Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Stability of perforated nanobeams incorporating surface energy effects

  • Almitani, Khalid H. (Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Abdelrahman, Alaa A. (Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University) ;
  • Eltaher, Mohamed A. (Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University)
  • Received : 2020.02.05
  • Accepted : 2020.04.14
  • Published : 2020.05.25
⟨ Previous Next ⟩

Abstract

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

Keywords

Acknowledgement

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-058-135-1441). The authors, therefore, acknowledge with thanks DSR technical and financial support.

References

  1. Abdelrahman, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A. M. and Hendi, A.A. (2019), "Free and forced analysis of perforated beams", Steel Compos. Struct., 31(5), 489-502. DOI: https://doi.org/10.12989/scs.2019.31.5.489.
  2. Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963.
  3. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2019), "On forced and free vibrations of cutout squared beams", Steel Compos. Struct., 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643.
  4. Almitani, K.H. (2018), "Buckling behaviors of symmetric and antisymmetric functionally graded beams", J. Appl. Comput. Mech., 4(2), 115-124. 10.22055/JACM.2017.23040.1147.
  5. 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
  6. 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
  7. Bellifa, H., Benrahou, K. H., Bousahla, A. A., Tounsi, A., & Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695
  8. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457
  9. Bendali, A., Labedan, R., Domingue, F. and Nerguizian, V. (2006), "Holes effects on RF MEMS parallel membranes capacitors", Proceedings of the 2006 Canadian Conference on Electrical and Computer Engineering (pp. 2140-2143). IEEE. DOI: 10.1109/CCECE.2006.277600
  10. Bourouina, H., Yahiaoui, R., Sahar, A. and Benamar, M.E.A. (2016), "Analytical modeling for the determination of nonlocal resonance frequencies of perforated nanobeams subjected to temperature-induced loads", Physica E, 75, 163-168. https://doi.org/10.1016/j.physe.2015.09.014
  11. Bourouina, H., Yahiaoui, R., Kerid, R., Ghoumid, K., Lajoie, I., Picaud, F. and Herlem, G. (2020), "The influence of hole networks on the adsorption-induced frequency shift of a perforated nanobeam using non-local elasticity theory", J. Phys. Chem. Solids, 136, 109201. https://doi.org/10.1016/j.jpcs.2019.109201.
  12. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A. 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.
  13. De Pasquale, G., Veijola, T. and Soma, A. (2009), "Modelling and validation of air damping in perforated gold and silicon MEMS plates", Journal of Micromechanics and Microengineering, 20(1), 015010. ttps://doi.org/10.1088/0960-1317/20/1/015010
  14. Ebrahimi, F., Daman, M. and Fardshad, R.E. (2017), "Surface effects on vibration and buckling behavior of embedded nanoarches", Struct Eng Mech, 64(1), 1-10. https://doi.org/10.12989/sem.2017.64.1.001.
  15. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013a), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030.
  16. Eltaher, M.A., Mahmoud, F.F., Assie, A.E. and Meletis, E.I. (2013b), "Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams", Appl. Math. Comput., 224, 760-774. https://doi.org/10.1016/j.amc.2013.09.002.
  17. Eltaher, M.A., Khairy, A., Sadoun, A.M. and, F.A. (2014a), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072.
  18. Eltaher, M.A., Hamed, M.A., Sadoun, A.M. and Mansour, A. (2014b), "Mechanical analysis of higher order gradient nanobeams", Appl. Math. Comput., 229, 260-272. https://doi.org/10.1016/j.amc.2013.12.076
  19. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016a), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5-6), 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026.
  20. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016b), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51. https://doi.org/10.12989/anr.2016.4.1.051.
