主要研究了三壁碳纳米管在多重边界约束条件下的振动特性. 基于Euler 梁模型将三壁碳纳米管模拟成三重相合梁系统, 其中管间通过范德华力 (van der Waals force) 相合, 但内管、中管、外管处于不同的边界约束中, 并研究了FFC (free-free-clamped) 型多重边界约束对 三壁碳纳米管振动的影响. 结果表明, FFC 型多重边界约束会导致三壁碳纳米管共振频率的降低, 尤其在低阶振动模态上; 同时, 这种影响会随着碳纳米管长度的增加而减弱.
Vibration characteristics of triple-walled carbon nanotubes (TWCNTs) with multiple boundary constraints are studied. TWCNTs are modeled as a coupling Euler beam system in which the inner, middle and outer tubes are simulated as 3 single beam, respec- tively. They are coupled through van der Waals interaction. Besides, different boundary conditions are imposed on the three beams. The effect of FFC multiple boundary con- straints on the vibration characteristics of TWCNTs are analyzed. The results show that FFC multiple boundary constraints can reduce resonant frequencies of TWCNTS, espe- cially on the lower modes. Meanwhile, it is also found that this effect will be weakened with the increase of the length of TWCNTs.
[1] Iijima S. Helical microtubules of graphitic carbon [J]. Nature, 1991, 354: 56-58.
[2] Dai H, Hafner J H. Nanotubes as nanoprobes in scanning probe microscopy [J]. Nature, 1996,384: 147-150.
[3] Postma H W C, Teepen T, Yao Z, et al. Carbon nanotube single-electron transistors at room temperature [J]. science, 2001, 293: 76-79.
[4] Baughman R H, Zakhido A A, Heer W A. Carbon nanotubes–the route toward applications [J]. Science, 2002, 297(5582): 787-792.
[5] Kwon Y W, Manthena C, Oh J J, et al. Vibrational characteristics of carbon nanotubes as nanomechanical resonators [J]. Nanosci Nanotechnol, 2005, 5(5): 703-712.
[6] Thostenson E T, Ren Z, Chou T W. Advances in the science and technology of carbon nanotubes and their composites: a review [J]. Compos Sci Technol, 2001, 61(13): 1899-1912.
[7] Garcia-Sanchez D, San P A, Esplandiu M J, et al. Mechanical detection of carbon nanotube resonator vibrations [J]. Phys Rev Lett, 2007, 99(8): 085501.
[8] Sakhaee-Pour A, Ahmadian M T, Vafai A. Vibrational analysis of single-walled carbon nanotubes using beam element [J]. Thin Wall Struct, 2009, 47(6): 646-652.
[9] Ansati R, Gholami R, Rouhi H. Vibration analysis of single-walled carbon nanotubes using different gradient elasticity theories [J]. Composites: Part B, 2012, 43(8): 2985-2989.
[10] Natsuki T, Ni Q, Endo M. Analysis of the vibration characteristics of double-walled carbon nanotubes [J]. Carbon, 2008, 46(12): 1570-1573.
[11] Xu K Y, Guo X N, Ru C Q. Vibration of a double-walled carbon nanotube aroused by nonlinear intertube van der Waals forces [J]. J Appl Phys, 2006, 99: 064303.
[12] Xu K Y, Aifantis E C, Yan Y H. Vibration of double-walled carbon nanotube with different boundary conditions between inner and outer tubes [J]. Appl Mech, 2008, 75: 021013.
[13] Pentaras D, Elishakoff I. Free vibration of triple-walled carbon nanotubes [J]. Acta Mech,2011, 221(3): 239-249.
[14] Benzair A, Tounsi A, Besseghier A, et al. The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory [J]. J Phys D: Appl Phys, 2008,
41(22).
[15] Wang L, Ni Q, Li M, et al. The thermal effect on vibration and instability of carbon nanotubes conveying fluid [J]. Phys E, 2008, 40(10): 3179-3182.
[16] Shen H S, Zhang C L. Buckling and postbuckling analysis of single-walled carbon nanotubes in thermal environments via molecular dynamics simulation [J]. Carbon, 2006, 44(13): 2608-2616.
[17] Sun C, Liu K. Vibration of multi-walled carbon nanotubes with initial axial loading [J]. Solid State Comm, 2007, 143(4): 202-207.
[18] Landerdale T A, O’reilly O M. Modeling MEMS resonators with rod-like components ac- counting for anisotropy, temperature, and strain dependencies [J]. Int J Solids Struct, 2005,
42(26): 6523-6549.
