Dynamic Stability of Single Walled Carbon Nanotube Based on Nonlocal Strain Gradient Theory
Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
فرشید
آقاداودی
1
(مربی
دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینیشهر)
محمد
هاشمیان
2
(استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینیشهر)
Keywords: Dynamic stability, Carbon Nanotube, Strain gradient, Euler-Bernouli beam, Non-local alasticity,
Abstract :
This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano- size structures such as single-walled carbon nanotubes. Influences of nonlocal effects, modulus parameter of elastic medium and aspect ratio of the SWCNT on the critical buckling loads and instability regions are analyzed. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanotubes.
[1] Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H., Ahmadian, M.T., The modified couple stress functionally graded Timoshenko beam formulation. Material Des., Vol. 32, 2011, pp. 1435–1443.
[2] Asghari, M., Geometrically nonlinear micro-plate formulation based on the modified couple stress theory, International Journal of Engineering Science, vol. 51, 2012, pp. 292–309.
[3] Ansari R., Free vibration analysis of size-dependentfunctionally graded microbeams based on the strain gradient Timoshenko beam theory,Composite Structures, vol. 94, 2011.
[4] Fu Y., Zhang J., Electromechanical dynamic buckling phenomenon in symmetric electric fields actuated microbeams considering material damping, Acta Mechanicals, vol. 212, 2010, pp. 29–42.
[5] Ferreira A., Batra R.C., Roque CMC, Qian LF, , Natural frequencies of functionally graded plates by a meshless method, Composite Structures, vol. 75, 2006, pp. 593–600.
[6] Seidel, Analytic and Computational Micromechanics of Clustering and Interphase Effects in Carbon Nanotube, 2007.
[7] Yang F., Chong,A.C.M., Lam D.C.C., Tong P. Couple stress based strain gradient theory for elasticity, International Journal of SolidsStructure, vol. 39, 2002, pp. 2731–2743.
[8] Tadi Beni Y., Karimipour I., Abadyan M., Modeling the instability of electrostatic nano-bridges and nano-cantilevers using modified strain gradient theory, Applied Mathematical Modelling, 2014, In press.
[9] Fakhrabadi M.M.S., Rastgoo A., Ahmadian M.T., Non-linear behaviors of carbon nanotubes under electrostatic actuation based on strain gradient theory, International Journal of Non-Linear Mechanics, vol. 67, 2014, pp. 236-244.
[10] Wang L., Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory, Computational Materials Science, vol. 49, No. 4, 2010, pp. 761-766.
[11] Miandoab E., Yousefi-Koma A., and Pishkenari H., Nonlocal and strain gradient based model for electrostatically actuated silicon nano-beams, Microsystem Technologies, vol. 21, No. 2, 2015, pp. 457-464.
[12] Koochi A., Sedighi H.M., Abadyan M., Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory.
[13] Nami, M.R., Janghorban, M., Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory, Iranian Journal of Materials Forming, vol. 1, No. 2, 2014, pp. 1-13.
[14] Ru C.Q., Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium, Journal of the Mechanics and Physics of Solids, vol. 49, 2001, pp. 1265-1279.
[15] Wang C.Y., Ru C.Q., Mioduchowski A., Axially compressed buckling of pressured multiwall carbon nanotubes, International Journal of Solids and Structures, vol. 40, 2003, pp. 3893-3911.
[16] Yoon J., Ru C.Q., A. Mioduchowski, Vibration and instability of carbon nanotubes conveying fluid, Composites Science and Technology, 65 (2005) 1326-1336.
[17] Païdoussis M.P., Fluid–Structure Interactions: Slender Structures and Axial Flow, Academic Press, 1998.
[18] Ghorbanpour Arani A., Rahmani R., Arefmanesh A., Golabi S., Buckling analysis of multi-walled carbon nanotubes under combined loading considering the effect of small length scale, Journal of Mechanical Science and Technology, vol. 22, 2008, pp. 429-439.
[19] Sun C., Liu K., Dynamic buckling of double-walled carbon nanotubes under step axial load, Acta Mechanica Solida Sinica, vol. 22, 2009, pp. 27-36.
[20] Ansari R., On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects, 2012.
[21] Ghorbanpour Arani A., Kolahchi R., Mosayyebi M., Jamali M., Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method, International Journal of Mechanics and Materials in Design, 2014, pp. 1-22.
[22] Ghorbanpour Arani A., Yousefi M., Amir S., Dashti P., Chehreh A.B., Dynamic Response of Viscoelastic CNT Conveying Pulsating Fluid Considering Surface Stress and Magnetic Field, Arabian Journal for Science and Engineering, vol. 40, No. 6, 2015, pp. 1707-1726.
[23] Mindlin, R.D., Second gradient of strain and surface tension in linear lasticity, Int. J. Solids Struct. 1, pp. 417–438 ,1965
[24] Fleck N.A., Muller G.M., Ashby M.F., Hutchinson J.W., Strain gradient plasticity: theory and experiment. Acta Metallurgy and Materials, vol. 42, 1994, pp. 475–487.
[25] Yan, Y., X.Q. He, L.X. Zhang, C.M. Wang, Dynamic behavior of triple-walled carbon nanotubes conveying fluid, Journal of Sound and Vibration, vol. 319 , 2009, pp. 1003-1018.
[26] Tadi Y., Cylindrical thin-shell model based on modified strain gradient theory, International Journal of Engineering Science, 2014.
[27] Herbert E., Lindberg, Little Book of Dynamic Buckling, 2003.
[28] Nayfeh A.H., Mook D.T., Nonlinear oscillations, Wiley classics library, 1995.