Acta Mechanica Solida Sinica

, Volume 23, Issue 5, pp 394–399 | Cite as

Large Deflection Theory of Nanobeams

  • Dujuan Zeng
  • Quanshui Zheng


One-dimensional nanostructured materials are often used as beams in many applications such as ultrahigh-frequency resonators and ultrasensitive sensors. Compared with usual macroscopic beams, nanobeams have much higher surface/volume ratios so that their surface energies may play a significant role. Besides, they often bear large deflections due to their typically large slenderness ratios and larger elastic ranges. There is, however, lack of a theory that takes into account of both the above two features owned by nanobeams. In this paper, we present such a theory and give applied examples to show that surface energy and large deflection may individually or jointly have notable effects.

Key words

nanobeam surface energy large deflection 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Jensen, K., Kim, K. and Zettl, A., An atomic-resolution nanomechanical mass sensor. Nature Nanotechnology, 2008, 3(9): 533–537.CrossRefGoogle Scholar
  2. [2]
    Patolsky, F. and Lieber, C. M., Nanowire nanosensors. Materials Today, 2005, 8(4): 20–28.CrossRefGoogle Scholar
  3. [3]
    Poncharal, P., Wang, Z.L. and Ugarte, D. et al., Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science, 1999, 283(5407): 1513–1516.CrossRefGoogle Scholar
  4. [4]
    Jensen, K., Weldon, J. and Garcia, H. et al., Nanotube radio. Nano Letters, 2007, 7: 3508–3511.CrossRefGoogle Scholar
  5. [5]
    Wang, X.D., Song, J.H. and Liu, J. et al., Direct-current nanogenerator driven by ultrasonic waves. Science, 2007, 316(5821): 102–105.CrossRefGoogle Scholar
  6. [6]
    Chen, C.Q., Shi, Y. and Zhang, Y.S. et al., Size dependence of Young’s modulus in ZnO nanowires. Physical Review Letters, 2006, 96: 075505.CrossRefGoogle Scholar
  7. [7]
    Cuenot, S., Fretigny, C. and Demoustier-Champagne, S. et al., Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Physical Review B, 2004, 69(6): 165410.CrossRefGoogle Scholar
  8. [8]
    Jing, G.Y., Duan, H.L. and Sun, X.M. et al., Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy. Physical Review B, 2006, 73(23): 235409.CrossRefGoogle Scholar
  9. [9]
    Miller, R.E. and Shenoy, V.B., Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 2000, 11(3): 139–147.CrossRefGoogle Scholar
  10. [10]
    Dingreville, R., Qu, J.M. and Cherkaoui, M., Surface free energy and its effect on the elastic behavior of nanosized particles, wires and films. Journal of the Mechanics and Physics of Solids, 2005, 53(8): 1827–1854.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Wang, J., Duan, H.L. and Huang, Z.P. et al., A scaling law for properties of nano-structured materials. Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences, 2006, 462: 1355–1363.CrossRefGoogle Scholar
  12. [12]
    Heidelberg, A., Ngo, L.T. and Wu, B. et al., A generalized description of the elastic properties of nanowires. Nano Letters, 2006, 6(6): 1101–1106.CrossRefGoogle Scholar
  13. [13]
    Gurtin, M.E. and Murdoh, A.I., A continuum theory elastic material surfaces. Archive for Rational Mechanics and Analysis, 1975, 57: 291–323.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Haiss, W., Surface stress of clean and absorbate-covered solids. Reports on Progress in Physics, 2001, 64: 591–648.CrossRefGoogle Scholar
  15. [15]
    Stafford, C.M., Vogt, B.D. and Harrison, C. et al., Elastic moduli of ultrathin amorphous polymer films. Macromolecules, 2006, 39(15): 5095–5099.CrossRefGoogle Scholar
  16. [16]
    Wen, B.M., Sader, J.E. and Boland, J.J., Mechanical properties of ZnO nanowires. Physical Review Letters, 2008, 101(17): 175502.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  1. 1.Department of Engineering MechanicsTsinghua UniversityBeijingChina

Personalised recommendations