Advances in nano research

  • 제12권4호
  • /
  • Pages.427-440
  • /
  • 2022
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A size-dependent study on buckling and post-buckling behavior of imperfect piezo-flexomagnetic nano-plate strips

  • Momeni-Khabisi, Hamed (Department of Mechanical Engineering, Ferdowsi University of Mashhad) ;
  • Tahani, Masoud (Department of Mechanical Engineering, Ferdowsi University of Mashhad)
  • 투고 : 2021.12.24
  • 심사 : 2022.02.02
  • 발행 : 2022.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

In the present study, the nonlocal strain gradient theory is used to predict the size-dependent buckling and post-buckling behavior of geometrically imperfect nano-scale piezo-flexomagnetic plate strips in two modes of direct and converse flexomagnetic effects. The first-order shear deformation plate theory is used to analyze analytically nano-strips with simply supported boundary conditions. The nonlinear governing equations of equilibrium and associated boundary conditions are derived using the principle of minimum total potential energy with consideration of the von Kármán-type of geometric nonlinearity. A closed-form solution of governing differential equation is obtained, which is easily usable for engineers and designers. To validate the presented formulations, whenever possible, a comparison with the results found in the open literature is reported for buckling loads. A parametric study is presented to examine the effect of scaling parameters, plate slenderness ratio, temperature, the mid-plane initial rise, flexomagnetic coefficient, different temperature distributions, and magnetic potential, in case of the converse flexomagnetic effect, on buckling and post-buckling loads in detail.

