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Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory

Yıl 2009, Cilt: 1 Sayı: 2, 47 - 56, 01.06.2009

Öz

Static analysis of carbon nanotubes (CNT) is presented using the nonlocal Bernoulli-Euler beam theory. Differential quadrature (DQ) method is used for bending analysis of numerical solution of carbon nanotubes. Numerical results are presented and compared with that available in the literature. Deflection and bending moment are presented for different boundary conditions. It is shown that reasonable accurate results are obtained

Kaynakça

  • [1] Iijima, S. Helical Microtubules of Graphitic Carbon. Nature, 354,56-58, 1991.
  • [2] Wang, C.M, Tan, V.B.C., Zhang, V. Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes. J. Sound Vib. 294, 1060-1072, 2006.
  • [3] Peddieson, J., Buchanan, G.R., McNitt, R.P. Application of nonlocal continuum models to nanotechnology. Int. J. Eng Sci, 41, 305-312, 2003.
  • [4] Zhang, Y.Q. Liu, G.R. Han, X, Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure. Physics Letters A, 349, 370-376, 2006.
  • [5] Wang, Q. Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J. Appl Phy, 98,124301, 2005.
  • [6] Wang, Q., Varadan, V.K. Application of Nonlocal Elastic Shell Theory in Wave Propagation Analysis of Carbon Nanotubes, Smart Materials and Structures, 16, 178-190, 2007.
  • [7] Wang, Q. Wang, C.M. On constitutive relation and small scale parameter of nonlocal continuum mechanics for modeling carbon nanotubes, Nanotechnology, 18,075702, 2007.
  • [8] Wang, L.F. Hu, H.Y. Flexural wave propagation in single-walled carbon nanotubes, Physical Review B, 71,195412, 2005.
  • [9] Li, C. Chou, T.W, Vibrational behavior of multi-walled-carbon-nanotube-based nanomechanical resonators. Applied Physics Letters, 84,121–123, 2004.
  • [10] Falvo, M.R. Clary, G.J. Taylor, R.M. Chi, V. Brooks, F.P. Washburn, S. Bending and buckling of carbon nanotubes under large strain. Nature, 389, 582–584, 1997.
  • [11] Fu, Y.M., Hong, J.W., Wang, X.Q. Analysis of nonlinear vibration for embedded carbon nanotubes. J. Sound Vib. 296, 746-756, 2006.
  • [12] Gibson, R.F., Ayorinde, E.O., Wen, Y.F. Vibrations of carbon nanotubes and their composites: a review. Compos. Sci. Technol. 67, 1–28, 2007.
  • [13] Ru, C.Q. Effective bending stiffness of carbon nanotubes. Phys. Rev. B 62, 9973–9976, 2000.
  • [14] Ru, C.Q. Elastic buckling of single-walled carbon nanotubes ropes under high pressure. Phys. Rev. B,62, 10405–10408, 2000.
  • [15] Tserpes, K.I. Papanikos, P. Finite element modeling of single-walled carbon nanotubes. Compos. Part B: Eng. 36, 468–477, 2005.
  • [16] Thostenson E.T, Ren Z. Chou T.W, Advances in the science and technology of carbon nanotubes and their composites:a review. Compos. Sci. Tech. 61, 1899-1912, 2001.
  • [17] Bert, C.W, Malik, M, Free vibration analysis of tapered rectangular plates by differential quadrature method: A semi-analytical approach, J. Sound Vibr. 190(1), 41-63, 1996.
  • [18] Bert, C.W., Jang S.K., and Striz, A.G. Two new approximate methods for analyzing free vibration of structural components, AIAA Journal 26, 612-618, 1987.
  • [19] Shu, C., Xue, H. Comparison of Two Approaches for Implementing Stream Function Boundary Conditions in DQ Simulation of Natural Convection in A Square Cavity, International Journal of Heat and Fluid Flow, 19,59-68, 1998.
  • [20] Civalek, Ö. Application of Differential Quadrature (DQ) and Harmonic Differential Quadrature (HDQ) For Buckling Analysis of Thin Isotropic Plates and Elastic Columns, Engineering Structures, 26(2), 171-186, 2004.
  • [21] Civalek, Ö., Ülker, M. Harmonic Differential Quadrature (HDQ) For Axisymmetric Bending Analysis Of Thin Isotropic Circular Plates, International Journal of Structural Engineering and Mechanics, 17(1), 1-14, 2004.
  • [22] Civalek, Ö., Ülker, M. HDQ-FD Integrated Methodology For Nonlinear Static and Dynamic Response of Doubly Curved Shallow Shells, International Journal of Structural Engineering and Mechanics, 19(5), 535-550,2005.
  • [23] Civalek, Ö. Geometrically Nonlinear Dynamic Analysis of Doubly Curved Isotropic Shells Resting on Elastic Foundation by a Combination of HDQ-FD Methods, Int. J. Pressure Vessels and Piping,82(6)470-479, 2005.
  • [24] Reddy, J.N. Nonlocal theories for bending, buckling and vibration of beams, Int J Eng Sciences 45, 288-307, 2007.
  • [25] Demir, Ç., Civalek, Ö., Akgöz, B. Free Vibration Analysis of Carbon Nanotubes Based On Shear Deformable Beam Theory By Discrete Singular Convolution Technique, Mathematical and Computational Applications, (in press), 2009.
  • [26] Demir, Ç. Carbon Nanotubes and Their engineering applications, M.Sc. Seminar, Institue of Natural and Applied Science of Akdeniz University, 2009.
  • [27] Akgöz, B. Nonlocal beam modeling of carbon nanotubes, Thesis of B.Sc., Akdeniz University, Civil Engineering Dept., 2009.
  • [28] Eringen, A.C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Applied Physics, 54, 4703-4710, 1983.
Yıl 2009, Cilt: 1 Sayı: 2, 47 - 56, 01.06.2009