  21. Eltaher, M.A., Kabeel, A.M., Almitani, K.H. and Abdraboh, A.M. (2018a), "Static bending and buckling of perforated nonlocal size-dependent nanobeams", Microsyst/Technologies, 24(12), 4881-4893. https://doi.org/10.1007/s00542-018-3905-3.
  22. Eltaher, M.A., Abdraboh, A.M. and Almitani, K.H. (2018b), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsys. Technologies, 24(9), 3925-3937. https://doi.org/10.1007/s00542-018-3910-6.
  23. Eltaher, M.A., Mohamed, N., Mohamed, S. and Seddek, L.F. (2019), "Postbuckling of curved carbon nanotubes using energy equivalent model", J. Nano Res., 57, 136-157. https://doi.org/10.4028/www.scientific.net/JNanoR.57.136.
  24. Eltaher, M.A. and Mohamed N.A., (2020), "Vibration of Nonlocal Perforated Nanobeams under General Boundary Conditions", Smart Struct. Syst., 25(4). 501-514. https://doi.org/10.12989/sss.2020.25.4.501.
  25. Eltaher, M.A., Mohamed, S.A. and Melaibari, A. (2020a), "Static stability of a unified composite beams under varying axial loads", Thin-Wall. Struct., 147, 106488. https://doi.org/10.1016/j.tws.2019.106488.
  26. Eltaher, M.A., Omar, F.A., Abdraboh, A.M., Abdalla, W.S. and Alshorbagy, A.E. (2020b), "Mechanical Behaviors of Piezoelectric Nonlocal Nanobeam with Cutouts", Smart Struct. Syst., 25(2), 219-228. https://doi.org/10.12989/sss.2020.25.2.219.
  27. Emam, S.A., Eltaher, M.A., Khater, M.E. and Abdalla, W.S. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238.
  28. Foroutan, S., Haghshenas, A., Hashemian, M., Eftekhari, S.A. and Toghraie, D, (2018), "Spatial buckling analysis of current-carrying nanowires in the presence of a longitudinal magnetic field accounting for both surface and nonlocal effects", Physica E, 97, 191-205. https://doi.org/10.1016/j.physe.2017.11.015.
  29. Esmaeili, M. and Beni, T.Y. (2019), "Vibration and buckling analysis of functionally graded flexoelectric smart beam", J. Appl. Comput. Mech., 5(5), 900-917. 10.22055/JACM.2019.27857.1439.
  30. Fu, Y., Zhang, J. and Jiang, Y. (2010), "Influences of the surface energies on the nonlinear static and dynamic behaviors of nanobeams", Physica E: Low-dimensional Syst. Nanostruct., 42(9), 2268-2273. https://doi.org/10.1016/j.physe.2010.05.001.
  31. Guha, K., Kumar, M., Agarwal, S. and Baishya, S. (2015), "A modified capacitance model of RF MEMS shunt switch incorporating fringing field effects of perforated beam", Solid-State Electronics, 114, 35-42. https://doi.org/10.1016/j.sse.2015.07.008.
  32. Guha, K., Laskar, N.M., Gogoi, H.J., Borah, A.K., Baishnab, K.L. and Baishya, S. (2017), "Novel analytical model for optimizing the pull-in voltage in a flexured MEMS switch incorporating beam perforation effect", Solid-State Electronics, 137, 85-94. https://doi.org/10.1016/j.sse.2017.08.007.
  33. Gurtin, M.E. and Murdoch, A. I. (1975), "A continuum theory of elastic material surfaces", Archive for Rational Mechanics and Analysis, 57(4), 291-323. https://doi.org/10.1007/BF00261375
  34. Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solids Struct., 14(6), 431-440. https://doi.org/10.1016/0020-7683(78)90008-2
  35. Hadipeykani, M., Aghadavoudi, F. and Toghraie, D. (2020), "A molecular dynamics simulation of the glass transition temperature and volumetric thermal expansion coefficient of thermoset polymer based epoxy nanocomposite reinforced by CNT: A statistical study", Physica A: Statistical Mechanics and its Applications, 123995. https://doi.org/10.1016/j.physa.2019.123995
  36. Hashemian, M., Foroutan, S. and Toghraie, D. (2019a), "Comprehensive beam models for buckling and bending behavior of simple nanobeam based on nonlocal strain gradient theory and surface effects", Mechanics of Materials, 139, 103209. https://doi.org/10.1016/j.mechmat.2019.103209.
  37. Hashemian, M., Vaez, A.H. and Toghraie, D. (2019b), "Investigation of viscous fluid flow and dynamic stability of CNTs subjected to axial harmonic load coupled using Bolotin's method", Int. J. Numer. Method. Heat Fluid Fl., https://doi.org/10.1108/HFF-12-2018-0739.
