Acta Mechanica Solida Sinica

, Volume 26, Issue 5, pp 500–513 | Cite as

Jumping Instabilities in the Post-Buckling of a Beam on a Partial Nonlinear Foundation

  • Yin Zhang
  • Kevin D Murphy


Mode jumping is an instability phenomenon in the post-buckling region, which causes a sudden change in the equilibrium configuration and is thus harmful to structure. The configuration of a partial elastic foundation can directly induce mode coupling from the buckling stage and through the whole post-buckling region. The mode coupling effect due to the configuration of partial foundation on mode jumping is investigated and demonstrated to be an important factor of determining mode jumping. By properly choosing the partial elastic foundation configuration, mode jumping can be avoided.


instability mode jumping tertiary jumping buckling beam elastic foundation 


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  1. 1.
    Thompson, J.M.T., Instabilities and Catastrophes in Science and Engineering. John Wiley & Sons New York, 1982.zbMATHGoogle Scholar
  2. 2.
    Thompson, J.M.T. and Hunt, G.W., Elastic Instability Phenomena. John Wiley & Sons New York, 1984.zbMATHGoogle Scholar
  3. 3.
    Bauer, L. and Reiss, E.L., Nonlinear buckling of rectangular plates. Journal of SIAM, 1965, 13: 603–626.Google Scholar
  4. 4.
    Bauer, L., Keller, H.B. and Reiss, E.L., Multiple eigenvalues lead to secondary bifurcation. SIAM Review, 1975, 17: 101–122.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Uemura, M. and Byon, O.I., Secondary buckling of a flat plate under uniaxial compression part 1: theoretical analysis of simply supported flat plate. International Journal of Non-Linear Mechanics, 1977, 12: 355–370.CrossRefGoogle Scholar
  6. 6.
    Supple, W.J., Coupled branching configurations in the elastic buckling of symmetric structural systems. International Journal of Mechanical Sciences, 1967, 9: 97–112.CrossRefGoogle Scholar
  7. 7.
    Supple, W.J., On the change in buckle pattern in elastic structures. International Journal of Mechanical Sciences, 1968, 10: 737–745.CrossRefGoogle Scholar
  8. 8.
    Supple, W.J., Changes of wave-form of plates in the post-buckling range. International Journal of Solids and Structures. 1970, 6: 1243–1258.CrossRefGoogle Scholar
  9. 9.
    Nakamura, T. and Uetani, K., The secondary buckling and post-secondary buckling behaviours of rectangular plates. International Journal of Mechanical Sciences, 1979, 21: 265–286.CrossRefGoogle Scholar
  10. 10.
    Maaskant, R. and Roorda, J., Mode jumping in biaxially compressed plates. International Journal of Solids and Structures, 1992, 29: 1209–1219.CrossRefGoogle Scholar
  11. 11.
    Everall, P.R. and Hunt, G.W., Mode jumping in the buckling of struts and plates: a comparative study. International Journal of Non-Linear Mechanics, 2000, 35: 1067–1079.CrossRefGoogle Scholar
  12. 12.
    Cheng, C. and Shang, X., Mode jumping of simply supported rectangular plates on nonlinear elastic foundation. International Journal of Non-Linear Mechanics, 1997, 32: 161–172.CrossRefGoogle Scholar
  13. 13.
    Zhang, Y. and Murphy, K.D., Secondary buckling and tertiary states of a beam on a non-linear elastic foundation. International Journal of Non-Linear Mechanics, 2005, 40: 795–805.CrossRefGoogle Scholar
  14. 14.
    Zhang, Y., Liu, Y., Chen, P. and Murphy, K.D., Buckling loads and eigenfrequencies of a braced beam resting on an elastic foundation. Acta Mechanica Solida Sinica, 2011, 24(5): 1–9.CrossRefGoogle Scholar
  15. 15.
    Zhang, Y., Extracting nanobelt mechanical properties from nanoindentation. Journal of Applied Physics, 2010, 107: 123518.CrossRefGoogle Scholar
  16. 16.
    Zhang, Y. and Zhao, Y.P., Modeling nanowire indentation test with adhesive effect. Journal of Applied Mechanics, 2011, 78: 011007.CrossRefGoogle Scholar
  17. 17.
    Chater, E., Hutchinson, J.W. and Neale, K.W., Buckle propagation on a beam on a nonlinear elastic foundation. In Collapse (Edited by Thompson, J.M.T. and Hunt, G.W.), Cambridge University Press, 1983, 31–46.Google Scholar
  18. 18.
    Bazant, Z. and Grassl, P., Size effect of cohesive delamination fracture triggered by sandwich skin wrinkling. Journal of Applied Mechanics, 2007, 74: 1134–1141.CrossRefGoogle Scholar
  19. 19.
    Youn, S.K., Study of buckle propagation and its arrest on a beam on a nonlinear foundation using finite element method. Computer and Structures, 1991, 39(3/4): 381–386.Google Scholar
  20. 20.
    Bowden, N., Brittain, S., Evans, A.G., Hutchinson, J.W. and Whitesides, G.M., Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer. Nature, 1998, 393: 146–149.CrossRefGoogle Scholar
  21. 21.
    Khang, D., Jiang, H., Huang, Y. and Rogers, J.A., A stretchable form of single crystal silicon for high-performance electronics on rubber substrates. Science, 2006, 311: 208–212.CrossRefGoogle Scholar
  22. 22.
    Suo, Z. Wrinkling of the oxide scale on an aluminum-containing alloy at high temperature. Journal of the Mechanics and Physics of Solids, 1995, 43: 829–846.CrossRefGoogle Scholar
  23. 23.
    Zhang, Y. and Murphy, K.D., Crack propagation in structures subjected to periodic excitation. Acta Mechanica Solida Sinica, 2007, 20(3): 236–246.CrossRefGoogle Scholar
  24. 24.
    Weitsman, Y., A tensionless contact between a beam and an elastic half-space. International Journal of Engineering Sciences, 1972, 10: 73–81.CrossRefGoogle Scholar
  25. 25.
    Gecit, M.R., Axisymmetric contact problem for an elastic layer and an elastic foundation. International Journal of Engineering Sciences, 1972, 10: 73–81.CrossRefGoogle Scholar
  26. 26.
    Parker, R.G., Supercritical speed stability of the trivial equilibrium of an axially-moving spring on an elastic foundation. Journal of Sound and Vibration, 1999, 221: 205–219.CrossRefGoogle Scholar
  27. 27.
    Elishakoff, I. and Impollonia, N., Does a partial elastic foundation increase the flutter velocity of a pipe conveying fluid? Journal of Applied Mechanics, 2001, 68: 206–212.CrossRefGoogle Scholar
  28. 28.
    Timoshenko, S.P., Theory of Elastic Stability, McGraw-Hill, New York, 1961.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Nonlinear Mechanics (LNM)Institute of Mechanics, Chinese Academy of SciencesBeijingChina
  2. 2.Department of Mechanical EngineeringUniversity of ConnecticutStorrsUSA

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