Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Buckling and free vibration analysis of FG-CNTRC-micro sandwich plate

  • Received : 2017.05.16
  • Accepted : 2017.10.22
  • Published : 2018.02.10
⟨ Previous Next ⟩

Abstract

Buckling and free vibration analysis of sandwich micro plate (SMP) integrated with piezoelectric layers embedded in orthotropic Pasternak are investigated in this paper. The refined Zigzag theory (RZT) is taken into consideration to model the SMP. Four different types of functionally graded (FG) distribution through the thickness of the SMP core layer which is reinforced with single-wall carbon nanotubes (SWCNTs) are considered. The modified couple stress theory (MCST) is employed to capture the effects of small scale effects. The sandwich structure is exposed to a two dimensional magnetic field and also, piezoelectric layers are subjected to external applied voltages. In order to obtain governing equation, energy method as well as Hamilton's principle is applied. Based on an analytical solution the critical buckling loads and natural frequency are obtained. The effects of volume fraction of carbon nanotubes (CNTs), different distributions of CNTs, foundation stiffness parameters, magnetic and electric fields, small scale parameter and the thickness of piezoelectric layers on the both critical buckling loads and natural frequency of the SMP are examined. The obtained results demonstrate that the effects of volume fraction of CNTs play an important role in analyzing buckling and free vibration behavior of the SMP. Furthermore, the effects of magnetic and electric fields are remarkable on the mechanical responses of the system and cannot be neglected.

