Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Instability analysis of viscoelastic CNTs surrounded by a thermo-elastic foundation

  • Amir, Saeed (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Khani, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Shajari, Ali Reza (Mechanical Properties Research Lab (MPRL), Faculty of Mechanical Engineering, K.N. Toosi University of Technology) ;
  • Dashti, Pedram (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2016.07.20
  • Accepted : 2017.01.26
  • Published : 2017.07.25
⟨ Previous Next ⟩

Abstract

Static and dynamic instability of a viscoelastic carbon nanotube (CNT) embedded on a thermo-elastic foundation are investigated, in this research. The CNT is modeled based on Euler-Bernoulli beam (EBB) and nonlocal small scale elasticity theory is utilized to analyze the structure. Governing equations of the system are derived using Hamilton's principle and differential quadrature (DQ) method is applied to solve the partial differential equations. The effects of variable axial load and diverse boundary conditions on static/vibration instability are studied. To verify the result of the DQ method, the Galerkin weighted residual approach is used for the instability analysis. It is observed appropriate agreement for results of two different solution methods and satisfactory accuracy with those obtained in prior studies. The results of this work could be useful for engineers and designers in order to produce and design nano/micro structures in thermo-elastic medium.

Keywords

Acknowledgement

Supported by : University of Kashan

References

  1. Aydogdu, M. (2012), "Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity", Mech. Res. Commun., 43, 34-40. https://doi.org/10.1016/j.mechrescom.2012.02.001
  2. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., 3(1), 29-37. https://doi.org/10.12989/anr.2015.3.1.029
  3. Boehle, M., Pianca, P., Lafdi, K. and Chinesta, F. (2015), "Modeling of an embedded carbon nanotube based composite strain sensor", Adv. Aircraft Spacecraft Sci., 2, 263-273. https://doi.org/10.12989/aas.2015.2.3.263
  4. Chang, T., Geng, J. and Guo, X. (2005), "Chirality-and sizedependent elastic properties of single-walled carbon nanotubes", Appl. Phys. Lett., 87(25), 251929. https://doi.org/10.1063/1.2149216
  5. Chang, W. and Lee, H. (2012), "Vibration analysis of viscoelastic carbon nanotubes", IET Micro Nano Lett., 7(12), 1308-1312. https://doi.org/10.1049/mnl.2012.0612
  6. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Bedia, E.A. (2016), "Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617
  7. Fang, B., Zhen, Y.X., Zhang, C.P. and Tang, Y. (2013), "Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory", Appl. Math. Model., 37(3), 1096-1107. https://doi.org/10.1016/j.apm.2012.03.032
  8. Gafour, Y., Zidour, M., Tounsi, A., Heireche, H. and Semmah, A. (2013), "Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory", Physica E, 48, 118-123. https://doi.org/10.1016/j.physe.2012.11.006
  9. Ghannadpour, S.A.M., Mohammadi, B. and Fazilati, J. (2013), "Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method", Compos. Struct., 96, 584-589. https://doi.org/10.1016/j.compstruct.2012.08.024
  10. Ghorbanpour Arani, A., Amir, S., Dashti, P. and Yousefi, M. (2014), "Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect", Comput. Mater. Sci., 86, 144-154. https://doi.org/10.1016/j.commatsci.2014.01.047
  11. Ghorbanpour Arani, A., Hashemian, M., Loghman, A. and Mohammadimehr, M. (2011), "Study of dynamic stability of the double-walled carbon nanotube under axial loading embedded in an elastic medium by the energy method", J. Appl. Mech. Tech. Phys., 52(5), 815-824. https://doi.org/10.1134/S0021894411050178
  12. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0
  13. Kiani, K. (2013), "Vibration analysis of elastically restrained double-walled carbon nanotubes on elastic foundation subjected to axial load using nonlocal shear deformable beam theories", Int. J. Mech. Sci., 68, 16-34. https://doi.org/10.1016/j.ijmecsci.2012.11.011
  14. Lei, Y., Adhikari, S. and Friswell, M.I. (2013), "Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beam", Int. J. Eng. Sci., 66-67, 1-13. https://doi.org/10.1016/j.ijengsci.2013.02.004
  15. Pradhan, S.C. and Mandal, U. (2013), "Finite element analysis of CNTs based on nonlocal elasticity and Timoshenko beam theory including thermal effect", Physica E, 53, 223-232. https://doi.org/10.1016/j.physe.2013.04.029
  16. Pradhan, S.C. and Phadikar, J.K. (2009), "Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory", Struct. Eng. Mech., 33(2), 193-213. https://doi.org/10.12989/sem.2009.33.2.193
  17. Ranjbartoreh, A.R., Wang, G.X., Ghorbanpour Arani, A. and Loghman, A. (2008), "Comparative consideration of axial stability of single-and double-walled carbon nanotube and its inner and outer tubes", Physica E, 41(2), 202-208. https://doi.org/10.1016/j.physe.2008.06.026
  18. 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
  19. Shen, H.S. and Zhang, C.L. (2011), "Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates", Comput. Mater. Sci., 50(3), 1022-1029. https://doi.org/10.1016/j.commatsci.2010.10.042
  20. Wang, B.L. and Wang, K.F. (2013), "Vibration analysis of embedded nanotubes using nonlocal continuum theory", Composites Part B, 47, 96-101. https://doi.org/10.1016/j.compositesb.2012.10.043
  21. Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007), "Vibration of nonlocal Timoshenko beams", Nanotechnology, 18(10), 105401. https://doi.org/10.1088/0957-4484/18/10/105401
  22. Wang, C.M., Zhang, Y.Y., Ramesh, S.S. and Kitipornchai, S. (2006), "Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 39(17), 3904-3909. https://doi.org/10.1088/0022-3727/39/17/029
  23. Yang, J., Ke, L.L. and Kitipornchai, S. (2010), "Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", Physica E, 42(5), 1727-1735. https://doi.org/10.1016/j.physe.2010.01.035
  24. Yoon, J., Ru, C.Q. and Mioduchowski, A. (2005), "Vibration and instability of carbon nanotubes conveying fluid", Compos. Sci. Technol., 65(9), 1326-1336. https://doi.org/10.1016/j.compscitech.2004.12.002
  25. Zhang, C.L. and Shen, H.S. (2006), "Temperature-dependent elastic properties of single-walled carbon nanotubes: Prediction from molecular dynamics simulation", Appl. Phys. Lett., 89(8), 81904. https://doi.org/10.1063/1.2336622