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Abstrakty
In the paper the eigenfrequencies of pristine and defective single-walled carbon nanotubes are investigated. The defects are in the form of point vacancies. The axial vibrations of structures are studied only. A special attention is focused on the effects of material and geometrical properties of nanostructures on the results. Three different models are considered: the Euler beam model, a continuous specially orthotropic model and a 3D nonlinear finite element model consistent with molecular mechanics formulations. The results demonstrate that the Euler beam model overestimates the values of natural frequencies.
Czasopismo
Rocznik
Tom
Strony
157--166
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Institute of Machine Design Cracow University of Technology al. Jana Pawa II 37, 31-864 Cracow, Poland
autor
- Institute of Machine Design Cracow University of Technology al. Jana Pawa II 37, 31-864 Cracow, Poland
autor
- Institute of Machine Design Cracow University of Technology al. Jana Pawa II 37, 31-864 Cracow, Poland
Bibliografia
- [1] Zhang, Y. Q., Liu, G. R. and Xie, X. Y.: Free transverse vibration of double–walled carbon nanotubes using a theory of nonlocal elasticity, Phys. Rev. B, 71, 195404–195407, 2005.
- [2] Wang, Q. and Varadan, V. K.: Vibration of carbon nanotubes studied using nonlocal continuum mechanics, Smart Mater. Struct., 15(2), 659–666, 2006.
- [3] Wang, Q., Zhou, G. Y. and Lin, K. C.: Scale effect on wave propagation of double–walled carbon nanotubes, Int. J. Solids Struct., 43(20), 6071–6084, 2006.
- [4] Hu, Y. G., Liew, K. M. and Wang, Q.: Nonlocal elastic beam models for flexural wave propagation of double-walled carbon nanotubes, J. Appl. Phys., 106(4), 044301–044306, 2009.
- [5] Ke, L. L., Xiang, Y., Yang, J. and Kitipornchai S.: Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory, Comput. Mater. Sci., 47(2), 409–417, 2009.
- [6] Mustapha, K. B. and Zhong, Z. W.: Free transverse vibration of an axially loaded non–prismatic single–walled carbon nanotube embedded in a two–parameter elastic medium, Comput. Mater. Sci., 50(2), 742–751, 2010.
- [7] Ru, C. Q.: Effective bending stiffness of carbon nanotubes, Phys. Rev. B, 62(15), 9973–9976, 2000.
- [8] Ru, C. Q.: Elastic buckling of single–walled carbon nanotube ropes under high pressure, Phys. Rev. B, 62(15), 10405–10408, 2000.
- [9] Yakobson, B. I., Brabec, C. J. and Bernholc, J.: Nanomechanics of carbon tubes: instabilities beyond linear range, Phys. Rev. Lett., 76(14), 2511–2514, 1996.
- [10] He, X. Q., Kitiporchai, S. and Liew, K. M.: Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction, J. Mech. Phys. Solids, 53(2), 303–326, 2005.
- [11] He, X. Q., Kitipornchai, S., Wang, C. M. and Liew, K. M.: Modeling of van der Waals force for infinitesimal deformation of multi-walled carbon nanotubes treated as cylindrical shells, Int. J. Solids Struct., 42(23), 6032–6047, 2005.
- [12] Kitipornchai, S., He, X. Q. and Liew, K. M.: Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix, J. Appl. Phys., 97(11), 114318–7, 2005.
- [13] Liew, K. M., He, X. Q. and Kitipornchai, S.: Buckling characteristics of embedded multi–walled carbon nanotubes, Proc. R. Soc. A, 461(2064), 3785–3805, 2005.
- [14] Muc, A.: Modeling of carbon nanotubes behaviour with the use of a thin shell theory, J. Theor. Appl. Mech., 49(2), 531–540, 2011.
- [15] Mielke, S. L., Troya, D., Zhang, S., Li, J. L., Xiao, S., Car, R., Ruoff, R. S., Schatz, G. C. and Belytschko, T.: The role of vacancy defects and holes in the fracture of carbon nanotubes, Chem. Phys. Lett., 390(4–6), 413–420, 2004.
- [16] Popov, V. N., Van Doren, V. E. and Balkanski, M.: Elastic properties of crystals of carbon nanotubes, Sol. Stat. Comm., 114(7), 395–399, 2000.
- [17] Salvetat, J. P., Briggs, G. A. D., Bonard, J. M., Bacsa, R. R., Kulik, A. J., Stockli, T., Burnham, N. A. and Forro, L.: Elastic and shear moduli of single–walled carbon nanotube ropes, Phys. Rev. Lett., 82(5), 944–947, 1999.
- [18] Muc, A.: Design and identification methods of effective mechanical properties for carbon nanotubes, Mat. Des., 31(4), 1671–1675, 2010.
- [19] Muc, A.: Modeling of CNTs/nanocomposites deformations and tensile fracture, Proc. 17th Int. Conf. Compos. Mat. (ICCM17), 1–9, 2009.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f5347970-b2d5-4d5f-944a-b5398a788d3b