Advertisement

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

  • Raheb Gholami
  • Reza Ansari
Regular Article
  • 41 Downloads

Abstract.

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton’s principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy’s third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

References

  1. 1.
    B. Ashrafi, P. Hubert, S. Vengallatore, Nanotechnology 17, 4895 (2006)ADSCrossRefGoogle Scholar
  2. 2.
    S.C. Tjong, Carbon nanotube reinforced composites: metal and ceramic matrices (John Wiley & Sons, 2009)Google Scholar
  3. 3.
    V. Unnikrishnan, G. Unnikrishnan, J. Reddy, F. Rostam-Abadi, Int. J. Mech. Mater. Des. 9, 181 (2013)CrossRefGoogle Scholar
  4. 4.
    S.B. Sinnott, R. Andrews, Crit. Rev. Solid State Mater. Sci. 26, 145 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    X.-Q. Fang, C.-S. Zhu, J.-X. Liu, X.-L. Liu, Physica B 529, 41 (2018)ADSCrossRefGoogle Scholar
  6. 6.
    C.-S. Zhu, X.-Q. Fang, J.-X. Liu, H.-Y. Li, Eur. J. Mech. A/Solids 66, 423 (2017)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    V.P. Veedu, A. Cao, X. Li, K. Ma, C. Soldano, S. Kar et al., Nat. Mater. 5, 457 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    K. Sun, J. Yu, C. Zhang, X. Zhou, Mater. Lett. 66, 92 (2012)CrossRefGoogle Scholar
  9. 9.
    K.-T. Lau, C. Gu, G.-H. Gao, H.-y. Ling, S.R. Reid, Carbon 42, 426 (2004)CrossRefGoogle Scholar
  10. 10.
    Y. Sun, Q. Chen, Appl. Phys. Lett. 95, 021901 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    L. Shao, R. Luo, S. Bai, J. Wang, Compos. Struct. 87, 274 (2009)CrossRefGoogle Scholar
  12. 12.
    P. Kumar, J. Srinivas, Compos. Struct. 177, 158 (2017)CrossRefGoogle Scholar
  13. 13.
    S. Tagrara, A. Benachour, M.B. Bouiadjra, A. Tounsi, Steel Compos. Struct. 19, 1259 (2015)CrossRefGoogle Scholar
  14. 14.
    J. Jam, Y. Kiani, Compos. Struct. 125, 586 (2015)CrossRefGoogle Scholar
  15. 15.
    R. Ansari, J. Torabi, Compos. Part B: Eng. 95, 196 (2016)CrossRefGoogle Scholar
  16. 16.
    N. George, P. Jeyaraj, S. Murigendrappa, Int. J. Struct. Stabil. Dyn. 17, 1750064 (2016)CrossRefGoogle Scholar
  17. 17.
    R. Ansari, J. Torabi, M.F. Shojaei, E. Hasrati, Compos. Struct. 157, 398 (2016)CrossRefGoogle Scholar
  18. 18.
    L. Zhang, Z. Lei, K. Liew, Compos. Struct. 122, 172 (2015)CrossRefGoogle Scholar
  19. 19.
    A. Alibeigloo, K. Liew, Int. J. Appl. Mech. 7, 1550002 (2015)CrossRefGoogle Scholar
  20. 20.
    M. Nejati, A. Asanjarani, R. Dimitri, F. Tornabene, Int. J. Mech. Sci. 130, 383 (2017)CrossRefGoogle Scholar
  21. 21.
    S. Kamarian, M. Salim, R. Dimitri, F. Tornabene, Int. J. Mech. Sci. 108, 157 (2016)CrossRefGoogle Scholar
  22. 22.
    E.A. Shahrbabaki, A. Alibeigloo, Compos. Struct. 111, 362 (2014)CrossRefGoogle Scholar
  23. 23.
    P. Phung-Van, M. Abdel-Wahab, K. Liew, S. Bordas, H. Nguyen-Xuan, Compos. Struct. 123, 137 (2015)CrossRefGoogle Scholar
  24. 24.
    L. Zhang, Z. Lei, K. Liew, J. Yu, Comput. Methods Appl. Mech. Eng. 273, 1 (2014)ADSCrossRefGoogle Scholar
  25. 25.
    Z. Lei, K.M. Liew, J. Yu, Comput. Methods Appl. Mech. Eng. 256, 189 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    H.-S. Shen, Compos. Part B: Eng. 43, 1030 (2012)CrossRefGoogle Scholar
  27. 27.
    H.-S. Shen, Y. Xiang, Compos. Part B: Eng. 52, 311 (2013)CrossRefGoogle Scholar
  28. 28.
    K. Liew, Z. Lei, J. Yu, L. Zhang, Comput. Methods Appl. Mech. Eng. 268, 1 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    L.-L. Ke, J. Yang, S. Kitipornchai, Compos. Struct. 92, 676 (2010)CrossRefGoogle Scholar
  30. 30.
    R. Ansari, M.F. Shojaei, V. Mohammadi, R. Gholami, F. Sadeghi, Compos. Struct. 113, 316 (2014)CrossRefGoogle Scholar
  31. 31.
    R. Ansari, E. Hasrati, M.F. Shojaei, R. Gholami, A. Shahabodini, Physica E 69, 294 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    R. Ansari, T. Pourashraf, R. Gholami, A. Shahabodini, Compos. Part B: Eng. 90, 267 (2016)CrossRefGoogle Scholar