  38. Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75-89. https://doi.org/10.12989/scs.2020.34.1.075.
  39. Hamidi, B.A., Hosseini, S.A., Hassannejad, R. and Khosravi, F. (2020), "Theoretical analysis of thermoelastic damping of silver nanobeam resonators based on Green-Naghdi via nonlocal elasticity with surface energy effects", The European Physical J. Plus, 135(1), 1-20. https://doi.org/10.1140/epjp/s13360-019-00037-8.
  40. Jena, S.K., Chakraverty, S., Malikan, M. and Tornabene, F. (2019), "Stability analysis of single-walled carbon nanotubes embedded in winkler foundation placed in a thermal environment considering the surface effect using a new refined beam theory", Mechanics Based Design of Structures and Machines, 1-15. https://doi.org/10.1080/15397734.2019.1698437.
  41. Kerid, R., Bourouina, H., Yahiaoui, R., Bounekhla, M. and Aissat, A. (2019), "Magnetic field effect on nonlocal resonance frequencies of structure-based filter with periodic square holes network", Physica E: Low-dimensional Systems and Nanostructures, 105, 83-89. https://doi.org/10.1016/j.physe.2018.05.021.
  42. Khabaz, M.K., Eftekhari, S.A., Hashemian, M. and Toghraie, D. (2020), "Optimal vibration control of multi-layer micro-beams actuated by piezoelectric layer based on modified couple stress and surface stress elasticity theories", Physica A: Statistical Mechanics and its Applications, 123998. https://doi.org/10.1016/j.physa.2019.123998.
  43. Khater, M.E., Eltaher, M.A., Abdel-Rahman, E. and Yavuz, M. (2014), "Surface and thermal load effects on the buckling of curved nanowires", Eng. Sci. Technol., 17(4), 279-283. https://doi.org/10.1016/j.jestch.2014.07.003.
  44. Lu, L., Guo, X. and Zhao, J. (2018), "On the mechanics of Kirchhoff and Mindlin plates incorporating surface energy", Int. J. Eng. Sci., 124, 24-40. https://doi.org/10.1016/j.ijengsci.2017.11.020.
  45. Luschi, L. and Pieri, F. (2014), "An analytical model for the determination of resonance frequencies of perforated beams", J. Micromech. Microeng., 24(5), 055004. https://doi.org/10.1088/0960-1317/24/5/055004.
  46. Luschi, L. and Pieri, F. (2016), "An analytical model for the resonance frequency of square perforated Lame-mode resonators", Sensors Actuat. B: Chemical, 222, 1233-1239. https://doi.org/10.1016/j.snb.2015.07.085.
  47. Mahmoud, F.F., Eltaher, M.A., Alshorbagy, A.E. and Meletis, E.I. (2012), "Static analysis of nanobeams including surface effects by nonlocal finite element", J. Mech. Sci. Technol., 26(11), 3555-3563. https://doi.org/10.1007/s12206-012-0871-z
  48. Malikan, M. and Eremeyev, V.A. (2020), "Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method", Materials Research Express.
  49. Mercan, K. and Civalek, O. (2017), "Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ", Compos. Part B: Eng., 114, 34-45. https://doi.org/10.1016/j.compositesb.2017.01.067.
  50. Mirkalantari, S.A., Hashemian, M., Eftekhari, S.A. and Toghraie, D. (2017), "Pull-in instability analysis of rectangular nanoplate based on strain gradient theory considering surface stress effects", Physica B: Condensed Matter, 519, 1-14. https://doi.org/10.1016/j.physb.2017.05.028
  51. 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.
  52. Mohamed, N., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling and post-buckling behaviors of higher order carbon nanotubes using energy equivalent mode", Engineering with Computer,1-14. https://doi.org/10.1007/s00366-020-00976-2.
  53. Mohammadimehr, M., Mehrabi, M., Hadizadeh, H. and Hadizadeh, H. (2018), "Surface and size dependent effects on static, buckling, and vibration of micro composite beam under thermo-magnetic fields based on strain gradient theory", Steel Compos. Struct., 26(4), 513-531. https://doi.org/10.12989/scs.2018.26.4.513.
  54. Ouakad, H.M., Sedighi, H.M. and Younis, M.I. (2017), "One-to-one and three-to-one internal resonances in MEMS shallow arches", J. Comput. Nonlinear Dynam., 12(5), 051025. https://doi.org/10.1115/1.4036815.
  55. Oveissi, S., Nahvi, H., and Toghraie, D. (2015), "Axial wave propagation analysis in fixed and dynamic of carbon nanotubes conveying fluid", Solid Mech. Eng., 8(2), 108-115.
