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On the interaction of a single-walled carbon nanotube with a moving nanoparticle using nonlocal Rayleigh, Timoshenko, and higher-order beam theories. (English) Zbl 1278.74091

Summary: Interaction of a moving nanoparticle with a single-walled carbon nanotube (SWCNT) is of concern. The SWCNT is simulated by an equivalent continuum structure (ECS) under simply supported boundary conditions. The moving nanoparticle is modeled by a moving point load by considering its full inertial effects and Coulomb friction with the inner surface of the ECS. The ECS under the moving nanoparticle is modeled based on the Rayleigh, Timoshenko, and higher-order beam theories in the context of the nonlocal continuum theory of Eringen. The dimensionless discrete equations of motion associated with the nonlocal beam models are then obtained by using Galerkin method. The effects of slenderness ratio of the ECS, ratio of mean radius to thickness of the ECS, mass weight and velocity of the moving nanoparticle, and small scale parameter on the dynamic response of the SWCNT are explored. The capabilities of various nonlocal beam theories in capturing the longitudinal and transverse displacements as well as the nonlocal axial force and bending moment are also scrutinized in some detail. The possibility of moving nanoparticle separation from the inner surface of the SWCNT is examined by monitoring the sign of the contact force. Subsequently, the role of important parameters on the possibility of this phenomenon is explored using various nonlocal beam theories.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74M25 Micromechanics of solids
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[1] Bianco, A., Carbon nanotubes for the delivery of therapeutic molecules, Expert Opin. Drug Discov., 1, 1, 57-65 (2004)
[2] Bianco, A.; Kostarelos, K.; Prato, M., Applications of carbon nanotubes in drug delivery, Curr. Opin. Chem. Biol., 9, 6, 674-679 (2005)
[3] Cao, G.; Chen, X.; Kysar, J. W., Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes, J. Mech. Phys. Solids, 54, 6, 1206-1236 (2006) · Zbl 1120.74682
[4] Chang, W. J.; Lee, H. L., Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model, Phys. Lett. A, 373, 10, 982-985 (2009) · Zbl 1236.74101
[5] Duan, W. H.; Wang, Q., Water transport with a carbon nanotube pump, ACS Nano., 4, 4, 2338-2344 (2010)
[6] Eringen, A. C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., 54, 4703-4710 (1983)
[7] Eringen, A. C., Nonlocal Continuum Field Theories (2002), Springer-Verlag: Springer-Verlag New York · Zbl 1023.74003
[8] Georgantzinos, S. K.; Giannopoulos, G. I.; Anifantis, N. K., An efficient numerical model for vibration analysis of single-walled carbon nanotubes, Comput. Mech., 43, 6, 731-741 (2009) · Zbl 1162.74462
[9] Gupta, S. S.; Batra, R. C., Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes, Comput. Mater. Sci., 43, 4, 715-723 (2008)
[10] Heireche, H.; Tounsi, A.; Benzair, A.; Maachou, M.; Adda Bedia, E. A., Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity, Physica E, 40, 8, 2791-2799 (2008)
[11] Holt, J. K.; Park, H. G.; Wang, Y.; Stadermann, M.; Artyukhin, A. B.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O., Fast mass transport through sub-2-nanometer carbon nanotubes, Science, 312, 5776, 1034-1037 (2006)
[12] Iijima, S., Helical microtubules of graphitic carbon, Nature, 354, 56-58 (1991)
[13] Joshi, A. Y.; Harsha, S. P.; Sharma, S. C., Vibration signature analysis of single walled carbon nanotube based nano mechanical sensors, Physica E, 42, 8, 2115-2123 (2010)
[14] Ke, C. H.; Pugno, N.; Peng, B.; Espinosa, H. D., Experiments and modeling of carbon nanotube-based NEMS devices, J. Mech. Phys. Solids, 53, 1314-1333 (2005) · Zbl 1120.74684
[15] Ke, C. H.; Espinosa, H. D.; Pugno, N., Numerical analysis of nanotube based NEMS devices part II: role of finite kinematics, stretching and charge concentrations, J. Appl. Mech. ASME, 72, 726-731 (2005) · Zbl 1111.74475
[16] Kiani, K., Longitudinal and transverse vibration of a single-walled carbon nanotube subjected to a moving nanoparticle accounting for both nonlocal and inertial effects, Physica E, 42, 9, 2391-2401 (2010)
[17] Kiani, K., Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle, part I: theoretical formulations, Acta Mech., 216, 165-195 (2011) · Zbl 1398.74145
[18] Kiani, K., Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle, part II: parametric study, Acta Mech., 216, 197-206 (2011) · Zbl 1398.74146
[19] Kiani, K.; Mehri, B., Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories, J. Sound Vib., 329, 11, 2241-2264 (2010)
