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DOI QR Code

Comparison of different cylindrical shell theories for stability of nanocomposite piezoelectric separators containing rotating fluid considering structural damping

  • Pour, H. Rahimi (Faculty of Mechanical Engineering, University of Kashan) ;
  • Arani, A. Ghorbanpour (Faculty of Mechanical Engineering, University of Kashan) ;
  • Sheikhzadeh, G.A. (Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2016.10.31
  • Accepted : 2017.02.24
  • Published : 2017.04.30

Abstract

Rotating fluid induced vibration and instability of embedded piezoelectric nano-composite separators subjected to magnetic and electric fields is the main contribution of present work. The separator is modeled with cylindrical shell element and the structural damping effects are considered by Kelvin-Voigt model. Single-walled carbon nanotubes (SWCNTs) are used as reinforcement and effective material properties are obtained by mixture rule. The perturbation velocity potential in conjunction with the linearized Bernoulli formula is used for describing the rotating fluid motion. The orthotropic surrounding elastic medium is considered by spring, damper and shear constants. The governing equations are derived on the bases of classical shell theory (CST), first order shear deformation theory (FSDT) and sinusoidal shear deformation theory (SSDT). The nonlinear frequency and critical angular fluid velocity are calculated by differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of the external voltage, magnetic field, visco-Pasternak foundation, structural damping and volume percent of SWCNTs on the stability of structure. The numerical results are validated with other published works as well as comparing results obtained by three theories. Numerical results indicate that with increasing volume fraction of SWCNTs, the frequency and critical angular fluid velocity are increased.

Keywords

viscoelastic separators;rotating fluid;different shell theories;orthotropic viscoelastic medium;DQM

Acknowledgement

Supported by : Pars Oil and Gas Co.

