. (2015), Free vibration analysis of FGM cylindrical shell partially resting on Pasternak elastic foundation with an oblique edge", Compos. Part B: Eng., 70, 263-276. https://doi.org/10.1016/j.compositesb.2014.11.024
  13. Kolahchi, R., Moniri Bidgoli, A.M. and Heydari M.M. (2015a), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55, 1001-1014. https://doi.org/10.12989/sem.2015.55.5.1001
  14. Kolahchi, R., Rabani Bidgoli, M. Beygipoor, Gh. and Fakhar, M.H. (2015b), "A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field", J. Mech. Sci. Tech., 29(9), 3669-3677. https://doi.org/10.1007/s12206-015-0811-9
  15. Kolahchi, R. and Moniribidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37, 265-274. https://doi.org/10.1007/s10483-016-2030-8
  16. Kutlu, A. and Omurtag, M.H. (2012), "Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method", Int. J. Mech. Sci., 65, 64-74. https://doi.org/10.1016/j.ijmecsci.2012.09.004
  17. Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2014), "Dynamic stability analysis of carbonnanotubereinforced functionally graded cylindrical panels using the element-free kp-Ritz method", Compos. Struct., 113, 328-338. https://doi.org/10.1016/j.compstruct.2014.03.035
  18. Liew, K.M., Lei, Z.X., Yu, J.L. and Zhang, L.W. (2014), "Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach", Comput. Meth. Appl. Mech. Eng., 268, 1-17. https://doi.org/10.1016/j.cma.2013.09.001
  19. Mirzavand, B. and Eslami, M.R. (2011), "A closed-form solution for thermal buckling of piezoelectric FGM rectangular plates with temperature-dependent properties", Acta Mech., 218, 87-101. https://doi.org/10.1007/s00707-010-0402-x
  20. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "Free vibration of functionally graded shells by a higherorder shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations", Euro. J. Mech. A/Solid., 37, 24-34. https://doi.org/10.1016/j.euromechsol.2012.05.005
  21. Ng, T.Y., Lam, Y.K., Liew, K.M. and Reddy J.N. (2001), "Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading", Int. J. Solid. Struct., 38, 1295-1300. https://doi.org/10.1016/S0020-7683(00)00090-1
  22. Nguyen, D. and Thang, P.T. (2015), "Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations", Aero. Sci. Tech., 40, 115-127. https://doi.org/10.1016/j.ast.2014.11.005
  23. Pellicano, F. and Avramov K.V. (2007), "Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk", Commun. Nonlin. Sci. Num. Simul., 12, 496-518. https://doi.org/10.1016/j.cnsns.2005.04.004
  24. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib., 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  25. Reddy, J.N. (1984), "A Simple Higher Order Theory for Laminated Composite Plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  26. Reddy, J.N. and Praveen, G.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plate", Int. J. Solid. Struct., 35, 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  27. 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, 3094-3111. https://doi.org/10.1016/j.apm.2011.09.073
  28. Shen, H.Sh. and Zhang, Ch.L. (2011), "Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates", Computat. Mater. Sci., 50, 1022-1029. https://doi.org/10.1016/j.commatsci.2010.10.042
  29. Sheng, G.G. and Wang, X. (2009a), "Active control of functionally graded laminated cylindrical shells", Compos. Struct., 90, 448-457. https://doi.org/10.1016/j.compstruct.2009.04.017
  30. Sheng, G.G. and Wang, X. (2009b), "Studies on dynamic behavior of functionally graded cylindrical shells with PZT layers under moving loads", J. Sound Vib., 323, 772-789 . https://doi.org/10.1016/j.jsv.2009.01.017
  31. Sheng, G.G. and Wang, X. (2010), "Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads", Compos. Struct., 93, 162-170. https://doi.org/10.1016/j.compstruct.2010.06.004
  32. Shu, C., Chen, W., Xue, H. and Du, H. (2001), "Numerical study of grid distribution effects on accuracy of DQ analysis of beams and plates by error estimation of derivative approximation", Int. J. Numer. Meth. Eng., 51, 159-179. https://doi.org/10.1002/nme.150
  33. Wang, L. and Ni, Q. (2009), "A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid", Mech. Res. Commun., 36, 833-837. https://doi.org/10.1016/j.mechrescom.2009.05.003
  34. Wattanasakulpong, N., Gangadhara Prusty, B., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049
  35. Xing, Y., Liu, B. and Xu, T. (2013), "Exact solutions for free vibration of circular cylindrical shells with classical boundary conditions", Int. J. Mech. Sci., 75, 178-188. https://doi.org/10.1016/j.ijmecsci.2013.06.005
  36. Yang, J. and Shen, H.S. (2003), "Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels", J. Sound Vib., 261, 871-893. https://doi.org/10.1016/S0022-460X(02)01015-5
  37. Zhang, L.W., Lei, Z.X., Liew, K.M. and Yu, J.L. (2014a), "Large deflection geometrically nonlinear analysis of carbon nanotube-reinforced functionally graded cylindrical panels", Comput. Meth. Appl. Mech. Eng., 273, 1-18. https://doi.org/10.1016/j.cma.2014.01.024
  38. Zhang, L.W., Lei, Z.X., Liew, K.M. and Yu, J.L. (2014b), "Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels", Compos. Struct., 111, 205-212. https://doi.org/10.1016/j.compstruct.2013.12.035

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