Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

doi:10.1007/s10483-016-2030-8

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (2): 265-274.doi: https://doi.org/10.1007/s10483-016-2030-8

• 论文 • 上一篇

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

R. KOLAHCHI¹, A. M. MONIRI BIDGOLI²

1. Department of Civil Engineering, Islamic Azad University, Khomein 38815/17, Iran;
2. College of Engineering, University of Tehran, Tehran 1417965463, Iran

收稿日期:2015-04-28 修回日期:2015-08-14 出版日期:2016-02-01 发布日期:2016-02-01
通讯作者: R. KOLAHCHI E-mail:r.kolahchi@gmail.com

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

R. KOLAHCHI¹, A. M. MONIRI BIDGOLI²

1. Department of Civil Engineering, Islamic Azad University, Khomein 38815/17, Iran;
2. College of Engineering, University of Tehran, Tehran 1417965463, Iran

Received:2015-04-28 Revised:2015-08-14 Online:2016-02-01 Published:2016-02-01
Contact: R. KOLAHCHI E-mail:r.kolahchi@gmail.com

摘要/Abstract

摘要：

In this study, a model for dynamic instability of embedded single-walled carbon nanotubes (SWCNTs) is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory (SSDBT). The modified couple stress theory (MCST) is considered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton's principle. The differential quadrature method (DQM) in conjunction with the Bolotin method is used in order to calculate the dynamic instability region (DIR) of SWCNTs. The effects of different parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The results depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system (NEMS) and micro-electro-mechanical system (MEMS).

关键词: dynamic instability, Bolotin method, sinusoidal shear deformation beam theory (SSDBT), modified couple stress theory (MCST), single-walled carbon nanotubes (SWCNTs)

Abstract:

Key words: single-walled carbon nanotubes (SWCNTs), Bolotin method, modified couple stress theory (MCST), sinusoidal shear deformation beam theory (SSDBT), dynamic instability

中图分类号:

74H55

R. KOLAHCHI, A. M. MONIRI BIDGOLI. Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(2): 265-274.

参考文献

[1] Wang, X., Li, Q., Xie, J., Jin, Z., Wang, J., Li, Y., Jiang, K., and Fan, S. Fabrication of ultralong and electrically uniform single-walled carbon nanotubes on clean substrates. Nano Letters, 9, 3137-3141(2009)
[2] Ghorbanpour Arani, A. and Kolahchi, R. Exact solution foe nonlocal axial buckling of linear carbon nanotube hetero-junctions. Journal of Mechanical Engineering Science, 228, 366-377(2014)
[3] Simsek, M. and Reddy, J. N. Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory. International Journal of Engineering Science, 64, 37-53(2013)
[4] Wang, L., Xu, Y. Y., and Ni, Q. Size-dependent vibration analysis of three-dimensional cylindrical microbeams based on modified couple stress theory: a unified treatment. International Journal of Engineering Science, 68, 1-10(2013)
[5] Thai, H. T. and Vo, T. P. A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, 54, 58-66(2012)
[6] Yoon, J., Ru, C. Q., and Mioduchowski, A. Vibration and instability of carbon nanotubes conveying fluid. Composite Science and Technology, 65, 1326-1336(2005)
[7] Kiani, K. Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model. Applied Mathematical Modelling, 37, 1836-1850(2013)
[8] Murmu, T. and Pradhan, S. C. Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E, 41, 1232-1239(2009)
[9] Lim, C. W. On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection. Applied Mathematics and Mechanics (English Edition), 31, 37-54(2010) DOI 10.1007/s10483-010-0105-7
[10] Mirramezani, M., Mirdamadi, H. R., and Ghayour, M. Innovative coupled fluid-structure interaction model for carbon nano-tubes conveying fluid by considering the size effects of nano-flow and nano-structure. Computational Materials Science, 77, 161-171(2013)
[11] Kaviani, F. and Mirdamadi, H. R. Wave propagation analysis of carbon nanotube conveying fluid including slip boundary condition and strain/inertial gradient theory. Computational Materials Science, 116, 75-87(2013)
[12] Ghorbanpour Arani, A., Kolahchi, R., and Hashemian, M. Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories. Journal of Mechanical Engineering Science, 228, 3258-3280(2014)
[13] Ghorbanpour Arani, A., Kolahchi, R., and Hashemian, M. Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories. Journal of Mechanical Engineering Science, 228, 3258-3280(2014)
[14] Malekzadeh, P. and Shojaee, M. Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams. Composites Part B: Engineering, 52, 84-92(2013)
[15] Akgöz, B. and Civalek, Ö. Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM). Composites Part B: Engineering, 55, 263-268(2013)
[16] Akgöz, B. and Civalek, Ö. Buckling analysis of functionally graded microbeams based on the strain gradient theory. Acta Mechanica, 224, 2185-2201(2013)
[17] Wang, B., Deng, Z. C., and Zhang, K. Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory. Applied Mathematics and Mechanics (English Edition), 34, 269-280(2013) DOI 10.1007/s10483-013-1669-8
[18] Xu, Z. J. and Deng, Z. C. Variational principles for buckling and vibration of MWCNTs modeled by strain gradient theory. Applied Mathematics and Mechanics (English Edition), 35, 1115-1128(2014) DOI 10.1007/s10483-014-1855-6
[19] Ghorbanpour Arani, A., Kolahchi, R., and Zarei, M. S. Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene with ZnO sensors and actuators using refined zigzag theory. Composite Structures, 132, 506-526(2015)
[20] Akgöz, B. and Civalek, Ö. Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium. International Journal of Engineering Science, 85, 90-104(2014)
[21] Bolotin, V. V. The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco (1964)
[22] Lanhe, W., Hongjun, W., and Daobin, W. Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method. Composite Structures, 77, 383-394(2007)
[23] Lei, X. W., Natsuki, T., Shi, J. X., and Ni, Q. Q. Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model. Composites Part B: Engineering, 43, 64-69(2012)
[24] Akgöz, B. and Civalek, Ö. A size-dependent shear deformation beam model based on the strain gradient elasticity theory. International Journal of Engineering Science, 70, 1-14(2013)

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

编辑推荐

Metrics

本文评价

[1]	Jianzhong LIN, Hailin YANG. A review on the flow instability of nanofluids[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(9): 1227-1238.
[2]	Bo ZHOU, Xueyao ZHENG, Zetian KANG, Shifeng XUE. Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(11): 1531-1546.
[3]	M. MOHAMMADIMEHR, M. A. MOHAMMADIMEHR, P. DASHTI. Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(4): 529-554.
[4]	Yi XIA;Jianzhong LIN;Fubing BAO;T. L. CHAN. Flow instability of nanofuilds in jet[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(2): 141-152.
[5]	E. M. TIAN T. P. SVOBODNY J. D. PHILLIPS. Thin liquid film morphology driven by electro-static field[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(8): 1039-1046.