DOI QR코드

DOI QR Code

Buckling treatment of piezoelectric functionally graded graphene platelets micro plates

  • 투고 : 2019.12.30
  • 심사 : 2021.01.05
  • 발행 : 2021.02.10

초록

Micro-electro-mechanical systems (MEMS) are widely employed in sensors, biomedical devices, optic sectors, and micro-accelerometers. New reinforcement materials such as carbon nanotubes as well as graphene platelets provide stiffer structures with controllable mechanical specifications by changing the graphene platelet features. This paper deals with buckling analyses of functionally graded graphene platelets micro plates with two piezoelectric layers subjected to external applied voltage. Governing equations are based on Kirchhoff plate theory assumptions beside the modified couple stress theory to incorporate the micro scale influences. A uniform temperature change and external electric field are regarded along the micro plate thickness. Moreover, an external in-plane mechanical load is uniformly distributed along the micro plate edges. The Hamilton's principle is employed to extract the governing equations. The material properties of each composite layer reinforced with graphene platelets of the considered micro plate are evaluated by the Halpin-Tsai micromechanical model. The governing equations are solved by the Navier's approach for the case of simply-supported boundary condition. The effects of the external applied voltage, the material length scale parameter, the thickness of the piezoelectric layers, the side, the length and the weight fraction of the graphene platelets as well as the graphene platelets distribution pattern on the critical buckling temperature change and on the critical buckling in-plane load are investigated. The outcomes illustrate the reduction of the thermal buckling strength independent of the graphene platelets distribution pattern while meanwhile the mechanical buckling strength is promoted. Furthermore, a negative voltage, -50 Volt, strengthens the micro plate stability against the thermal buckling occurrence about 9% while a positive voltage, 50 Volt, decreases the critical buckling load about 9% independent of the graphene platelet distribution pattern.

