Skip to main content
SpringerLink
Log in

A general comparison the surface layer degree on the out-of-phase and in-phase vibration behavior of a skew double-layer magneto–electro–thermo-elastic nanoplate

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

The present study investigates and compares the value of the surface layers on the out-of-phase and in-phase vibration behavior of skew double-layer magneto–electro–thermo-elastic (DLMETE) nanoplates. These two nanoplates are coupled by an elastic medium named van der Waals forces; furthermore, the DLMETE nanoplates are surrounded by Winkler and the shear moduli of elastic foundations. The two nanoplates are moving in the same direction in the out-of-phase case; in contrast, in the in-phase mode, those two nanoplates are moving in the opposite direction. Manipulation of the refined plate, surface energy, and nonlocal hypotheses is done to expand the governing equations; furthermore, Hamilton’s principle is utilized to derive the equilibrium equations. Galerkin method is also employed to solve these equations. In addition, for the validation of those equations, the Navier’s method is used. The present research is, therefore, concerned with the effect of the main parameters, namely, external electric potential, external magnetic potential, in-plane mechanical force, elastic foundations, skew angle, and temperature change, on the rate of surface layers of the out-of-phase and in-phase vibration behavior of a skew DLMETE nanoplate. By increasing the skew angles, the in-phase and out-of-phase natural frequency ratios are shown to be converged; following a specific value of skew angle Ψ ≥ 70°, they overlap. By raising the skew angles, the effects of the van der Waals modulus on the vibration behavior are undermined. Therefore, the results of the present work could contribute to designing NEMS/MEMS components which make use of smart composite nanostructures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Z. Lang, L. Xuewu, Buckling and vibration analysis of functionally graded magnetoelectro-thermo-elastic circular cylindrical shells. Appl. Math. Model. 37, 2279–2292 (2013)

    Article  MathSciNet  Google Scholar 

  2. K. Prashanthi, P. Shaibani, A. Sohrabi, T. Natarajan, T. Thundat, Nanoscale magnetoelectric coupling in multiferroic BiFeO3 nanowires. Phys. Status Solidi (RRL) Rapid Res. Lett. 6, 244–246 (2012)

    Article  ADS  Google Scholar 

  3. Y. Wang, J. Hu, Y. Lin, C.W. Nan, Multiferroic magnetoelectric composite nanostructures. NPG Asia Mater. 2, 61–68 (2010)

    Article  Google Scholar 

  4. A.Q. Jiang, C. Wang, K.J. Jin, X.B. Liu, J.F. Scott, C.S. Hwang, T.A. Tang, H.B. Lu, G.Z. Yang, A resistive memory in semiconducting BiFeO3 thin-film capacitors. Adv. Mater. 23, 1277–1281 (2011)

    Article  Google Scholar 

  5. E.W. Wong, P.E. Sheehan, C.M. Lieber, Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes. Science 277, 1971–1975 (1997)

    Article  Google Scholar 

  6. Y.H. Chua, T. Zhao, M.P. Cruz, Q. Zhan, P.L. Yang, L.W. Martin, M. Huijben, C.H. Yang, F. Zavaliche, H. Zheng, R. Ramesh, Ferroelectric size effects in multiferroic BiFeO3 thin films. Appl. Phys. Lett. 90, 252906 (2007)

    Article  ADS  Google Scholar 

  7. W. Ren, L. Bellaiche, Size effects in multiferroic BiFeO3 nanodots: a first-principles-based study. Phys. Rev. B 82, 113403 (2010)

    Article  ADS  Google Scholar 

  8. M.H. Zhao, Z.L. Wang, S.X. Mao, Piezoelectric characterization of individual zinc oxide nanobelt probed by piezoresponse force microscope. Nano Lett. 4, 587–590 (2004)

    Article  ADS  Google Scholar 

  9. A.C. Eringen, Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10, 425–435 (1972)

    Article  Google Scholar 

  10. M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323 (1975)

    Article  MathSciNet  Google Scholar 

  11. R.D. Mindlin, Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78 (1964)

    Article  MathSciNet  Google Scholar 

  12. D. Lam, F. Yang, A. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003)

    Article  ADS  Google Scholar 

  13. F. Yang, A. Chong, D. Lam, P. Tong, Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)

    Article  Google Scholar 

  14. M. Karimi, H.R. Mirdamadi, A.R. Shahidi, Positive and negative surface effects on the buckling and vibration of rectangular nanoplates under biaxial and shear in-plane loadings based on nonlocal elasticity theory. J. Braz. Soc. Mech. Sci. Eng. 39, 1391–1404 (2017)