키워드

참고문헌

  1. Asrari, R., Ebrahimi, F. and Kheirikhah, M.M. (2020), "On post-buckling characteristics of functionally graded smart magneto-electro-elastic nanoscale shells", Adv. Nano Res., 9(1), 33-45. https://doi.org/10.12989/anr.2020.9.1.033.
  2. Bagheri, R. and Tadi Beni, Y. (2021), "On the size-dependent nonlinear dynamics of viscoelastic/flexoelectric nanobeams", J. Vib. Control, 27(17-18), 2018-2033. https://doi.org/10.1177/1077546320952225.
  3. Barati, M.R. and Zenkour, A.M. (2019), "Thermal post-buckling analysis of closed circuit flexoelectric nanobeams with surface effects and geometrical imperfection", Mech. Adv. Mater. Struct., 26(17), 1482-1490. https://doi.org/10.1080/15376494.2018.1432821.
  4. Belyaev, B.A., Izotov, A.V., Solovev, P.N. and Boev, N.M. (2020), "Strain-gradient-induced unidirectional magnetic anisotropy in nanocrystalline thin permalloy films", Physica Status Solidi (RRL), 14(1), 1900467. https://doi.org/10.1002/pssr.201900467.
  5. Cai, R., Antohe, V.A., Nysten, B., Piraux, L. and Jonas, A.M. (2020), "Thermally induced flexo-type effects in nanopatterned multiferroic layers", Adv. Funct. Mater., 30(14), 1910371. https://doi.org/10.1002/adfm.201910371.
  6. Eliseev, E.A., Morozovska, A.N., Glinchuk, M.D. and Blinc, R. (2009), "Spontaneous flexoelectric/flexomagnetic effect in nanoferroics", Phys. Rev. B, 79(16), 165433. https://link.aps.org/doi/10.1103/PhysRevB.79.165433.
  7. Eliseev, E.A., Glinchuk, M.D., Khist, V., Skorokhod, V.V., Blinc, R. and Morozovska, A.N. (2011), "Linear magnetoelectric coupling and ferroelectricity induced by the flexomagnetic effect in ferroics", Phys. Rev. B, 84(17), 174112. https://link.aps.org/doi/10.1103/PhysRevB.84.174112.
  8. Eliseev, E.A., Morozovska, A.N., Khist, V.V. and Polinger, V. (2019), Chapter Six- Effective Flexoelectric and Flexomagnetic Response of Ferroics In Solid State Physics, 70, 237-289, Academic Press, Massachusetts, U.S.A.
  9. Fahrner, W.R. (2005), Nanotechnology and Nanoelectronics: Materials, Devices, Measurement Techniques, Springer, Berlin, Germany.
  10. Fenjan, R.M., Hamad, L.B. and Faleh, N.M. (2020), "Mechanicalhygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects", Adv. Aircr. Spacecr., 7(2), 169-186. https://doi.org/10.12989/aas.2020.7.2.169.
  11. Gunda, J.B. (2014), "Thermal post-buckling and large amplitude free vibration analysis of Timoshenko beams: Simple closed-form solutions", Appl. Math. Model., 38(17-18), 4548-4558. https://doi.org/10.1016/j.apm.2014.02.019.
  12. Gupta, R., Gunda, J.B., Ranga Janardhan, G. and Venkateswara, R.G. (2010), "Post-buckling analysis of composite beams: Simple and accurate closed-form expressions", Compos. Struct., 92(8), 1947-1956. https://doi.org/10.1016/j.compstruct.2009.12.010.
  13. Kundalwal, S.I. and Ray, M.C. (2016), "Smart damping of fuzzy fiber reinforced composite plates using 1-3 piezoelectric composites", J. Vib. Control., 22(6), 1526-1546. https://doi.org/10.1177/1077546314543726.
  14. Kundalwal, S.I., Shingare, K.B. and Rathi, A. (2019), "Effect of flexoelectricity on the electromechanical response of graphene nanocomposite beam", Int. J. Mech. Mater. Des., 15(3), 447-470. https://doi.org/10.1007/s10999-018-9417-6.
  15. Lee, D., Yoon, A., Jang, S.Y., Yoon, J.G., Chung, J.S., Kim, M., Scott, J.F. and Noh, T.W. (2011), "Giant flexoelectric effect in ferroelectric epitaxial thin films", Phys. Rev. Lett, 107(5), 057602. https://doi.org/10.1103/PhysRevLett.107.057602.
  16. Li, L. and Hu, Y. (2017), "Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects", Int. J. Mech. Sci., 120, 159-170. https://doi.org/10.1016/j.ijmecsci.2016. 11.025.
  17. Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02. 001.
  18. Lu, L., Guo, X. and Zhao, J. (2017b), "A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms", Int. J. Eng. Sci., 119, 265-277. https://doi.org/10.1016/j.ijengsci.2017. 06.024.
  19. Lukashev, P. and Sabirianov, R.F. (2010), "Flexomagnetic effect in frustrated triangular magnetic structures", Phys. Rev. B, 82(9), 094417. https://doi.org/10.1103/PhysRevB.82.094417.
  20. Malikan, M. and Eremeyev, V.A. (2021a), "Flexomagnetic response of buckled piezomagnetic composite nanoplates", Compos. Struct., 267, 113932. https://doi.org/10.1016/j.compstruct. 2021.113932.
  21. Malikan, M. and Eremeyev, V.A. (2021b), "Flexomagneticity in buckled shear de- formable hard-magnetic soft structures", Continuum Mech. Therm., 34(1), 1-16. https://doi.org/10.1007/s00161-021-01034-y.
