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Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection

  • Seyed Sajad Mirjavadi
  • Behzad Mohasel Afshari
  • Mohammad Reza Barati
  • A. M. S. Hamouda
Technical Paper
  • 7 Downloads

Abstract

Nonlinear free/forced vibration of a functionally graded graphene nanoplatelet (GNP) reinforced microbeam having geometrical imperfection which is rested on a non-linear elastic substrate have been studied in the present research. Graphene Platelets have been uniformly and non-uniformly scattered in the cross section area of the microbeam. Non-uniform distribution of GNPs is considered to be linear or non-linear type. Geometric imperfection is considered similar to the first vibration mode of microbeam. Size effects due to micro-rotations are captured in this study by means of modified couple stress elasticity. In the case of forced vibration, a uniform harmonic load is exerted to the top surface of microbeam. Harmonic balance method has been implemented to solve the non-linear governing equation of microbeam having quadratic and cubic nonlinearities. In this regard, frequency-amplitude curves are obtained and their trends are studied by changing of GNP amount and distribution, geometric imperfection, forced amplitude and hardening foundation.

Notes

Acknowledgements

The first and second authors would like to thank FPQ (Fidar project Qaem) for providing the fruitful and useful help.

References

  1. Ahouel M, Houari MSA, Bedia EA, Tounsi A (2016) Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept. Steel Compos Struct 20(5):963–981CrossRefGoogle Scholar
  2. Alibeigloo A (2014) Free vibration analysis of functionally graded carbon nanotube-reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity. Eur J Mech A Solids 44:104–115MathSciNetCrossRefGoogle Scholar
  3. Allahkarami F, Nikkhah-Bahrami M (2018) The effects of agglomerated CNTs as reinforcement on the size-dependent vibration of embedded curved microbeams based on modified couple stress theory. Mech Adv Mater Struct 25(12):995–1008CrossRefGoogle Scholar
  4. Ansari R, Torabi J, Shojaei MF (2016) Vibrational analysis of functionally graded carbon nanotube-reinforced composite spherical shells resting on elastic foundation using the variational differential quadrature method. Eur J Mech A Solids 60:166–182MathSciNetCrossRefGoogle Scholar
  5. Aragh BS (2017) Mathematical modelling of the stability of carbon nanotube-reinforced panels. Steel Compos Struct 24(6):727–740Google Scholar
  6. Asghari M, Ahmadian MT, Kahrobaiyan MH, Rahaeifard M (2010) On the size-dependent behavior of functionally graded micro-beams. Mater Des (1980–2015) 31(5):2324–2329CrossRefGoogle Scholar
  7. Bafekrpour E, Simon GP, Naebe M, Habsuda J, Yang C, Fox B (2013) Preparation and properties of composition-controlled carbon nanofiber/phenolic nanocomposites. Compos B Eng 52:120–126CrossRefGoogle Scholar
  8. Barati MR, Zenkour AM (2018) Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions. Mech Adv Mater Struct:1–9Google Scholar
  9. Bessaim A, Houari MSA, Bernard F, Tounsi A (2015) A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates. Struct Eng Mech 56(2):223–240CrossRefGoogle Scholar
  10. Dai HL, Wang YK, Wang L (2015) Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory. Int J Eng Sci 94:103–112MathSciNetCrossRefGoogle Scholar
  11. Ebrahimi F, Habibi S (2017) Low-velocity impact response of laminated FG-CNT reinforced composite plates in thermal environment. Adv Nano Res 5(2):69–97Google Scholar
  12. Ebrahimi F, Habibi S (2018) Nonlinear eccentric low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate resting on elastic foundations in hygrothermal environments. Mech Adv Mater Struct 25(5):425–438CrossRefGoogle Scholar
  13. Esawi AM, Farag MM (2007) Carbon nanotube reinforced composites: potential and current challenges. Mater Des 28(9):2394–2401CrossRefGoogle Scholar
  14. Farokhi H, Ghayesh MH (2015) Thermo-mechanical dynamics of perfect and imperfect Timoshenko microbeams. Int J Eng Sci 91:12–33MathSciNetCrossRefGoogle Scholar
  15. Farokhi H, Ghayesh MH, Amabili M (2013) Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory. Int J Eng Sci 68:11–23MathSciNetCrossRefGoogle Scholar