    Article  Google Scholar 

  15. M.H. Ghayesh, A. Farajpour, Nonlinear coupled mechanics of nanotubes incorporating both nonlocal and strain gradient effects. Mech. Adv. Mater. Struct. (2018). https://doi.org/10.1080/15376494.2018.1473537

    Article  MATH  Google Scholar 

  16. M.H. Ghayesh, H. Farokhi, Nonlinear behaviour of electrically actuated microplate-based MEMS resonators. Mech. Syst. Signal Process. 109, 220–234 (2018)

    Article  ADS  Google Scholar 

  17. M. Karimi, A.R. Shahidi, Finite difference method for sixth order derivatives of differential equations in buckling of nanoplates due to coupled surface energy and non-local elasticity theories. Int. J. Nano Dimens. 6, 525–538 (2015)

    Google Scholar 

  18. M. Sobhy, Levy-type solution for bending of single-layered graphene sheets in thermal environment using the two-variable plate theory. Int. J. Mech. Sci. 90, 171–178 (2015)

    Article  Google Scholar 

  19. D. Karličić, P. Kozić, M. Cajić, Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation. Eur. J. Mech. A Solids 72, 66–78 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  20. F. Ebrahimi, A. Dabbagh, Effect of humid-thermal environment on wave dispersion characteristics of single-layered graphene sheets. Appl. Phys. A 124, 301 (2018)

    Article  ADS  Google Scholar 

  21. A. Kiani, M. Sheikhkhoshkar, A. Jamalpoor, M. Khanzadi, Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory. J. Intell. Mater. Syst. Struct. 29, 741–763 (2018)

    Article  Google Scholar 

  22. F. Ebrahim, M.R. Barati, Nonlocal thermal buckling analysis of embedded magnetoelectro-thermo-elastic nonhomogeneous nanoplates. Iran. J. Sci. Technol. Trans. Mech. Eng. 40, 243–264 (2016)

    Article  Google Scholar 

  23. J. He, C.M. Lilley, Surface effect on the elastic behavior of static bending nanowires. Nano Lett. 8, 1798–1802 (2008)

    Article  ADS  Google Scholar 

  24. R. Dingreville, J. Qu, M. Cherkaoui, Surface free energy and its effect on the elastic behavior of nano-sized particles wires and films. J. Mech. Phys. Solids 53, 1827–1854 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  25. M. Karimi, A.R. Shahidi, Finite difference method for biaxial and uniaxial buckling of rectangular silver nanoplates resting on elastic foundations in thermal environments based on surface stress and nonlocal elasticity theories. J. Solid Mech. 8, 719–733 (2016)

    Google Scholar 

  26. M. Karimi, A.R. Shahidi, Buckling analysis of skew magneto-electro-thermo-elastic nanoplates considering surface energy layers and utilizing the Galerkin method. Appl. Phys. A 124, 681 (2018)

    Article  ADS  Google Scholar 

  27. F. Ebrahimi, M.R. Barati, Static stability analysis of embedded flexoelectric nanoplates considering surface effects. Appl. Phys. A 123, 666 (2017)

    Article  ADS  Google Scholar 

  28. M. Karimi, M.H. Shokrani, A.R. Shahidi, Size-dependent free vibration analysis of rectangular nanoplates with the consideration of surface effects using finite difference method. J. Appl. Comput. Mech. 1, 122–133 (2015)

    Google Scholar 

  29. M. Karimi, A.R. Shahidi, Thermo-mechanical vibration, buckling, and bending of orthotropic graphene sheets based on nonlocal two-variable refined plate theory using finite difference method considering surface energy effects. Proc. Inst. Mech. Eng. Part N J. Nanomater. Nanoeng. Nanosyst. 231, 111–130 (2017)

    Google Scholar 

  30. R. Ansari, R. Gholami, Surface effect on the large amplitude periodic forced vibration of first-order shear deformable rectangular nanoplates with various edge supports. Acta Astronaut. 118, 72–89 (2016)

    Article  ADS  Google Scholar 

  31. M. Karimi, H.A. Haddad, A.R. Shahidi, Combining surface effects and non-local two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates. Micro Nano Lett. 10, 276–281 (2015)

    Article  Google Scholar 

  32. M. Karimi, A.R. Shahidi, Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermo-mechanical and shear loadings. Appl. Phys. A 123, 304 (2017)

    Article  ADS  Google Scholar 

  33. W. Wenjun, P. Li, F. Jin, Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications. Smart Mater. Struct. 25, 095026 (2016)