  33. 33.
    L. Zhang, K. Liew, J. Reddy, Comput. Methods Appl. Mech. Eng. 298, 1 (2016)ADSCrossRefGoogle Scholar
  34. 34.
    H.-S. Shen, Y. Xiang, Compos. Struct. 111, 291 (2014)CrossRefGoogle Scholar
  35. 35.
    M. Rafiee, X. He, K. Liew, Int. J. Non-Linear Mech. 59, 37 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    R. Gholami, R. Ansari, Y. Gholami, Compos. Struct. 174, 45 (2017)CrossRefGoogle Scholar
  37. 37.
    H. Wu, S. Kitipornchai, J. Yang, Appl. Math. Model. 42, 735 (2017)MathSciNetCrossRefGoogle Scholar
  38. 38.
    R. Ansari, R. Gholami, Compos. Struct. 154, 707 (2016)CrossRefGoogle Scholar
  39. 39.
    A. Alibeigloo, Compos. Struct. 118, 482 (2014)CrossRefGoogle Scholar
  40. 40.
    H.-S. Shen, Z.H. Zhu, Comput. Mater. Contin. 18, 155 (2010)Google Scholar
  41. 41.
    Z.-X. Wang, H.-S. Shen, Nonlinear Dyn. 70, 735 (2012)CrossRefGoogle Scholar
  42. 42.
    M.R. Nami, M. Janghorban, Adv. Compos. Mater. 24, 439 (2015)CrossRefGoogle Scholar
  43. 43.
    A. Setoodeh, M. Shojaee, Polym. Compos. (2017)  https://doi.org/10.1002/pc.24289
  44. 44.
    R. Ansari, J. Torabi, M.F. Shojaei, Compos. Part B: Eng. 109, 197 (2017)CrossRefGoogle Scholar
  45. 45.
    H. Hedayati, B.S. Aragh, Appl. Math. Comput. 218, 8715 (2012)MathSciNetGoogle Scholar
  46. 46.
    M. Mohammadzadeh-Keleshteri, H. Asadi, M. Aghdam, Compos. Struct. 171, 100 (2017)CrossRefGoogle Scholar
  47. 47.
    R. Ansari, J. Torabi, R. Hassani, Comput. Math. Appl. (2017)  https://doi.org/10.1016/j.camwa.2017.09.022
  48. 48.
    M. Keleshteri, H. Asadi, Q. Wang, Comput. Methods Appl. Mech. Eng. 325, 689 (2017)ADSCrossRefGoogle Scholar
  49. 49.
    E. Ventsel, T. Krauthammer, Thin plates and shells: theory: analysis, and applications (CRC Press, 2001)Google Scholar
  50. 50.
    I.E. Harik, S. Pashanasangi, J. Struct. Eng. 111, 1517 (1985)CrossRefGoogle Scholar
  51. 51.
    S. Vaidyanathan, H. Busby, D. Houser, Comput. Struct. 51, 255 (1994)CrossRefGoogle Scholar
  52. 52.
    T. Anderson, A. Nayfeh, B. Balachandran, J. Vib. Acoust. 118, 21 (1996)CrossRefGoogle Scholar
  53. 53.
    T. Anderson, A. Nayfeh, B. Balachandran, Nonlinear Dyn. 11, 17 (1996)CrossRefGoogle Scholar
  54. 54.
    T. Anderson, B. Balachandran, A. Nayfeh, Trans. ASME-L J. Vib. Acoust. 116, 480 (1994)CrossRefGoogle Scholar
  55. 55.
    M.F. Shojaei, R. Ansari, Appl. Math. Model. 49, 705 (2017)MathSciNetCrossRefGoogle Scholar
  56. 56.
    A.M. Esawi, M.M. Farag, Mater. Des. 28, 2394 (2007)CrossRefGoogle Scholar
  57. 57.
    J. Fidelus, E. Wiesel, F. Gojny, K. Schulte, H. Wagner, Compos. Part A: Appl. Sci. Manufact. 36, 1555 (2005)CrossRefGoogle Scholar
  58. 58.
    H.-S. Shen, Compos. Struct. 91, 9 (2009)CrossRefGoogle Scholar
  59. 59.
    R. Ansari, M. Faghih Shojaei, R. Gholami, Compos. Struct. 136, 669 (2016)CrossRefGoogle Scholar
  60. 60.
    R. Ansari, R. Gholami, Acta Astron. 118, 72 (2016)CrossRefGoogle Scholar
  61. 61.
    R. Ansari, R. Gholami, Int. J. Appl. Mech. 8, 1650053 (2016)CrossRefGoogle Scholar
  62. 62.
    R. Ansari, R. Gholami, A. Shahabodini, J. Mech. 32, 539 (2016)CrossRefGoogle Scholar
  63. 63.
    S. Ibrahim, B. Patel, Y. Nath, Int. J. Non-Linear Mech. 44, 1073 (2009)ADSCrossRefGoogle Scholar
  64. 64.
    H.B. Keller, Numerical solution of bifurcation and nonlinear eigenvalue problems, in Applications of Bifurcation Theory, edited by P.H. Rabinowitz (Academic Press, 1977) pp. 359--384Google Scholar
  65. 65.
    Y. Han, J. Elliott, Comput. Mater. Sci. 39, 315 (2007)CrossRefGoogle Scholar
  66. 66.
    M. Griebel, J. Hamaekers, Comput. Methods Appl. Mech. Eng. 193, 1773 (2004)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Lahijan BranchIslamic Azad UniversityLahijanIran
  2. 2.Department of Mechanical EngineeringUniversity of GuilanRashtIran

Personalised recommendations