Öz

Kaynakça

  • [1] Iijima, S. Helical Microtubules of Graphitic Carbon. Nature, 354,56-58, 1991.
  • [2] Wang, C.M, Tan, V.B.C., Zhang, V. Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes. J. Sound Vib. 294, 1060-1072, 2006.
  • [3] Peddieson, J., Buchanan, G.R., McNitt, R.P. Application of nonlocal continuum models to nanotechnology. Int. J. Eng Sci, 41, 305-312, 2003.
  • [4] Zhang, Y.Q. Liu, G.R. Han, X, Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure. Physics Letters A, 349, 370-376, 2006.
  • [5] Wang, Q. Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J. Appl Phy, 98,124301, 2005.
  • [6] Wang, Q., Varadan, V.K. Application of Nonlocal Elastic Shell Theory in Wave Propagation Analysis of Carbon Nanotubes, Smart Materials and Structures, 16, 178-190, 2007.
  • [7] Wang, Q. Wang, C.M. On constitutive relation and small scale parameter of nonlocal continuum mechanics for modeling carbon nanotubes, Nanotechnology, 18,075702, 2007.
  • [8] Wang, L.F. Hu, H.Y. Flexural wave propagation in single-walled carbon nanotubes, Physical Review B, 71,195412, 2005.
  • [9] Li, C. Chou, T.W, Vibrational behavior of multi-walled-carbon-nanotube-based nanomechanical resonators. Applied Physics Letters, 84,121–123, 2004.
  • [10] Falvo, M.R. Clary, G.J. Taylor, R.M. Chi, V. Brooks, F.P. Washburn, S. Bending and buckling of carbon nanotubes under large strain. Nature, 389, 582–584, 1997.
  • [11] Fu, Y.M., Hong, J.W., Wang, X.Q. Analysis of nonlinear vibration for embedded carbon nanotubes. J. Sound Vib. 296, 746-756, 2006.
  • [12] Gibson, R.F., Ayorinde, E.O., Wen, Y.F. Vibrations of carbon nanotubes and their composites: a review. Compos. Sci. Technol. 67, 1–28, 2007.
  • [13] Ru, C.Q. Effective bending stiffness of carbon nanotubes. Phys. Rev. B 62, 9973–9976, 2000.
  • [14] Ru, C.Q. Elastic buckling of single-walled carbon nanotubes ropes under high pressure. Phys. Rev. B,62, 10405–10408, 2000.
  • [15] Tserpes, K.I. Papanikos, P. Finite element modeling of single-walled carbon nanotubes. Compos. Part B: Eng. 36, 468–477, 2005.
  • [16] Thostenson E.T, Ren Z. Chou T.W, Advances in the science and technology of carbon nanotubes and their composites:a review. Compos. Sci. Tech. 61, 1899-1912, 2001.
  • [17] Bert, C.W, Malik, M, Free vibration analysis of tapered rectangular plates by differential quadrature method: A semi-analytical approach, J. Sound Vibr. 190(1), 41-63, 1996.
  • [18] Bert, C.W., Jang S.K., and Striz, A.G. Two new approximate methods for analyzing free vibration of structural components, AIAA Journal 26, 612-618, 1987.
  • [19] Shu, C., Xue, H. Comparison of Two Approaches for Implementing Stream Function Boundary Conditions in DQ Simulation of Natural Convection in A Square Cavity, International Journal of Heat and Fluid Flow, 19,59-68, 1998.
  • [20] Civalek, Ö. Application of Differential Quadrature (DQ) and Harmonic Differential Quadrature (HDQ) For Buckling Analysis of Thin Isotropic Plates and Elastic Columns, Engineering Structures, 26(2), 171-186, 2004.
  • [21] Civalek, Ö., Ülker, M. Harmonic Differential Quadrature (HDQ) For Axisymmetric Bending Analysis Of Thin Isotropic Circular Plates, International Journal of Structural Engineering and Mechanics, 17(1), 1-14, 2004.
  • [22] Civalek, Ö., Ülker, M. HDQ-FD Integrated Methodology For Nonlinear Static and Dynamic Response of Doubly Curved Shallow Shells, International Journal of Structural Engineering and Mechanics, 19(5), 535-550,2005.
  • [23] Civalek, Ö. Geometrically Nonlinear Dynamic Analysis of Doubly Curved Isotropic Shells Resting on Elastic Foundation by a Combination of HDQ-FD Methods, Int. J. Pressure Vessels and Piping,82(6)470-479, 2005.
  • [24] Reddy, J.N. Nonlocal theories for bending, buckling and vibration of beams, Int J Eng Sciences 45, 288-307, 2007.
  • [25] Demir, Ç., Civalek, Ö., Akgöz, B. Free Vibration Analysis of Carbon Nanotubes Based On Shear Deformable Beam Theory By Discrete Singular Convolution Technique, Mathematical and Computational Applications, (in press), 2009.
  • [26] Demir, Ç. Carbon Nanotubes and Their engineering applications, M.Sc. Seminar, Institue of Natural and Applied Science of Akdeniz University, 2009.
  • [27] Akgöz, B. Nonlocal beam modeling of carbon nanotubes, Thesis of B.Sc., Akdeniz University, Civil Engineering Dept., 2009.
  • [28] Eringen, A.C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Applied Physics, 54, 4703-4710, 1983.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA65GC69HH
Bölüm Makaleler
Yazarlar

