Advances in nano research

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A refined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams

  • Bensaid, Ismail (IS2M Laboratory, Faculty of Technology, Mechanical Engineering Department, University of Tlemcen)
  • Received : 2016.08.26
  • Accepted : 2017.02.12
  • Published : 2017.06.25
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Abstract

This paper proposes a new nonlocal higher-order hyperbolic shear deformation beam theory (HSBT) for the static bending and vibration of nanoscale-beams. Eringen's nonlocal elasticity theory is incorporated, in order to capture small size effects. In the present model, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the upper and bottom surfaces of the nanobeams without using shear correction factor. Employing Hamilton's principle, the nonlocal equations of motion are derived. The governing equations are solved analytically for the edges of the beam are simply supported, and the obtained results are compared, as possible, with the available solutions found in the literature. Furthermore, the influences of nonlocal coefficient, slenderness ratio on the static bending and dynamic responses of the nanobeam are examined.

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References

  1. Aissani, K., Bachir Bouiadjra, M., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., Int. J., 55(4), 743-762. https://doi.org/10.12989/sem.2015.55.4.743
  2. Ansari, R. and Sahmani, S. (2011), "Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories", Int. J. Eng. Sci., 49(11), 1244-1255. https://doi.org/10.1016/j.ijengsci.2011.01.007
  3. Arash, B. and Wang, Q. (2012), "A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes", Comput. Mater. Sci., 51(1), 303-313. https://doi.org/10.1016/j.commatsci.2011.07.040
  4. Aydogdu, M. (2009), "A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration", Phys. E Low Dimens. Syst. Nanostruct, 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  5. Behera, L. and Chakraverty, S. (2013), "Free vibration of Euler and Tomoshenko nanobeams using boundary characteristic orthogonal polynomials", Appl. Nanosci., 4(3), 347-358. https://doi.org/10.1007/s13204-013-0202-4
  6. Benguediab, S., Semmah, A., Larbi chaht, F., Mouaz, S. and Tounsi, A. (2014), "An investigation on the characteristics of bending, buckling and vibration of nanobeams via nonlocal beam theory", Int. J. Compos. Meth., 11(6), 1350085-1-14. https://doi.org/10.1142/S0219876213500850
  7. Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., Int. J., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351
  8. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  9. Ekinci, K.L. and Roukes, M.L. (2005), "Nanoelectromechanical systems", Rev. Sci. Instrum, 76(5496), 061101. https://doi.org/10.1063/1.1927327
  10. El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  11. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  12. 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
  13. Frankland, S.J.V., Caglar, A., Brenner, D.W. and Griebel, M. (2002), "Molecular simulation of the influence of chemical cross-links on the shear strength of carbon nanotube polymer interfaces", J. Phys. Chem. B, 106(12), 3046-3048. https://doi.org/10.1021/jp015591+
  14. Kheroubi, B., Benzair, A., Tounsi, A. and Semmah, A (2016), "A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams", Adv. Nano Res., Int. J., 4(4), 35-47. https://doi.org/10.21474/IJAR01/2361
  15. Lavrik, N.V., Sepaniak, M.J. and Datskos, P.G. (2004), "Cantilever transducers as a platform for chemical and biological sensors", Rev. Sci. Instrum, 75(7), 2229-2253. https://doi.org/10.1063/1.1763252
  16. Levinson, M. (1981), "A new rectangular beam theory", J. Sound Vib., 74(1), 81-87. https://doi.org/10.1016/0022-460X(81)90493-4
  17. Li, X., Bhushan, B., Takashima, K., Baek, C.W. and Kim, Y.K. (2003), "Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques", Ultramicroscopy, 97(1), 481-494. https://doi.org/10.1016/S0304-3991(03)00077-9
  18. Liew, L.M., He, X.Q. and Wong, C.H. (2004), "On the study of elastic and plastic properties of multi-walled carbon nanotubes under axial tension using molecular dynamics simulation", Acta Materialia, 52(9), 2521-2527. https://doi.org/10.1016/j.actamat.2004.01.043
  19. Nguyen, T-K. (2015), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3
  20. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3-5), 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  21. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons Inc., USA.
  22. 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
  23. Thai, H-T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. https://doi.org/10.1016/j.ijengsci.2011.11.011
  24. Thai, H-T. and Thuc, P.V. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009
  25. Thai, H-T., Nguyen, T-K., Vo, T.P. and Lee, J. (2014), "Analysis of functionally graded sandwich plates using a new first-order shear deformation theory", Eur. J. Mech., 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008
  26. Tounsi, A., Benguediab, S., Houari, M.S.A. and Semmah, A. (2013a), "A new nonlocal beam theory with thickness stretching effect for nanobeams", Int. J. Nanosci., 12(4), 1350025. https://doi.org/10.1142/S0219581X13500257
  27. Tounsi, A., Semmah, A. and Bousahla, A.A. (2013b), "Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory", ASCE J. Nanomech. Micromech., 3(3), 37-42. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000057
  28. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  29. Wang, Q. and Liew, K.M. (2007), "Application of nonlocal continuum mechanics to static analysis of micro-and nano structures", Phys. Lett. A, 363(3), 236-242. https://doi.org/10.1016/j.physleta.2006.10.093
  30. Zenkour, A.M. and Sobhy, M. (2015), "A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment", Phys. E Low Dimens. Syst. Nanostruct., 70, 121-128. https://doi.org/10.1016/j.physe.2015.02.022

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