    Article  ADS  Google Scholar 

  34. M.H. Ghayesh, H. Farokhi, Nonlinear dynamics of doubly curved shallow microshells. Nonlinear Dyn. 92, 803–814 (2018)

    Article  Google Scholar 

  35. M.H. Shokrani, M. Karimi, M.S. Tehrani, H.R. Mirdamadi, Buckling analysis of double-orthotropic nanoplates embedded in elastic media based on non-local two-variable refined plate theory using the GDQ method. J. Braz. Soc. Mech. Sci. Eng. 38, 2589–2606 (2016)

    Article  Google Scholar 

  36. M. Sobhy, Hygrothermal vibration of orthotropic double-layered graphene sheets embedded in an elastic medium using the two-variable plate theory. Appl. Math. Model. 40, 85–99 (2016)

    Article  MathSciNet  Google Scholar 

  37. M.S. Atanasov, D. Karličić, P. Kozićn, Forced transverse vibrations of an elastically connected nonlocal orthotropic double-nanoplate system subjected to an in-plane magnetic field. Acta Mech. 228, 2165–2185 (2017)

    Article  MathSciNet  Google Scholar 

  38. M. Karimi, A.R. Shahidi, S. Ziaei-Rad, Surface layer and nonlocal parameter effects on the in-phase and out-of-phase natural frequencies of a double-layer piezoelectric nanoplate under thermo-electro-mechanical loadings. Microsyst. Technol. 23, 4903–4915 (2017)

    Article  Google Scholar 

  39. M. Arefi, A.M. Zenkour, Effect of thermomagneto-electromechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal sheardeformation plate theory. J. Sandw. Struct. Mater. (2017). https://doi.org/10.1177/1099636217697497

    Article  Google Scholar 

  40. D. Karličić, M. Cajić, S. Adhikari, P. Kozić, T. Murmu, Vibrating nonlocal multi-nanoplate system under inplane magnetic field. Eur. J. Mech. A Solids 64, 29–45 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  41. B. Shahriari, S. Shirvani, Small-scale effects on the buckling of skew nanoplates based on non-local elasticity and second-order strain gradient theory. J. Mech. (2017). https://doi.org/10.1017/jmech.2017.16

    Article  Google Scholar 

  42. A. Alibeygi Beni, P. Malekzadeh, Nonlocal free vibration of orthotropic non-prismatic skew nanoplates. Compos. Struct. 94, 3215–3222 (2012)

    Article  Google Scholar 

  43. H. Babaei, A.R. Shahidi, Free vibration analysis of quadrilateral nanoplates based on nonlocal continuum models using the Galerkin method: the effects of small scale. Meccanica 48, 971 (2013)

    Article  MathSciNet  Google Scholar 

  44. M. Rahmati, S.R. Alavi, S. Ziaei-Rad, Improving the read/write performance of hard disk drives under external excitation sources based on multi-objective optimization. Microsyst. Technol. 23, 3331–3345 (2017)

    Article  Google Scholar 

  45. S.R. Alavi, M. Rahmati, S. Ziaei-Rad, A new approach to design safe-supported HDD against random excitation by using optimization of rubbers spatial parameters. Microsyst. Technol. 23, 2023–2032 (2017)

    Article  Google Scholar 

  46. S.R. Alavi, M. Rahmati, S. Ziaei-Rad, Optimization of passive control performance for different hard disk drives subjected to shock excitation. J. Cent. South Univ. 24, 891–899 (2017)

    Article  Google Scholar 

  47. M. Rahmati, S. Khodaei, Nonlocal vibration and instability analysis of carbon nanotubes conveying fluid considering the influences of nanoflow and non-uniform velocity profile. Microfluid. Nanofluid. 22, 117 (2018)

    Article  Google Scholar 

  48. M. Karimi, H.R. Mirdamadi, A.R. Shahidi, Shear vibrationand buckling of double-layer orthotropic nanoplates based on RPT resting on elastic foundations by DQM including surface effects. Microsyst. Technol. 23, 765–797 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Esfahān, 84156-83111, Iran

    Morteza Karimi & Ali Reza Shahidi

Authors
  1. Morteza Karimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Reza Shahidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Morteza Karimi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karimi, M., Shahidi, A.R. A general comparison the surface layer degree on the out-of-phase and in-phase vibration behavior of a skew double-layer magneto–electro–thermo-elastic nanoplate. Appl. Phys. A 125, 106 (2019). https://doi.org/10.1007/s00339-018-2168-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-018-2168-2

Search

Navigation