Ö. Civalek Bu kişi benim

Ç Demir Bu kişi benim

B. Akgöz Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2009
Yayımlandığı Sayı Yıl 2009 Cilt: 1 Sayı: 2

Kaynak Göster

APA Civalek, Ö., Demir, Ç., & Akgöz, B. (2009). Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory. International Journal of Engineering and Applied Sciences, 1(2), 47-56.
AMA Civalek Ö, Demir Ç, Akgöz B. Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory. IJEAS. Haziran 2009;1(2):47-56.
Chicago Civalek, Ö., Ç Demir, ve B. Akgöz. “Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory”. International Journal of Engineering and Applied Sciences 1, sy. 2 (Haziran 2009): 47-56.
EndNote Civalek Ö, Demir Ç, Akgöz B (01 Haziran 2009) Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory. International Journal of Engineering and Applied Sciences 1 2 47–56.
IEEE Ö. Civalek, Ç. Demir, ve B. Akgöz, “Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory”, IJEAS, c. 1, sy. 2, ss. 47–56, 2009.
ISNAD Civalek, Ö. vd. “Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory”. International Journal of Engineering and Applied Sciences 1/2 (Haziran 2009), 47-56.
JAMA Civalek Ö, Demir Ç, Akgöz B. Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory. IJEAS. 2009;1:47–56.
MLA Civalek, Ö. vd. “Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory”. International Journal of Engineering and Applied Sciences, c. 1, sy. 2, 2009, ss. 47-56.
Vancouver Civalek Ö, Demir Ç, Akgöz B. Static Analysis of Single Walled Carbon Nanotubes (Swcnt) Based on Eringen’s Nonlocal Elasticity Theory. IJEAS. 2009;1(2):47-56.

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