  56. Oveissi, S., Eftekhari, S.A., & Toghraie, D. (2016a), "Longitudinal vibration and instabilities of carbon nanotubes conveying fluid considering size effects of nanoflow and nanostructure", Physica E, 83, 164-173. https://doi.org/10.1016/j.physe.2016.05.010
  57. Oveissi, S., Toghraie, D. and Eftekhari, S.A. (2016b), "Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid", Physica E, 83, 275-283. https://doi.org/10.1016/j.physe.2016.05.004.
  58. Oveissi, S., Toghraie, D.S. and Eftekhari, S.A. (2017), "Analysis of transverse vibrational response and instabilities of axially moving CNT conveying fluid", Int. J. Fluid Mech. Res., 44(2). DOI: 10.1615/InterJFluidMechRes.2017016740.
  59. Oveissi, S., Toghraie, D.S. and Eftekhari, S.A. (2018), "Investigation on the effect of axially moving carbon nanotube, nanoflow, and Knudsen number on the vibrational behavior of the system", Int. J. Fluid Mech. Res., 45(2). 10.1615/InterJFluidMechRes.2018021036.
  60. Pirmoradian, M., Torkan, E., Abdali, N., Hashemian, M. and Toghraie, D. (2020), "Thermo-mechanical stability of single-layered graphene sheets embedded in an elastic medium under action of a moving nanoparticle", Mech. Mater., 141, 103248. https://doi.org/10.1016/j.mechmat.2019.103248.
  61. Pirmoradian, M., Torkan, E. and Toghraie, D. (2020b), "Study on size-dependent vibration and stability of DWCNTs subjected to moving nanoparticles and embedded on two-parameter foundations", Mech. Mater., 142, 103279. https://doi.org/10.1016/j.mechmat.2019.103279.
  62. Rao, K.S., Sailaja, B.V.S., Sravani, K.G., Vineetha, K.V., Kumar, P.A., Prathyusha, D. and Guha, K. (2019), "New Analytical Capacitance Modeling of the Perforated Switch Considering the Fringing Effect", IEEE Access, 7, 27026-27036. 10.1109/ACCESS.2018.2889724.
  63. Rebeiz, G. M. (2004). RF MEMS: theory, design, and technology. John Wiley & Sons.
  64. Saffari, S., Hashemian, M. and Toghraie, D. (2017), "Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects", Physica B: Condensed Matter, 520, 97-105. https://doi.org/10.1016/j.physb.2017.06.029.
  65. Sedighi, H.M. and Daneshmand, F. (2014), "Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term", J. Appl. Comput. Mech., 1(1), 1-9. 10.22055/jacm.2014.10545.
  66. Sedighi, H.M. and Bozorgmehri, A. (2016), "Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory", Acta Mechanica, 227(6), 1575-1591. https://doi.org/10.1007/s00707-016-1562-0.
  67. Shen, J.P., Li, C., Fan, X.L. and Jung, C.M. (2017), "Dynamics of silicon nanobeams with axial motion subjected to transverse and longitudinal loads considering nonlocal and surface effects", Smart Struct. Syst., 19(1), 105-113. https://doi.org/10.12989/sss.2017.19.1.105.
  68. Yang, F.A.C.M., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress-based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  69. Yousefzadeh, S., Akbari, A., Najafi, M., Akbari, O.A. and Toghraie, D. (2019), "Analysis of buckling of a multi-layered nanocomposite rectangular plate reinforced by single-walled carbon nanotubes on elastic medium considering nonlocal theory of Eringen and variational approach", Indian J. Physics, 1-15. https://doi.org/10.1007/s12648-019-01546-z.
  70. Wang, L. (2012), "Surface effect on buckling configuration of nanobeams containing internal flowing fluid: A nonlinear analysis", Physica E: Low-dimensional Systems and Nanostructures, 44(4), 808-812. https://doi.org/10.1016/j.physe.2011.12.006.

Cited by

  1. On bending analysis of perforated microbeams including the microstructure effects vol.76, pp.6, 2020, https://doi.org/10.12989/sem.2020.76.6.765
  2. Nonlinear nonlocal-surface energy-based vibrations of a bidirectionally excited nanobeam at its supports vol.96, pp.2, 2021, https://doi.org/10.1088/1402-4896/abcdc4
  3. Static analysis of cutout microstructures incorporating the microstructure and surface effects vol.38, pp.5, 2020, https://doi.org/10.12989/scs.2021.38.5.583
  4. Vibration of multilayered functionally graded deep beams under thermal load vol.24, pp.6, 2020, https://doi.org/10.12989/gae.2021.24.6.545