Smart Structures and Systems

  • 제17권2호
  • /
  • Pages.257-274
  • /
  • 2016
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

On bending, buckling and vibration of graphene nanosheets based on the nonlocal theory

  • Liu, Jinjian (School of Urban Rail Transportation, Soochow University) ;
  • Chen, Ling (School of Urban Rail Transportation, Soochow University) ;
  • Xie, Feng (School of Urban Rail Transportation, Soochow University) ;
  • Fan, Xueliang (School of Urban Rail Transportation, Soochow University) ;
  • Li, Cheng (School of Urban Rail Transportation, Soochow University)
  • 투고 : 2015.07.06
  • 심사 : 2015.12.08
  • 발행 : 2016.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

The nonlocal static bending, buckling, free and forced vibrations of graphene nanosheets are examined based on the Kirchhoff plate theory and Taylor expansion approach. The nonlocal nanoplate model incorporates the length scale parameter which can capture the small scale effect. The governing equations are derived using Hamilton's principle and the Navier-type solution is developed for simply-supported graphene nanosheets. The analytical results are proposed for deflection, natural frequency, amplitude of forced vibration and buckling load. Moreover, the effects of nonlocal parameter, half wave number and three-dimensional sizes on the static, dynamic and stability responses of the graphene nanosheets are discussed. Some illustrative examples are also addressed to verify the present model, methodology and solution. The results show that the new nanoplate model produces larger deflection, smaller circular frequencies, amplitude and buckling load compared with the classical model.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Phys. E., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  2. Bedroud, M., Nazemnezhad, R. and Hosseini-Hashemi, S. (2015), "Axisymmetric/ asymmetric buckling of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity", Meccanica, 50, 1791-1806. https://doi.org/10.1007/s11012-015-0123-2
  3. Eberhardt, O. and Wallmersperger, T. (2014), "Mechanical properties and deformation behavior of carbon nanotubes calculated by a molecular mechanics approach", Smart Struct. Syst., 13(4), 685-709. https://doi.org/10.12989/sss.2014.13.4.685
  4. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030
  5. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  6. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  7. Hosseini-Hashemi, S., Kermajani, M. and Nazemnezhad, R. (2015), "An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory", Eur. J. Mech. A-Solids., 51, 29-43. https://doi.org/10.1016/j.euromechsol.2014.11.005
  8. Hosseini, M., Sadeghi-Goughari, M., Atashipour, S.A. and Eftekhari, M. (2014), "Vibration analysis of single-walled carbon nanotubes conveying nanoflow embedded in a viscoelastic medium using modified nonlocal beam model", Arch. Mech., 66(4), 217-244.
  9. Liew, K.M., He, X.Q. and Kitipornchai, S. (2006), "Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix", Acta. Mater., 54(16), 4229-4236. https://doi.org/10.1016/j.actamat.2006.05.016
  10. Li, C., Lim, C.W. and Yu, J.L. (2011), "Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axial load", Smart Mater. Struct., 20(1), 015023. https://doi.org/10.1088/0964-1726/20/1/015023
  11. Murmu, T. and Pradhan, S.C. (2009), "Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory", Physica. E., 41(8), 1451-1456. https://doi.org/10.1016/j.physe.2009.04.015
  12. Pradhan, S.C. and Phadikar, J.K. (2009), "Nonlocal elasticity theory for vibration of nanoplates", J. Sound Vib., 325(1), 206-223. https://doi.org/10.1016/j.jsv.2009.03.007
  13. Pradhan, S.C. and Kumar, A. (2011), "Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method", Compos. Struct., 93(2), 774-779. https://doi.org/10.1016/j.compstruct.2010.08.004
  14. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  15. Sahmani, S. and Bahrami, M. (2015), "Nonlocal plate model for dynamic pull-in instability analysis of circular higher-order shear deformable nanoplates including surface stress effect", J. Mech. Sci. Tech., 29(3), 1151-1161. https://doi.org/10.1007/s12206-015-0227-6
  16. Shen, Z.B., Tang, H.L., Li, D.K. and Tang, G.J. (2012), "Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory", Comput. Mater. Sci., 61, 200-205. https://doi.org/10.1016/j.commatsci.2012.04.003
  17. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  18. Yan, J.W., Tong, L.H., Li, C., Zhu, Y. and Wang, Z.W. (2015), "Exact solutions of bending deflections for nano-beams and nano-plates based on nonlocal elasticity theory", Compos. Struct., 125, 304-313. https://doi.org/10.1016/j.compstruct.2015.02.017
  19. Yin, F., Chen, C.P. and Chen, D.L. (2015), "Vibration analysis of nano-beam with consideration of surface effects and damage effects", Nonlinear Eng., 4(1), 61-66.
  20. Zhang, Y., Zhang, L.W., Liew, K.M. and Yu, J.L. (2015), "Transient analysis of single-layered graphene sheet using the kp-Ritz method and nonlocal elasticity theory", Appl. Math. Comput., 258, 489-501.
  21. Zhang, Y., Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2015), "Nonlocal continuum model for vibration of single-layered graphene sheets based on the element-free kp-Ritz method", Eng. Anal. Bound. Elem., 56, 90-97. https://doi.org/10.1016/j.enganabound.2015.01.020

피인용 문헌

  1. A semi-continuum-based bending analysis for extreme-thin micro/nano-beams and new proposal for nonlocal differential constitution vol.172, 2017, https://doi.org/10.1016/j.compstruct.2017.03.070
  2. Nonlocal Thermo-Electro-Mechanical coupling vibrations of axially moving piezoelectric nanobeams vol.45, pp.4, 2017, https://doi.org/10.1080/15397734.2016.1242079
  3. Transverse free vibration and stability of axially moving nanoplates based on nonlocal elasticity theory vol.45, 2017, https://doi.org/10.1016/j.apm.2016.12.006
  4. Electro-mechanical vibration of nanoshells using consistent size-dependent piezoelectric theory vol.22, pp.6, 2016, https://doi.org/10.12989/scs.2016.22.6.1301
  5. Dynamics of silicon nanobeams with axial motion subjected to transverse and longitudinal loads considering nonlocal and surface effects vol.19, pp.1, 2017, https://doi.org/10.12989/sss.2017.19.1.105
  6. Nonlocal thermo-electro-mechanical vibration analysis of smart curved FG piezoelectric Timoshenko nanobeam vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.351
  7. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory vol.21, pp.4, 2016, https://doi.org/10.12989/sss.2018.21.4.397
  8. Analytical solution for scale-dependent static stability analysis of temperature-dependent nanobeams subjected to uniform temperature distributions vol.26, pp.4, 2018, https://doi.org/10.12989/was.2018.26.4.205
  9. Exact nonlocal solutions of circular nanoplates subjected to uniformly distributed loads and nonlocal concentrated forces vol.42, pp.1, 2016, https://doi.org/10.1007/s40430-019-2144-6
  10. Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model vol.34, pp.5, 2016, https://doi.org/10.12989/scs.2020.34.5.643
  11. On the vibration and buckling analysis of quadrilateral and triangular nanoplates using nonlocal spline finite strip method vol.42, pp.4, 2016, https://doi.org/10.1007/s40430-020-2245-2
  12. Numerical investigation on scale-dependent vibrations of porous foam plates under dynamic loads vol.7, pp.2, 2020, https://doi.org/10.12989/smm.2020.7.2.085
  13. Size-dependent vibration of single-crystalline rectangular nanoplates with cubic anisotropy considering surface stress and nonlocal elasticity effects vol.170, pp.None, 2022, https://doi.org/10.1016/j.tws.2021.108518