Advertisement

Parametrically excited nonlinear dynamic instability of reinforced piezoelectric nanoplates

  • Majid Ghadiri
  • S. Hamed S. HosseiniEmail author
Regular Article
  • 30 Downloads

Abstract.

The nonlinear dynamic instability of reinforced piezoelectric nanoplates exposed to a parametric excitation and an electric voltage is the objective of the present paper. Firstly, a piezoelectric nanoplate reinforced with two graphene layers and resting on a visco-elastic foundation is modeled. Secondly, the piezoelectric nonlocal elasticity theory, the Kelvin-Voigt model, von Karman nonlinear relations and Hamilton’s principle, respectively, are used to derive the nonlinear governing differential equation of motion. In the next step, to transform partial differential equation to ordinary one and then, solve the equation, the Galerkin technique and multiple time scales method are employed respectively. At the end, the modulation equation of reinforced piezoelectric nanoplates is obtained. Emphasizing the effect of the electric voltage and parametric excitation on dynamic instability of the system, trivial and nontrivial steady-state solutions are discussed. The main results emphasize that the damping coefficient is responsible of the bifurcation point variation, while the amplitude response depends on the term of natural frequency. Therefore, damping can have a strong influence on the system.

References

  1. 1.
    C.L. Kane, E.J. Mele, Phys. Rev. Lett. 78, 1932 (1997)CrossRefADSGoogle Scholar
  2. 2.
    A. Maiti, A. Svizhenko, M.P. Anantram, Phys. Rev. Lett. 88, 126805 (2002)CrossRefADSGoogle Scholar
  3. 3.
    B. Arash, Q. Wang, Sci. Rep. 3, 1782 (2013)CrossRefADSGoogle Scholar
  4. 4.
    R. Potekin, S. Kim, D.M. McFarland, L.A. Bergman, H. Cho, A.F. Vakakis, Nonlinear Dyn. 92, 287 (2018)CrossRefGoogle Scholar
  5. 5.
    M.A. Mahmoud, Crit. Rev. Solid State Mater. Sci. 41, 386 (2016)CrossRefADSGoogle Scholar
  6. 6.
    Y. Ji, M. Choe, B. Cho, S. Song, J. Yoon, H.C. KO, T. Lee, Nanotechnology 23, 105202 (2012)CrossRefADSGoogle Scholar
  7. 7.
    S. Jeong, J.Y. Cho, T.H. Sung, H.H. Yoo, Smart Mater. Struct. 26, 035035 (2017)CrossRefADSGoogle Scholar
  8. 8.
    S.Y. Khoo, Z.S. Radeef, Z.C. Ong, Y.H. Huang, W.T. Chong, Z. Ismail, Measurement 107, 41 (2017)CrossRefGoogle Scholar
  9. 9.
    J. Zhang, Z. Fang, C. Shu, J. Zhang, Q. Zhang, C. Li, Sensors Actuat. A: Phys. 262, 123 (2017)CrossRefGoogle Scholar
  10. 10.
    J. Song, G. Hu, K.T. Tse, S.W. Li, K.C.S. Kwok, Appl. Phys. Lett. 111, 223903 (2017)CrossRefADSGoogle Scholar
  11. 11.
    J. Zhang, C. Wang, J. Appl. Phys. 111, 094303 (2012)CrossRefADSGoogle Scholar
  12. 12.
    C. Li, J.J. Liu, M. Cheng, X.L. Fan, Compos. Part B: Eng. 116, 153 (2017)CrossRefGoogle Scholar
  13. 13.
    D.P. Zhang, Y.J. Lei, Z.B. Shen, Int. J. Mech. Sci. 131, 1001 (2017)CrossRefGoogle Scholar
  14. 14.
    H.B. Li, Y.D. Li, X. Wang, X. Huang, J. Sound Vib. 358, 285 (2015)CrossRefADSGoogle Scholar
  15. 15.