References

  1. Amabili, M. (2008), Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, New York, NY, USA.
  2. Amabili, M. (2011), "Nonlinear vibrations of laminated circular cylindrical shells, Comparison of different shell theories", Compos. Struct., 94, 207-220. https://doi.org/10.1016/j.compstruct.2011.07.001
  3. Amabili, M., Pellicano, F. and Paidoussis, M.P. (2001), "Nonlinear stability of circular cylindrical shells in annular and unbounded axial flow", J. Appl. Mech., 68, 827-834. https://doi.org/10.1115/1.1406957
  4. Bahadori, R. and Najafizadeh, M.M. (2015), "Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler-Pasternak elastic foundation by First-order Shear Deformation Theory and using Navierdifferential quadrature solution methods", Appl. Math. Model., 39(16), 4877-4894. https://doi.org/10.1016/j.apm.2015.04.012
  5. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: A review", Appl. Mech. Rev., 49, 1-27. https://doi.org/10.1115/1.3101882
  6. Bochkarev, S.A. and Matveenko, V.P. (2012a), "Stability analysis of stationary and rotating circular cylindrical shells conveying flowing and rotating fluid", Mech. Solids, 47(5), 560-565. https://doi.org/10.3103/S0025654412050093
  7. Bochkarev, S.A. and Matveenko, V.P. (2012b), "Stability analysis of cylindrical shells containing a fluidwith axial and circumferential velocity components", J. Appl. Mech. Tech. Phys., 53(5), 768-776. https://doi.org/10.1134/S0021894412050161
  8. Bochkarev, S.A. and Matveenko, V.P. (2013a), "Numerical analysis of stability of a stationary or rotating circular cylindrical shell containing axially flowing and rotating fluid International", J. Mech. Sci. Thech., 68, 258-269. https://doi.org/10.1016/j.ijmecsci.2013.01.024
  9. Bochkarev, S.A. and Matveenko, V.P. (2013b), "Stability of a cylindrical shell subject to an annular flowof rotating fluid", J. Sound Vib., 332(18), 4210-4222. https://doi.org/10.1016/j.jsv.2013.03.010
  10. Chen, T.L.C. and Bert, C.W. (2010), "Dynamic stability of isotropic or composite-material cylindrical shells containing swirling fluid flow", J. Appl. Mech., 44, 112-116.
  11. Cortelezzi, L., Pong, A. and Paidoussis, M.P. (2004), "Flutter of rotating shells with aco-rotating axial flow", J. Appl. Mech., 71(1), 143-145. https://doi.org/10.1115/1.1636794
  12. Dong, K. and Wang, X. (2006), "Wave propagation in laminated piezoelectric cylindrical shells in hydrothermal environment", Struct. Eng. Mech., Int. J., 24(4), 395-410. https://doi.org/10.12989/sem.2006.24.4.395
  13. Dowell, E.H., Srinivasan, A.V., McLean, J.D. and Ambrose, J. (1974), "Aeroelastic stability ofcylindrical shells subjected to a rotating flow", AIAA J., 12(12), 1644-1651. https://doi.org/10.2514/3.49573
  14. Fantuzzi, N., Bacciocchi, M., Tornabene, F., Viola, E. and Ferreira, A.J.M. (2015), "Radial basis functions based on differential quadrature method for the free vibration analysis of laminated composite arbitrarily shaped plates", Compos. Part B: Eng., 78, 65-78. https://doi.org/10.1016/j.compositesb.2015.03.027
  15. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube reinforced composites", J. Sound Vib., 329(10), 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020
  16. Fukuda, H. and Kawata, K. (1974), "On Young's modulus of short fibre composites", Fibre Sci. Technol., 7(3), 207-222. https://doi.org/10.1016/0015-0568(74)90018-9
  17. Ganesan, R. and Ramu, S.A. (1995), "Vibration and stability of fluid conveying pipes with stochastic parameters", Struct. Eng. Mech., Int. J., 3(4), 313-324. https://doi.org/10.12989/sem.1995.3.4.313
  18. Ghorbanpour Arani, A., Haghshenas, E., Amir, S., Mozdianfard, M.R. and Latifi, M. (2013a), "Electro-thermo-mechanical response of thick-walled piezoelectric cylinder reinforced by boron-nitride nanotubes", Streng. Mat., 45(1), 102-115. https://doi.org/10.1007/s11223-013-9437-2
  19. Ghorbanpour Arani, A., Kolahchi, R. and Khoddami Maraghi, Z. (2013b), "Nonlinear vibration and instability of embedded double-walled boron nitride nanotubes based on nonlocal cylindrical shell theory", Appl. Math. Model., 37(14), 7685-7707. https://doi.org/10.1016/j.apm.2013.03.020
  20. Ghorbanpour Arani, A., Haghparast, E., Khoddami Maraghi, Z. and Amir, S. (2015a), "Static stress analysis of carbon nano-tube reinforced composite CNTRC cylinder under non-axisymmetric thermo-mechanical loads and uniform electro-magnetic fields", Compos. Part B, 68, 136-145. https://doi.org/10.1016/j.compositesb.2014.08.036
  21. Ghorbanpour Arani, A., Abdollahian, M. and Kolahchi, R. (2015b), "Nonlinear vibration of embedded smart composite microtube conveying fluid based on modified couple stress theory", Polym. Compos., 36(7), 1314-1324. https://doi.org/10.1002/pc.23036
  22. Ghorbanpour Arani, A., Kolahchi, R. and Zarei, M.Sh. (2015c), "Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory", Compos. Struct., 132, 506-526. https://doi.org/10.1016/j.compstruct.2015.05.065