키워드

참고문헌

  1. Aghazadeh, R., Dag, S. and Cigeroglu, E., (2018), "Modelling of graded rectangular micro-plates with variable length scale parameters", Struct. Eng. Mech., 65(5), 573-585. https://doi.org/10.12989/sem.2018.65.5.573.
  2. Arvin, H. (2018), "The flapwise bending free vibration analysis of micro-rotating Timoshenko beams using the differential transform method", J. Vib. Control, 24(20), 4868-4884. https://doi.org/10.1177/1077546317736706.
  3. Belkorissat, I., Sid, M., Houari, A., Tounsi, A., AddaBedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063.
  4. Bouderba, B., Houari, M.S.A. and Tounsi, A., (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085.
  5. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425.
  6. Choudhary, P.K. and Jana, P., (2018), "Position optimization of circular/elliptical cutout within an orthotropic rectangular plate for maximum buckling load", Steel Compos. Struct., 29(1), 39-51. https://doi.org/10.12989/scs.2018.29.1.039.
  7. Ebrahimi, N. and Beni, Y.T. (2016), "Electro-mechanical vibration of nanoshells using consistent size-dependent piezoelectric theory", Steel Compos. Struct., 22(6), 1301-1336. https://doi.org/10.12989/scs.2016.22.6.1301.
  8. Huang, Y., Yang, Z., Liu, A. and Fu, J., (2018), "Nonlinear buckling analysis of functionally graded graphene reinforced composite shallow arches with elastic rotational constraints under uniform radial load", Materials, 11(6), 910. https://doi.org/10.3390/ma11060910.
  9. Jiang, G., Li, F. and Zhang, C., (2018), "Postbuckling and nonlinear vibration of composite laminated trapezoidal plates", Steel Compos. Struct., 26(1), 17-29. https://doi.org/10.12989/scs.2018.26.1.017.
  10. Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A., (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., 15(4), 399-423. https://doi.org/10.12989/scs.2013.15.4.399.
  11. Kiani, Y., Bagherizadeh, E. and Eslami, M. R., (2012), "Thermal and mechanical buckling of sandwich plates with FGM face sheets resting on the Pasternak elastic foundation", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 226(1), 32-41.: https://doi.org/10.1177/0954406211413657.
  12. Lei, Z. and Zhang, Y. (2018), "Characterizing buckling behavior of matrix-cracked hybrid plates containing CNTR-FG layers", Steel Compos. Struct., 28(4), 495-508. https://doi.org/10.12989/scs.2018.28.4.495.
  13. Liew, K.M., Yang, J. and Kitipornchai, S. (2003), "Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading", Int. J. Solid. Struct., 40(15), 3869-3892. https://doi.org/10.1016/S0020-7683(03)00096-9.
  14. Matsunaga, H. (2009), "Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory", Compos. Struct., 90(1), 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004.
  15. Meirovitch, L. (1997), Principles and techniques of vibrations. NewYork, McGraw Hill.
  16. Reddy J.N. (2003), Mechanics of laminated composite plates and shells: theory and analysis, Second Edition. Florida, CRC Press.
  17. Roy, K., Mohammadjani, C. and Lim, J.B. (2019a), "Experimental and numerical investigation into the behaviour of face-to-face built-up cold-formed steel channel sections under compression", Thin-Wall. Struct., 134, 291-309. https://doi.org/10.1016/j.tws.2018.09.045.
  18. Roy, K., Ting, T.C.H., Lau, H.H. and Lim, J.B. (2018a), "Nonlinear behaviour of back-to-back gapped built-up coldformed steel channel sections under compression", J. Constr. Steel Res., 147, 257-276. https://doi.org/10.1016/j.jcsr.2018.04.007.
  19. Roy, K., Ting, T.C.H., Lau, H.H. and Lim, J.B. (2018b), "Nonlinear behavior of axially loaded back-to-back built-up cold-formed steel un-lipped channel sections", Steel Compos. Struct., 28(2), 233-250. http://dx.doi.org/10.12989/scs.2018.28.2.233.
  20. Roy, K., Ting, T.C.H., Lau, H.H. and Lim, J.B. (2019b), "Experimental and numerical investigations on the axial capacity of cold-formed steel built-up box sections", J. Constr. Steel Res., 160, 411-427. https://doi.org/10.1016/j.jcsr.2019.05.038.
  21. Shariyat, M. (2009), "Dynamic buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo-electro-mechanical loadings, considering the temperature-dependency of the material properties", Compos. Struct., 88(2), 228-239. https://doi.org/10.1016/j.compstruct.2008.03.044.
  22. Shen, H. S., Xiang, Y., Lin, F. and Hui, D. (2017), "Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments", Compos. Part B: Eng., 119, 67-78. https://doi.org/10.1016/j.compositesb.2017.03.020 .
  23. Song, M., Yang, J. and Kitipornchai, S. (2018), "Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Part B: Eng., 134, 106-113, https://doi.org/10.1016/j.compositesb.2017.09.043.
  24. Wang, Q. (2002), "On buckling of column structures with a pair of piezoelectric layers", Eng. Struct., 24(2), 199-205. https://doi.org/10.1016/S0141-0296(01)00088-8.
  25. Wang, Y., Feng, C., Zhao, Z. and Yang, J., (2018), "Buckling of graphene platelet reinforced composite cylindrical shell with cutout", Int. J. Struct. Stab. Dynam., 18(3), 1850040. https://doi.org/10.1142/S0219455418500402.
  26. Wu, H., Kitipornchai, S. and Yang, J. (2017), "Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates", Mater. Design, 132, 430-441. https://doi.org/10.1016/j.matdes.2017.07.025.
  27. Yaghoobi, H., Fereidoon, A., Khaksari Nouri, M. and Mareishi, S. (2015), "Thermal buckling analysis of piezoelectric functionally graded plates with temperature-dependent properties", Mech. Adv. Mater. Struct., 22(10), 864-875. https://doi.org/10.1080/15376494.2013.864436.