    A.G. Arani, M.H. Zamani, Arab. J. Sci. Eng. 43, 4675 (2018)CrossRefGoogle Scholar
  16. 16.
    M. Sobhy, A.M. Zenkour, Compos. Part B: Eng. 154, 492 (2018)CrossRefGoogle Scholar
  17. 17.
    S. Zeng, B.L. Wang, K.F. Wang, Compos. Struct. 207, 340 (2019)CrossRefGoogle Scholar
  18. 18.
    A. Ghorbanpour Arani, M. Jamali, A.H. Ghorbanpour-Arani, R. Kolahchi, M. Mosayyebi, Proc. Inst. Mech. Eng., Part C 231, 387 (2017)CrossRefGoogle Scholar
  19. 19.
    F. Ebrahimi, A. Dabbagh, J. Vib. Control 25, 933 (2018)CrossRefGoogle Scholar
  20. 20.
    A. Ghorbanpour Arani, M.H. Zamani, J. Sandw. Struct. Mater. (2017)  https://doi.org/10.1177/1099636217721405
  21. 21.
    M. Arefi, M. Kiani, M.H. Zamani, J. Sandw. Struct. Mater. (2018)  https://doi.org/10.1177/1099636218795378
  22. 22.
    M. Arefi, A.M. Zenkour, Compos. Struct. 162, 108 (2017)CrossRefGoogle Scholar
  23. 23.
    M. Arefi, A.M. Zenkour, Acta Mech. 228, 475 (2017)CrossRefMathSciNetGoogle Scholar
  24. 24.
    M. Arefi, A.M. Zenkour, Mech. Res. Commun. 84, 27 (2017)CrossRefGoogle Scholar
  25. 25.
    M. Arefi, A.M. Zenkour, Compos. Struct. 159, 479 (2017)CrossRefGoogle Scholar
  26. 26.
    M. Arefi, M.H. Zamani, M. Kiani, J. Intell. Mater. Syst. Struct. 29, 774 (2018)CrossRefGoogle Scholar
  27. 27.
    A.C. Eringen, D.G.B. Edelen, Int. J. Eng. Sci. 10, 233 (1972)CrossRefGoogle Scholar
  28. 28.
    A.C. Eringen, Int. J. Eng. Sci. 21, 741 (1983)CrossRefGoogle Scholar
  29. 29.
    M. Ghadiri, N. Shafiei, A. Akbarshahi, Appl. Phys. A 122, 673 (2016)CrossRefADSGoogle Scholar
  30. 30.
    S. Sahmani, A.M. Fattahi, Eur. Phys. J. Plus 132, 231 (2017)CrossRefGoogle Scholar
  31. 31.
    Y.Q. Zhang, G.R. Liu, J.S. Wang, Phys. Rev. B 70, 205430 (2004)CrossRefADSGoogle Scholar
  32. 32.
    R. Barretta, L. Feo, R. Luciano, F.M. de Sciarra, Compos. Struct. 129, 80 (2015)CrossRefGoogle Scholar
  33. 33.
    F. Ebrahimi, S.H.S. Hosseini, J. Therm. Stresses 39, 606 (2016)CrossRefGoogle Scholar
  34. 34.
    R. Kolahchi, M.S. Zarei, M.H. Hajmohammad, A.N. Oskouei, Thin-Walled Struct. 113, 162 (2017)CrossRefGoogle Scholar
  35. 35.
    R. Kolahchi, Aerospace Sci. Technol. 66, 235 (2017)CrossRefGoogle Scholar
  36. 36.
    S.R. Asemi, A. Farajpour, M. Mohammadi, Compos. Struct. 116, 703 (2014)CrossRefGoogle Scholar
  37. 37.
    A. Ghorbanpour-Arani, F. Kolahdouzan, M. Abdollahian, Appl. Math. Mech. 39, 529 (2018)CrossRefGoogle Scholar
  38. 38.
    B. Karami, D. Shahsavari, L. Li, M. Karami, M. Janghorban, Proc. Inst. Mech. Eng., Part C 233, 287 (2019)CrossRefGoogle Scholar
  39. 39.
    C. Li, C.W. Lim, J.L. Yu, Smart Mater. Struct. 20, 015023 (2010)CrossRefADSGoogle Scholar
  40. 40.
    I.M. Fokou, C.N.D. Buckjohn, M.S. Siewe, C. Tchawoua, Eur. Phys. J. Plus 132, 344 (2017)CrossRefGoogle Scholar
  41. 41.
    Y. Huang, J. Fu, A. Liu, Compos. Part B: Eng. 164, 226 (2019)CrossRefGoogle Scholar
  42. 42.
    Y.Z. Wang, Y.S. Wang, L.L. Ke, Physica E 83, 195 (2016)CrossRefADSGoogle Scholar
  43. 43.