[20] Kiani, K.; Nikkhoo, A.; Mehri, B., Prediction capabilities of classical and shear deformable beam models excited by a moving mass, J. Sound Vib., 320, 3, 632-648 (2009)
[21] Lee, H. L.; Chang, W. J., A closed-form solution for critical buckling temperature of a single-walled carbon nanotube, Physica E, 41, 8, 1492-1494 (2009)
[22] Lee, H. L.; Chang, W. J., Vibration analysis of a viscous-fluid-conveying single-walled carbon nanotube embedded in an elastic medium, Physica E, 41, 4, 529-532 (2009)
[23] Li, C.; Chou, T. W., Elastic wave velocities in single-walled carbon nanotubes, Phys. Rev. B: Condens. Matter, 73, 245407 (2006)
[24] Liew, K. M.; Hu, Y.; He, X. Q., Flexural wave propagation in single-walled carbon nanotubes, J. Comput. Theor. Nanosci., 5, 4, 581-586 (2008)
[25] Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. J., Nanoscale hydrodynamics: enhanced flow in carbon nanotubes, Nature, 438, 44 (2005)
[26] Pugno, N., Non-linear dynamics of nanotube based NEMS. Transworld research network, Sound Vib., 2, 197-211 (2004), Special issue on recent research developments
[27] Pugno, N., New quantized failure criteria: application to nanotubes and nanowires, Int. J. Fract., 141, 313-323 (2006) · Zbl 1197.74127
[28] Pugno, N. M., The role of defects in the design of space elevator cable: from nanotube to megatube, Acta Mater., 55, 5269-5279 (2007)
[29] Pugno, N. M., Young’s modulus reduction of defective nanotubes, Appl. Phys. Lett., 90, 0431061-0431063 (2007)
[30] Pugno, N.; Ke, C. H.; Espinosa, H. D., Analysis of doubly clamped nanotube devices in the finite deformation regime, J. Appl. Mech. ASME, 72, 445-449 (2005) · Zbl 1111.74599
[31] Pugno, N.M., Bosia, F., Carpinteri, A., 2008. Multiscale stochastic simulations for tensile testing of nanotube-based macroscopic cables. 4(8), 1044-1052.; Pugno, N.M., Bosia, F., Carpinteri, A., 2008. Multiscale stochastic simulations for tensile testing of nanotube-based macroscopic cables. 4(8), 1044-1052.
[32] Reddy, C. D.; Lu, C.; Rajendran, S.; Liew, K. M., Free vibration analysis of fluid-conveying single-walled carbon nanotubes, Appl. Phys. Lett., 90, 133122 (2007)
[33] Selim, M. M.; Abe, S.; Harigaya, K., Effects of initial compression stress on wave propagation in carbon nanotubes, Eur. Phys. J., B 69, 4, 523-528 (2009)
[34] Shi, M. X.; Li, Q. M.; Liu, B.; Feng, X. Q.; Huang, Y., Atomic-scale finite element analysis of vibration mode transformation in carbon nanorings and single-walled carbon nanotubes, Int. J. Solids Struct., 46, 25-26, 4342-4360 (2009) · Zbl 1176.74086
[35] Skoulidas, A. I.; Ackerman, D. M.; Johnson, J. K.; Sholl, D. S., Rapid transport of gases in carbon nanotubes, Phys. Rev. Lett., 89, 185901 (2002)
[36] Sun, Y.; Liew, K. M., The buckling of single-walled carbon nanotubes upon bending: the higher order gradient continuum and mesh-free method, Comput. Meth. Appl. Mech. Eng., 197, 33-40, 3001-3013 (2008) · Zbl 1194.74083
[37] Vodenitcharova, T.; Zhang, L. C., Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube, Int. J. Solids Struct., 43, 10, 3006-3024 (2006) · Zbl 1120.74498
[38] Wang, Q., Wave propagation in carbon nanotubes via nonlocal continuum mechanics, J. Appl. Phys., 98, 124301 (2005)
[39] Wang, Q., Torsional instability of carbon nanotubes encapsulating C60 fullerenes, Carbon, 47, 2, 507-512 (2009)
[40] Wang, Q., Atomic transportation via carbon nanotubes, Nano Lett., 9, 1, 245-249 (2009)
[41] Wang, L.; Hu, H., Flexural wave propagation in single-walled carbon nanotubes, Phys. Rev. B: Condens. Matter, 71, 195412 (2005)
[42] Wang, Q.; Wang, C. M., The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology, 18, 075702 (2007)
[43] Wang, Y.; Wang, X. X.; Ni, X. G.; Wu, H. A., Simulation of the elastic response and the buckling modes of single-walled carbon nanotubes, Comput. Mater. Sci., 32, 2, 141-146 (2005)
[44] Yang, J.; Ke, L. L.; Kitipornchai, S., Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Physica E, 42, 5, 1727-1735 (2010)
[45] Yao, X.; Han, Q., A continuum mechanics nonlinear postbuckling analysis for single-walled carbon nanotubes under torque, Eur. J. Mech. Solid., 27, 5, 796-807 (2008) · Zbl 1146.74020
[46] Yao, X.; Han, Q.; Xin, H., Bending buckling behaviors of single- and multi-walled carbon nanotubes, Comput. Mater. Sci., 43, 4, 579-590 (2008)
[47] Zhang, C. L.; Shen, H. S., Buckling and postbuckling analysis of single-walled carbon nanotubes in thermal environments via molecular dynamics simulation, Carbon, 44, 13, 2608-2616 (2006)
[48] Zhang, H.; Zhang, S. Y.; Wang, T. H., Flexural vibration analyses of piezoelectric ceramic tubes with mass loads in ultrasonic actuators, Ultrasonics, 47, 82-89 (2007)
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