Advances in nano research

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Effect of non-uniform temperature distributions on nonlocal vibration and buckling of inhomogeneous size-dependent beams

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Salari, Erfan (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • Received : 2017.10.21
  • Accepted : 2018.10.24
  • Published : 2018.12.25
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Abstract

In the present investigation, thermal buckling and free vibration characteristics of functionally graded (FG) Timoshenko nanobeams subjected to nonlinear thermal loading are carried out by presenting a Navier type solution. The thermal load is assumed to be nonlinear distribution through the thickness of FG nanobeam. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model and the material properties are assumed to be temperature-dependent. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling and vibration analysis of graded nanobeams including size effect. Moreover, in following a parametric study is accompanied to examine the effects of the several parameters such as nonlocal parameter, thermal effect, power law index and aspect ratio on the critical buckling temperatures and natural frequencies of the size-dependent FG nanobeams in detail. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. Also, it is found that the small scale effects and nonlinear thermal loading have a significant effect on thermal stability and vibration characteristics of FG nanobeams.

Keywords

References

  1. Alizada, A.N., Sofiyev, A.H. and Kuruoglu, N. (2012), "Stress analysis of a substrate coated by nanomaterials with vacancies subjected to uniform extension load", Acta Mechanica, 223(7), 1371-1383. https://doi.org/10.1007/s00707-012-0649-5
  2. Ansari, R. and Norouzzadeh, A. (2016), "Nonlocal and surface effects on the buckling behavior of functionally graded nanoplates: An isogeometric analysis", Phys. E: Low-dimens. Syst. Nanostruct., 84, 84-97.
  3. Ansari, R., Gholami, R. and Sahmani, S. (2011), "Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory", Compos. Struct., 94(1), 221-228. https://doi.org/10.1016/j.compstruct.2011.06.024
  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. Bafekrpour, E., Simon, G.P., Habsuda, J., Naebe, M., Yang, C. and Fox, B. (2012), "Fabrication and characterization of functionally graded synthetic graphite/phenolic nanocomposites", Mater. Sci. Eng.: A, 545, 123-131. https://doi.org/10.1016/j.msea.2012.02.097
  6. Carbonari, R.C., Silva, E.C. and Paulino, G.H. (2009), "Multi-actuated functionally graded piezoelectric micro-tools design: A multiphysics topology optimization approach", Int. J. Numer. Methods Eng., 77(3), 301-336. https://doi.org/10.1002/nme.2403
  7. Daneshmehr, A., Rajabpoor, A. and Hadi, A. (2015), "Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories", Int. J. Eng. Sci., 95, 23-35.
  8. Ebrahimi, F. and Barati, M.R. (2016), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", Int. J. Smart Nano Mater., 7(3), 119-143.
  9. Ebrahimi, F. and Rastgoo, A. (2008), "Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers", Smart Mater. Struct., 17(1), 015044. https://doi.org/10.1088/0964-1726/17/1/015044
  10. Ebrahimi, F. and Salari, E. (2015), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), p.125007. https://doi.org/10.1088/0964-1726/24/12/125007
  11. Ebrahimi, F., Rastgoo, A. and Kargarnovin, M.H. (2008), "Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers", J. Mech. Sci. Technol., 22(6), 1058-1072. https://doi.org/10.1007/s12206-008-0303-2
  12. Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Technol., 23(8), 2107-2124. https://doi.org/10.1007/s12206-009-0358-8
  13. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  14. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Thermal Stress., 40(5), 535-547. https://doi.org/10.1080/01495739.2016.1230483
  15. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Computat., 218(14), 7406-7420.
  16. 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
  17. Fu, Y., Du, H. and Zhang, S. (2003), "Functionally graded TiN/TiNi shape memory alloy films", Mater. Lett., 57(20), 2995-2999. https://doi.org/10.1016/S0167-577X(02)01419-2
  18. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), p. 56. https://doi.org/10.1038/354056a0
  19. Kiani, Y. and Eslami, M.R. (2013), "An exact solution for thermal buckling of annular FGM plates on an elastic medium", Compos. Part B: Eng., 45(1), 101-110. https://doi.org/10.1016/j.compositesb.2012.09.034
  20. Lee, Z., Ophus, C., Fischer, L.M., Nelson-Fitzpatrick, N., Westra, K.L., Evoy, S., Radmilovic, V., Dahmen, U. and Mitlin, D. (2006), "Metallic NEMS components fabricated from nanocomposite Al-Mo films", Nanotechnology, 17(12), p. 3063. https://doi.org/10.1088/0957-4484/17/12/042
  21. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory", Int. J. Solids Struct., 46(5), 1176-1185. https://doi.org/10.1016/j.ijsolstr.2008.10.012
  22. Lun, F.Y., Zhang, P., Gao, F.B. and Jia, H.G. (2006), "Design and fabrication of micro-optomechanical vibration sensor", Microfabr. Technol., 120(1), 61-64.
  23. Lv, Z., Qiu, Z., Zhu, J., Zhu, B. and Yang, W. (2018), "Nonlinear free vibration analysis of defective FG nanobeams embedded in elastic medium", Compos. Struct..
  24. Mahmoudpour, E., Hosseini-Hashemi, S.H. and Faghidian, S.A. (2018), "Nonlinear vibration analysis of FG nano-beams resting on elastic foundation in thermal environment using stress-driven nonlocal integral model", Appl. Math. Model., 57, 302-315. https://doi.org/10.1016/j.apm.2018.01.021
  25. Rahaeifard, M., Kahrobaiyan, M.H. and Ahmadian, M.T. (2009), "Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials", ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, January, pp. 539-544.
  26. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  27. 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
  28. Sofiyev, A.H. and Kuruoglu, N. (2015), "Buckling of non-homogeneous orthotropic conical shells subjected to combined load", Steel Compos. Struct., Int. J., 19(1), 1-19. https://doi.org/10.12989/scs.2015.19.1.001
  29. Tang, Y.G., Liu, Y. and Zhao, D. (2018), "Effects of neutral surface deviation on nonlinear resonance of embedded temperature-dependent functionally graded nanobeams", Compos. Struct., 184, 969-979.
  30. Thermophysical Properties Research Center (1967), Thermophysical properties of high temperature solid materials; Volume 1, Elements.-Pt. 1. Ed. Yeram Sarkis Touloukian, Macmillan.
  31. 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
  32. Witvrouw, A. and Mehta, A. (2005), "The use of functionally graded poly-SiGe layers for MEMS applications", In: Materials Science Forum, Volume 492, pp. 255-260. Trans Tech Publications.
  33. Zhang, D.G. (2013), "Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory", Compos. Struct., 100, 121-126. https://doi.org/10.1016/j.compstruct.2012.12.024
  34. Zhang, Y.Q., Liu, G.R. and Wang, J.S. (2004), "Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression", Phys. Rev. B, 70(20), p. 205430.

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