  22. Malikan, M., Uglov, N.S. and Eremeyev, V.A. (2020), "On instabilities and post-buckling of piezomagnetic and flexomagnetic nanostructures", Int. J. Eng. Sci., 157, 103395. https://doi.org/10.1016/j.ijengsci.2020.103395.
  23. Malikan, M., Wiczenbach, T. and Eremeyev, V.A. (2021), "On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions", Continuum Mech. Therm., 33(4), 1281- 1297. https://doi.org/10.1007/s00161-021-00971-y.
  24. Mir, M. and Tahani, M. (2020), "Graphene-based mass sensors: Chaotic dynamics analysis using the nonlocal strain gradient model", Appl. Math. Model., 81, 799-817. https://doi.org/ 10.1016/j.apm.2020.01.022.
  25. Mirjavadi, S.S., Forsat, M., Barati, M.R., Abdella, G.M., Hamouda, A.M.S., Afshari, B.M. and Rabby, S. (2019), "Post-buckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents", Microsyst. Technol., 25(9), 3477-3488. https://doi.org/10.1007/s00542-018-4241-3.
  26. Mohamed, N., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.
  27. Moosavi, S.M., Sarani, Z., Chia, C.H., Gan, S., Azahari, N.A. and Kaco, H. (2017), "Hydrothermal synthesis, magnetic properties and characterization of CoFe2O4 nanocrystals", Ceram. Int., 43(10), 7889-7894. https://doi.org/10.1016/j.ceramint.2017. 03.110.
  28. Moradi, R., Radhi, A. and Behdinan, K. (2020), "Damped dynamic behavior of an advanced piezoelectric sandwich plate", Compos. Struct., 243, 112243. https://doi.org/10.1016/j.compstruct.2020.112243.
  29. Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3-4), 321-339. https://doi.org/ 10.1016/j.ijengsci.2004.09.006.
  30. Pyatakov, A.P. and Zvezdin, A.K. (2009), "Flexomagnetoelectric interaction in multiferroics", Eur. Phys. J. B, 71(3), 419-427. https://doi.org/10.1140/epjb/e2009-00281-5.
  31. Radgolchin, M. and Tahani, M. (2021), "Nonlinear vibration analysis of beam microgyroscopes using nonlocal strain gradient theory", Sens. Imag., 22(1), 1-25. https://doi.org/10.1007/s11220-021-00336-4.
  32. Reddy, J.N. (2006), Theory and Analysis of Elastic Plates and Shells (2nd ed.), CRC Press, Florida, U.S.A.
  33. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007. 04.004.
  34. Reddy, J.N. (2010), "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates", Int. J. Eng. Sci., 48(11), 1507-1518. https://doi.org/10.1016/j.ijengsci.2010.09.020.
  35. Shi, W., Guo, Y., Zhang, Z. and Guo, W. (2019), "Strain gradient mediated magnetism and polarization in monolayer V Se2", J. Phys. Chem. C, 123(40), 24988-24993. https:// doi.org/10.1021/acs.jpcc.9b08445.
  36. Shi, Y., Li, N., Ye, J. and Ma, J. (2021), "Enhanced magneto-electric response in nanostructures due to flexoelectric and flexomagnetic effects", J. Magn. Magn. Mater., 521, 167523. https://doi.org/10.1016/j.jmmm.2020. 167523.
  37. Shingare, K.B. and Kundalwal, S.I. (2019), "Static and dynamic response of graphene nanocomposite plates with flexoelectric effect", Mech. Mater., 134, 69-84. https://doi.org/10.1016/j.mechmat.2019.04.006.
  38. Sidhardh, S. and Ray, M.C. (2018), "Flexomagnetic response of nanostructures", J. Appl. Phys., 124(24), 244101. https://doi.org/10. 1063/1.5060672. https://doi.org/10.1063/1.5060672
  39. Sladek, J., Sladek, V., Xu, M. and Deng, Q. (2021), "A cantilever beam analysis with flexomagnetic effect", Meccanica, 56(9), 2281-2292. https://doi. org/10.1007/s11012-021-01357-9.
  40. Sun, X.P., Hong, Y.Z., Dai, H.L. and Wang, L. (2017), "Nonlinear frequency analysis of buckled nanobeams in the presence of longitudinal magnetic field", Acta Mechanica Solida Sinica, 30(5), 465-473. https://doi.org/10.1016/j.camss.2017.08. 002.
  41. Wang, B. and Li, X.F. (2021), "Flexoelectric effects on the natural frequencies for free vibration of piezoelectric nanoplates", J. Appl. Phys., 129(3), 034102. https://doi.org/10.1063/5.0032343.
  42. Xu, X. and Zheng, M. (2019), "Analytical solutions for buckling of size-dependent Timoshenko beams", Appl. Math. Mech., 40(7), 953-976. https://doi.org/10.1007/s10483-019-2494-8.
  43. Zhang, J.X., Zeches, R.J., He, Q., Chu, Y.H. and Ramesh, R. (2012), "Nanoscale phase boundaries: A new twist to novel functionalities", Nanoscale, 4(20), 6196-6204. http://doi.org/10.1039/C2NR31174G.
  44. Zhang, N., Zheng, S. and Chen, D. (2019), "Size-dependent static bending of flexomagnetic nanobeams", J. Appl. Phys., 126(22), 223901. https://doi.org/10.1063/1.5128940.