  23. Ghorbanpour Arani, A., Karimi, M.S. and Rabani Bidgoli, M. (2016), "Nonlinear vibration and instability of rotating piezoelectric nano-composite sandwich cylindrical shells containing axially flowing and rotating fluid-particle mixture", Polym. Compos.
  24. Gosselin, F. and Paidoussis, M.P. (2009), "Blocking in the rotating axial flow in a co-rotatingflexible shell", J. Appl. Mech., 76(1), 011001. https://doi.org/10.1115/1.2998486
  25. Gupta, U.S., Lal, R. and Sharma, S. (2006), "Vibration analysis of non-homogeneous circular plate of nonlinear thickness variation by differential quadrature method", J. Sound Vib., 298(4), 892-906. https://doi.org/10.1016/j.jsv.2006.05.030
  26. Jalili, N. (2010), Piezoelectric-Based Vibration Control from Macro to Micro/Nano Scale Systems Springer Science, New York.
  27. Kumar, D. and Srivastava, A. (2016), "Elastic properties of CNT and graphene-reinforced nanocomposites using RVE ", Steel Compos. Struct., Int. J., 21(5), 1085-1103. https://doi.org/10.12989/scs.2016.21.5.1085
  28. Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2014), "Dynamic stability analysis of carbon nanotube-reinforced 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
  29. Liew, K.M. and Liu, F.L. (2000), "Differential quadrature method for vibration analysis of shear deformable annular sector plates", J. Sound Vib., 230(2), 335-356. https://doi.org/10.1006/jsvi.1999.2623
  30. Mantari, J.L. and Guedes Soares, C. (2014), "Optimized sinusoidal higher order shear deformation theory for the analysis of functionally graded plates and shells", Compos. Part B, 56, 126-136. https://doi.org/10.1016/j.compositesb.2013.07.027
  31. Nie, G. and Zhong, Z. (2007), "Semi-analytical solution for threedimensional vibration of functionally graded circular plates", Comput. Methods Appl. Mech. Eng., 196(49), 4901-4910. https://doi.org/10.1016/j.cma.2007.06.028
  32. Nie, G. and Zhong, Z. (2010), "Dynamic analysis of multidirectional functionally graded annular plate", Appl. Math. Model., 34(3), 608-616. https://doi.org/10.1016/j.apm.2009.06.009
  33. Paidoussis, M.P., Misra, A.K. and Nguyen, V.B. (1992), "Internal-and annular-flow-induced instabilities of a clamped-clamped or cantilevered cylindrical shell in acoaxial conduit, the effects of system parameters", J. Sound Vib., 159(2), 193-205. https://doi.org/10.1016/0022-460X(92)90031-R
  34. Rabani Bidgoli, M., Karimi, M.S. and Ghorbanpour Arani, A. (2016), "Viscous fluid induced vibration and instability of FGCNT-reinforced cylindrical shells integrated with piezoelectric layers", Steel Compos. Struct., Int. J., 19(3), 713-733.
  35. Sofiyev, A.H. (2011), "Thermal buckling of FGM shells resting on a two-parameter elastic foundation", Thin-Wall. Struct., 49(10), 1304-1311. https://doi.org/10.1016/j.tws.2011.03.018
  36. Sofiyev, A.H. (2016), "Nonlinear free vibration of shear deformable orthotropic functionally graded cylindrical shells", Compos. Struct., 142, 35-44. https://doi.org/10.1016/j.compstruct.2016.01.066
  37. Sun, A., Xu, X., Lim, C.W., Zhou, Zh. and Xiao, Sh. (2016), "Accurate thermo-electro-mechanical buckling of shear deformable piezoelectric fiber-reinforced composite cylindrical shells", Compos. Struct., 141, 221-231. https://doi.org/10.1016/j.compstruct.2016.01.054
  38. Tahouneh, V. (2016), "Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates", Steel Compos. Struct., Int. J., 20(3), 623-649. https://doi.org/10.12989/scs.2016.20.3.623
  39. Tahouneh, V. and Yas, M.H. (2014), "Influence of equivalent continuum model based on the Eshelby-Mori-Tanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotube-reinforced annular plates", Polym. Compos., 35(8), 1644-1661. https://doi.org/10.1002/pc.22818
  40. Tahouneh, V., Yas, M.H., Tourang, H. and Kabirian, M. (2013), "Semi-analytical solution for three-dimensional vibration of thick continuous grading fiber reinforced (CGFR) annular plates on Pasternak elastic foundations with arbitrary boundary conditions on their circular edges", Meccanica, 48(6), 1313-1336. https://doi.org/10.1007/s11012-012-9669-4
  41. Thai, H.T. and Vo, T.P. (2013), "A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates", Appl. Math. Model., 37(5), 3269-3281. https://doi.org/10.1016/j.apm.2012.08.008
  42. Tornabene, F. and Ceruti, A. (2013), "Mixed static and dynamic optimization of four-parameter functionally graded completely doubly curved and degenerate shells and panels using GDQ method", Math. Prob. Eng., 2013, 1-33.
  43. Yang, H., Jin, G., Liu, Zh., Wang, X. and Miao, X. (2015), "Vibration and damping analysis of thick sandwich cylindrical shells with a viscoelastic core under arbitrary boundary conditions", Int. J. Mech. Sci., 92, 162-177. https://doi.org/10.1016/j.ijmecsci.2014.12.003