Keywords

Acknowledgement

Supported by : University of Kashan

References

  1. Alibeigloo, A. (2013), "Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity", Compos. Struct., 95, 612-622. https://doi.org/10.1016/j.compstruct.2012.08.018
  2. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenge", Mater. Design., 28(9), 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022
  3. Ferreira, A.J.M., Fasshauer, G.E., Batra, R.C. and Rodrigues, J.D. (2008), "Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter", Compos. Struct ., 86(4), 328-343. https://doi.org/10.1016/j.compstruct.2008.07.025
  4. Fiedler, B., Gojny, F.H., Wichmann, M.H.G., Nolte, M.C.M. and Schulte, K. (2006), "Fundamental aspects of nano-reinforced composites", Compos. Sci. Technol., 66(16), 3115-3125. https://doi.org/10.1016/j.compscitech.2005.01.014
  5. Ghorbanpour Arani, A., Abdollahian, M. and Jalaei, M.H. (2015a), "Vibration of bioliquid-filled microtubules embeded in cytoplasm including surface effects using modified couple stress theory", J. Theor. Biol., 367, 29-38. https://doi.org/10.1016/j.jtbi.2014.11.019
  6. Ghorbanpour Arani, A., Kolahchi, R. and Zarei, M.s. (2015b), "Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensor and actuators using refined Zigzag theory", Compos. Struct., 132, 506-526. https://doi.org/10.1016/j.compstruct.2015.05.065
  7. Ghorbanpour Arani, A., Mosayyebi, M., Kolahdouzan, F., Kolahchi R. and Jamali, M. (2016), "Refined Zigzag theory for vibration analysis of viscoelastic FG-CNTRC micro plates integrated with piezoelectric layers", P. I. Mech. Eng G-J Aer. DOI: 10.1177/0954410016667150
  8. Hosseini, M. and Sadeghi-Goughari, M. (2016), "Vibration and instability analysis of nanotubes conveying fluid subjectrd to a longitudinal magnetic field", App. Math. Model., 40(4), 2560-2576. https://doi.org/10.1016/j.apm.2015.09.106
  9. Hosseini-Hashemi, S.H., Khorshidi, K. and Amabili, M. (2008), "Exact solution for linear buckling of rectangular Mindlin plates", J. sound. Vib., 315(1-2), 318-342. https://doi.org/10.1016/j.jsv.2008.01.059
  10. Iurlaro, L., Gherlone, M., Di Sciuva, M. and Tessler, A. (2013), "Assessment of the refined zigzag theory for bending, vibration, and buckling of sandwich plates: A comparative study of different theories", Compos. Struct., 106, 777-792. https://doi.org/10.1016/j.compstruct.2013.07.019
  11. Jung, W.Y., Han, S.C. and Park, W.T. (2014), "A modified couple stress theory for buckling analysis of S-FGM nanoplates embedded in Pasternak elastic medium", Compos. Part B., 60, 746-756. https://doi.org/10.1016/j.compositesb.2013.12.058
  12. Kiani, K. (2013), "Characterization of free vibration of elastically supported double-walled carbon nanotubes subjected to a longitudinally varying magnetic field", Acta. Mech., 224(12), 3139-3151. https://doi.org/10.1007/s00707-013-0937-8
  13. Kiani, K. (2014a), "Free vibration of conducting nanoplates exposed to unidirectional in-plane magnetic fields using nonlocal shear deformable plates theories", Physica. E., 57, 179-192. https://doi.org/10.1016/j.physe.2013.10.034
  14. Kiani, K. (2014b), "Magnetically affected single-walled carbon nanotubes as nanosensors", Mech. Res. Commun., 60, 33-39. https://doi.org/10.1016/j.mechrescom.2014.05.005
  15. Kiani, K. (2014c), "Revisiting the free transverse vibration of embedded single-layer graphene sheets acted upon by in-plane magnetic field", J. Mech. Sci. Technol., 28(9), 3511-3516. https://doi.org/10.1007/s12206-014-0811-1
  16. Kiani, K. (2015a), "Elastic wave propagation in magnetically affected double-walled carbon nanotubes", Meccanica, 50(4), 1003-2026. https://doi.org/10.1007/s11012-014-9957-2
  17. Kiani, K. (2015b), "Column buckling of magnetically affected stocky nanowires carrying electric current", J. Phys. Chem. Solids., 83, 140-151. https://doi.org/10.1016/j.jpcs.2015.03.020
  18. Lei, Z.X., Liew, K.M. and Yu, J.L. (2012), "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168.
  19. Li, Y.S. and Pan, E. (2015), "Static bending and free vibration of a functionally graded piezoelectric microplate based on modified couple stress theory", Int. J. Eng. Sci., 97, 40-59. https://doi.org/10.1016/j.ijengsci.2015.08.009
  20. Lou, J., He, L., Du, J. and Wu, H. (2016), "Buckling and post-buckling analyses of piezoelectric hybrid microplate subject to thermo-electro-mechanical loads based on the modified couple stress theory", Compos. Struct., 153, 332-344. https://doi.org/10.1016/j.compstruct.2016.05.107
  21. Lou, J. and He, L. (2015), "Closed-form solutions for nonlinear bending and free vibration of FG microplates based on the modified couple stress theory", Compos. Struct., 131, 810-820. https://doi.org/10.1016/j.compstruct.2015.06.031
  22. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributionbs", Steel Compos. Struct., Int. J., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  23. Mizusawa, T. (1993), "Buckling of rectangular Mindlin plates with tapered thickness by the spline strip method", Int. J. Solids. Struct., 30(2), 1663-1677. https://doi.org/10.1016/0020-7683(93)90196-E
  24. Mohammad Abadi, M. and Daneshmehr, A.R. (2014), "Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundry conditoins", Int. J. Eng. Sci., 74, 1-14. https://doi.org/10.1016/j.ijengsci.2013.08.010
  25. Moita, J.S., Araujo, A.L., Franco Correia, V.M., Mota Soares, C.M. and Mota Soares, C.A. (2015), "Buckling and geometrically nonlinear analysis of sandwich structures", Int. J. Mech. Sci., 92 154-161. https://doi.org/10.1016/j.ijmecsci.2014.12.008
  26. Narendar, S., Gupta, S.S. and Gopalakrishnan, S. (2012), "Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernolli beam theory", Appl. Math. Model., 36(9), 4529-4538. https://doi.org/10.1016/j.apm.2011.11.073
  27. Nateghi, A., Salamat-talab, M., Rezapour, J. and Daneshian, B. (2012), "Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory", Appl. Math. Model., 36(10), 4971-4987. https://doi.org/10.1016/j.apm.2011.12.035
  28. Rabani Bidgoli, M., Karimi, M. and Ghorbanpour Arani, A. (2015), "Viscous fluid induced vibration and instability of FGCNT-reinforced cylindrical shells integrated with piezoelectric layers", Steel Compos. Struct., Int. J., 19(3), 713-733. https://doi.org/10.12989/scs.2015.19.3.713
  29. Ramamoorthy, M., Rajamohan, V. and AK, J. (2014), "Vibration analysis of a partially treated laminated composite magnetorheological fluid sandwich plate", J. Vib. Control., 22(3), 869-895. https://doi.org/10.1177/1077546314532302
  30. Salvetat, D. and Rubio, A. (2002), "Mechanical properties of carbon nanotubes: a fiber digest for beginners", Carbon, 40(10), 1729-1734. https://doi.org/10.1016/S0008-6223(02)00012-X
  31. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  32. Shufrin, I. and Eisenberger, M. (2005), "Stability and vibration of shear deformable plates-first order and higher order analysis", Int. J. Solids. Struct., 42(3-4), 1225-1251. https://doi.org/10.1016/j.ijsolstr.2004.06.067
  33. Tessler, A., Di Sciuva, M. and Gherlone, M. (2009), "Refined Zigzag theory for laminated composite and sandwich plates", Technical, Report NASA-TP-2009-215561.
  34. Tessler, A., Di Sciuva, M. and Gherlone, M. (2010), "A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics", J. Mech. Mater. Struct., 5(2), 341-367. https://doi.org/10.2140/jomms.2010.5.341
  35. Upadhyay, A.K. and Shukla, K.K. (2013), "Post-buckling behavior of composite and sandwich skew plates", Int. Nonlinear Mech., 55, 120-127. https://doi.org/10.1016/j.ijnonlinmec.2013.05.010
  36. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Pres. Ves. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012
  37. Zhang, D.G. and Zhou, H.M. (2015), "Mechanical and thermal post-buckling analysis of FGM rectangular plates with various supported boundaries resting on nonlinear elastic foundation", Thin-Wall. Struct., 89, 142-152. https://doi.org/10.1016/j.tws.2014.12.021

Cited by

  1. Ozonization of SWCNTs on thermal/mechanical properties of basalt fiber-reinforced composites vol.31, pp.5, 2019, https://doi.org/10.12989/scs.2019.31.5.517
  2. Post-buckling analysis of Mindlin Cut out-plate reinforced by FG-CNTs vol.34, pp.2, 2018, https://doi.org/10.12989/scs.2020.34.2.289
  3. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2018, https://doi.org/10.12989/anr.2021.11.2.115
  4. Free vibration analysis of carbon nanotube RC nanobeams with variational approaches vol.11, pp.2, 2021, https://doi.org/10.12989/anr.2021.11.2.157
  5. Bending analysis of the multi-phase nanocomposite reinforced circular plate via 3D-elasticity theory vol.40, pp.4, 2021, https://doi.org/10.12989/scs.2021.40.4.601
  6. Forced vibration analysis of a micro sandwich plate with an isotropic/orthotropic cores and polymeric nanocomposite face sheets vol.28, pp.3, 2018, https://doi.org/10.12989/cac.2021.28.3.259