    C. Li, C.W. Lim, J.L. Yu, Smart Mater. Struct. 20, 015023 (2010)CrossRefADSGoogle Scholar
  44. 44.
    P. Alevras, S. Theodossiades, H. Rahnejat, Appl. Phys. Lett. 110, 233901 (2017)CrossRefADSGoogle Scholar
  45. 45.
    Y.A. Amer, A.T. El-Sayed, A.A. Kotb, Nonlinear Dyn. 85, 2497 (2016)CrossRefGoogle Scholar
  46. 46.
    R.V. Bobryk, D. Yurchenko, J. Sound Vib. 366, 407 (2016)CrossRefADSGoogle Scholar
  47. 47.
    M. Darabi, R. Ganesan, Compos. Struct. 176, 82 (2017)CrossRefGoogle Scholar
  48. 48.
    Y.Z. Wang, Appl. Math. Model. 48, 621 (2017)CrossRefMathSciNetGoogle Scholar
  49. 49.
    S. Krylov, I. Harari, Y. Cohen, J. Micromech. Microeng. 15, 1188 (2005)CrossRefADSGoogle Scholar
  50. 50.
    F. Ebrahimi, S.H.S. Hosseini, Eur. Phys. J. Plus 132, 172 (2017)CrossRefGoogle Scholar
  51. 51.
    A.C. Eringen, Int. J. Eng. Sci. 10, 1 (1972)CrossRefMathSciNetGoogle Scholar
  52. 52.
    A.C. Eringen, J. Appl. Phys. 54, 4703 (1983)CrossRefADSGoogle Scholar
  53. 53.
    J.N. Reddy, An Introduction to Continuum Mechanics (Cambridge University Press, 2013)Google Scholar
  54. 54.
    J.N. Reddy, Theory and Analysis of Elastic Plates and Shells (CRC Press, 2006)Google Scholar
  55. 55.
    L.L. Ke, Y.S. Wang, Smart Mater. Struct. 21, 025018 (2012)CrossRefADSGoogle Scholar
  56. 56.
    R. Lakes, R.S. Lakes, Viscoelastic Materials (Cambridge University Press, 2009)Google Scholar
  57. 57.
    Y. Wang, F.M. Li, Y.Z. Wang, Physica E 67, 65 (2015)CrossRefADSGoogle Scholar
  58. 58.
    J.N. Reddy, Theory and Analysis of Elastic Plates and Shells (CRC Press, 2006)Google Scholar
  59. 59.
    A.G. Arani, A. Shiravand, M. Rahi, R. Kolahchi, Physica B 407, 4123 (2012)CrossRefADSGoogle Scholar
  60. 60.
    I.S. Raju, G.V. Rao, K.K. Raju, J. Sound Vib. 49, 415 (1976)CrossRefADSGoogle Scholar
  61. 61.
    L.E. Shen, H.S. Shen, C.L. Zhang, Comput. Mater. Sci. 48, 680 (2010)CrossRefGoogle Scholar
  62. 62.
    A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations (John Wiley & Sons, 2008)Google Scholar
  63. 63.
    H. Nourbakhsh, R. Mohammadzadeh, M. Rafiee, R. Rafiee, Appl. Mech. Mater. 110, 4178 (2012)Google Scholar
  64. 64.
    S.C. Pradhan, J.K. Phadikar, J. Sound Vib. 325, 206 (2009)CrossRefADSGoogle Scholar
  65. 65.
    A.G. Arani, R. Kolahchi, A.A.M. Barzoki, M.R. Mozdianfard, S.M.N. Farahani, Proc. Inst. Mech. Eng., Part C 227, 862 (2013)CrossRefGoogle Scholar
  66. 66.
    H.N. Chu, J. Appl. Mech. 23, 532 (1956)MathSciNetGoogle Scholar
  67. 67.
    T. Wah, Int. J. Mech. Sci. 5, 425 (1963)CrossRefGoogle Scholar
  68. 68.
    C. Mei, K.A.M.O.L.P.H.A.N. Decha-Umphai, AIAA J. 23, 1104 (1985)CrossRefADSGoogle Scholar
  69. 69.
    C.Y. Chia, M.K. Prabhakara, J. Appl. Mech. 45, 623 (1978)CrossRefADSGoogle Scholar
  70. 70.
    T. Manoj, M. Ayyappan, K.S. Krishnan, B. Nageswara Rao, Z. Angew. Math. Mech. 80, 183 (2000)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringImam Khomeini International UniversityQazvinIran

Personalised recommendations