  16. Feng C, Kitipornchai S, Yang J (2017) Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs). Eng Struct 140:110–119CrossRefGoogle Scholar
  17. Ghayesh MH, Farokhi H (2017) Global dynamics of imperfect axially forced microbeams. Int J Eng Sci 115:102–116MathSciNetCrossRefGoogle Scholar
  18. Hu K, Wang YK, Dai HL, Wang L, Qian Q (2016) Nonlinear and chaotic vibrations of cantilevered micropipes conveying fluid based on modified couple stress theory. Int J Eng Sci 105:93–107MathSciNetCrossRefGoogle Scholar
  19. Kilic U, Daghash SM, Ozbulut OE (2018) Mechanical characterization of polymer nanocomposites reinforced with graphene nanoplatelets. International congress on polymers in concrete. Springer, Cham, pp 689–695CrossRefGoogle Scholar
  20. Kitipornchai S, Chen D, Yang J (2016) Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater Des 116:656–665CrossRefGoogle Scholar
  21. Kong S, Zhou S, Nie Z, Wang K (2008) The size-dependent natural frequency of Bernoulli-Euler micro-beams. Int J Eng Sci 46(5):427–437CrossRefGoogle Scholar
  22. Kwon H, Bradbury CR, Leparoux M (2011) Fabrication of functionally graded carbon nanotube-reinforced aluminum matrix composite. Adv Eng Mater 13(4):325–329CrossRefGoogle Scholar
  23. Li YS, Pan ES (2015) Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory. Int J Eng Sci 97:40–59MathSciNetCrossRefGoogle Scholar
  24. Mehar K, Panda SK, Mahapatra TR (2017) Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure. Eur J Mech A Solids 65:384–396MathSciNetCrossRefGoogle Scholar
  25. Mohammadimehr M, Monajemi AA, Afshari H (2017) Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams. Microsyst Technol:1–15Google Scholar
  26. Reddy RMR, Karunasena W, Lokuge W (2018) Free vibration of functionally graded-GPL reinforced composite plates with different boundary conditions. Aerosp Sci Technol 78:147–156CrossRefGoogle Scholar
  27. Rokni H, Milani AS, Seethaler RJ (2015) Size-dependent vibration behavior of functionally graded CNT-reinforced polymer microcantilevers: modeling and optimization. Eur J Mech A Solids 49:26–34MathSciNetCrossRefGoogle Scholar
  28. Rostami R, Mohammadimehr M, Ghannad M, Jalali A (2018) Forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by CNTs based on MCST with temperature-variable material properties. Theor Appl Mech Lett 8(2):97–108CrossRefGoogle Scholar
  29. Sahmani S, Aghdam MM (2017) Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams. Compos Struct 179:77–88CrossRefGoogle Scholar
  30. Shen HS (2009) Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Compos Struct 91(1):9–19CrossRefGoogle Scholar
  31. Shenas AG, Ziaee S, Malekzadeh P (2018) A unified higher-order beam theory for free vibration and buckling of fgcnt-reinforced microbeams embedded in elastic medium based on unifying stress–strain gradient framework. Iran J Sci Technol Trans Mech Eng:1–24Google Scholar
  32. Thai CH, Ferreira AJM, Rabczuk T, Nguyen-Xuan H (2018) Size-dependent analysis of FG-CNTRC microplates based on modified strain gradient elasticity theory. Eur J Mech A Solids 72:521–538MathSciNetCrossRefGoogle Scholar
  33. Torabi J, Ansari R, Hassani R (2019) Numerical study on the thermal buckling analysis of CNT-reinforced composite plates with different shapes based on the higher-order shear deformation theory. Eur J Mech A Solids 73:144–160MathSciNetCrossRefGoogle Scholar
  34. Toupin RA (1962) Elastic materials with couple-stresses. Arch Ration Mech Anal 11(1):385–414MathSciNetCrossRefGoogle Scholar
  35. Zarasvand KA, Golestanian H (2017) Investigating the effects of number and distribution of GNP layers on graphene reinforced polymer properties: physical, numerical and micromechanical methods. Compos Sci Technol 139:117–126CrossRefGoogle Scholar
  36. Zeighampour H, Beni YT (2014) Analysis of conical shells in the framework of coupled stresses theory. Int J Eng Sci 81:107–122MathSciNetCrossRefGoogle Scholar
  37. Zhao Z, Feng C, Wang Y, Yang J (2017) Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs). Compos Struct 180:799–808CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringQatar UniversityDohaQatar
  2. 2.School of Mechanical Engineering, College of EngineeringSharif University of TechnologyTehranIran
  3. 3.Fidar Project Qaem CompanyTehranIran

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