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August 8, 2023
Published
August 8, 2023
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Abstract

In this paper structural analysis of nonhomogeneous nanotubes has been carried out using nonlocal elasticity theory. Governing differential equations of nonhomogeneous nanotubes are derived. Nonlocal theory of elasticity has been employed to include the scale effect of the nanotubes. Nonlocal parameter, elastic modulus, density and diameter of the cross sections are assumed to be functions of spatial coordinates. General Differential Quadrature (GDQ) method has been employed to solve the governing differential equations of the nanotubes. Various boundary conditions have been applied to the nanotubes. Present results considering nonlocal theory are in good agreement with the results available in the literature. Effect of various geometrical and material parameters on the structural response of the nonhomogeneous nanotubes has been investigated. Present results of the nonhomogeneous nanotubes are useful in the design of the nanotubes.

Keywords

Nanotubes, Differential Quadrature Method, Nonhomogeneous, Bending, Vibration, Buckling

Article Details

How to Cite
Phadikar, J. K., & Pradhan, S. (2023). Bending Vibration and Buckling Analysis Of Nonhomogeneous Nanotubes Using Nonlocal Elasticity Theory and Gdq Method. Journal of Aerospace Sciences and Technologies, 61(4), 482–495. https://doi.org/10.61653/joast.v61i4.2009.588
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References

  1. Iijima, S., "Helical Microtubules of Graphitic Carbon", Nature, Vol. 354, 1991, pp.56-58.
  2. Thostenson, E. T., Ren, Z. and Chou, T. W., "Advances in Science and Technology of Carbon Nanotubes and There Composites: A Review", Composites Science and Technology, Vol. 61, 2001, pp.1899-912.
  3. Gibson, R. F., Ayorinde, O. E. and Yuan-Feng Wen., "Vibration of Carbon Nanotubes and There Composites: A Review", Composites Science and Technology, Vol. 67, 2007, pp.1-28.
  4. Ball, P., "Roll up for the Revolution", Nature (London), Vol. 414, 2001, pp. 142-144.
  5. Baughman, R. H., Zakhidov, A. A. and de Heer, W. A., "Carbon Nanotubes - The Route Toward Applications", Science, Vol. 297, 2002, pp.787-792.
  6. Bodily, B. H. and Sun, C. T., "Structural and Equivalent Continuum Properties of Single-walled Carbon Nanotubes", International Journal of Materials and Product Technology, Vol.18(4/5/6), 2003, pp.381- 97.
  7. Li, C. and Chou, T. W., "A Structural Mechanics Approach for the Analysis of Carbon Nanotubes", International Journal of Solids and Structures, Vol. 40, 2003, pp.2487-99.
  8. Li, C. and Chou, T. W., "Single-walled Nanotubes as Ultrahigh Frequency Nanomechanical Oscillators, Physical Review B, Vol. 68, 2003, Art no: 073405.
  9. Yoon, J., Ru, C. Q. and Mioduchowski, A., "A Noncoaxial Resonance of an Isolated Multiwall Carbon Nanotube", Physical Review B, Vol. 66, 2002, Art no: 233402.
  10. Yoon, J., Ru, C. Q. and Mioduchowski, A., "Vibration of Embedded Multiwall Carbon Nanotubes", Composites Science and Technology, Vol.63, 2003, pp. 1533-42.
  11. Wang, C. M., Tan V. B. C. and Zhang, Y.Y., "Timoshenko Beam Model for Vibration Analysis of Multi-walled Carbon Nanotubes", Journal of Sound and Vibration, Vol.294, 2006, pp.1060-72.
  12. Wang, Q. and Vardan, V. K., "Wave Characteristics of Carbon Nanotubes", International Journal of Solids and Structures, Vol.43, 2005, pp.254-65.
  13. Aydogdu, M., "Vibration of Multiwalled Carbon Nanotubes by Generalized Shear Deformation Theory", International Journal of Mechanical Sciences, Vol. 50, 2008, pp. 837-844.
  14. Eringen, A. C., On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves", Journal of Applied Physics, Vol. 54, 1983, pp. 4703-4710.
  15. Eringen, A. C., "Nonlocal Continuum Field Theories", Springer-Verlag, NewYork, 2002.
  16. Peddieson, J., Buchanan, G. R. and McNitt, R. P., Application of Nonlocal Continuum Models to Nanotechnology", International Journal of Engineering Science, Vol.41, 2003, pp.305-312.
  17. Wang, Q., Zhou, G. Y. and Lin, K. C., "Scale effect on Wave Propagation of Double Walled Carbon Nanotubes", International Journal of Solids and Structures, Vol.43, 2006, pp.6071-6084.
  18. Wang, Q. and Varadan, V. K., "Vibration of Carbon Nanotubes Studied Using Nonlocal Continuum Mechanics", Smart Materials and Structures, Vol.15, 2006, pp.659-666.
  19. Lu, P., Lee, H. P., Lu, C. and Zhang, P. Q., "Application of Nonlocal Beam Models for Carbon Nanotubes, International Journal of Solids and Structures, Vol.44, 2007, pp.5289-5300.
  20. Seeman, N. C., "DNA Engineering and its Application to Nanotechnology", Trends in Biotechnology, Vol.17(11), 1999, pp.437-43.
  21. Rothemund Paul, W. K., Ekani-nkodo Axel., Papadakis Nick., Kumar Ashish., Fygenson Deborah Kuchnir and Winfree Erik., "Design and Characterization of Programmable DNA Nanotubes", Journal of American Society, Vol.126, 2004, pp.16344-52.
  22. Bellman, R. E., Kashef, B. G. and Casti, J., "Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Equations", Journal of Computational Physics, Vol.10, 1972, p.40.
  23. Bert, C. W., Jang, S. K and Striz A. G., "Two New Approximate Methods for Analyzing Free Vibration of Structural Components", AIAA Journal, Vol.26, 1988, pp.612-618.
  24. Bert, C. W. and Malik M., "Differential Quadrature In computational mechanics: A Review", Applied Mechanics Review, Vol.49, 1996, pp.1-27.
  25. Shu, C., "Differential Quadrature and its Application in Engineering", Springer, Berlin, 2000.
  26. Yang, B., "Stress, Strain, and Structural Dynamics", Elsevier Science and Technology Publishers, 2005.
  27. Reddy, J. N., "Nonlocal Theories for Bending, Buckling and vibration of Beams", International Journal of Engineering Science, Vol. 45, 2007, pp.288-307.
  28. Wang, Q., Varadan, V. K. and Quekc, S. T., "Small Scale Effect on Elastic Buckling of Carbon Nanotubes with Nonlocal Continuum Models", Physics Letters A, Vol.357, 2006, pp.130-135.
  29. Murmu, T. and Pradhan, S. C., "Buckling Analysis of a Single-walled Carbon Nanotubes Embedded in an Elastic Medium Based on Nonlocal Continuum Mechanics", PHYSICA E: Low-Dimensional Systems and Nanostructures, Vol.41, 2009, pp.1232- 1239.