Advertisement

Prediction of Buckling Load from Vibration Measurements

  • P. Mandal
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 104)

Abstract

The linear relationship between buckling load and the square of the frequency of a structure is limited to the cases in which the fundamental vibration mode and the lowest buckling mode are the same. For cases where the two modes are different researchers in the past have suggested some empirical equations. In this study (mainly numerical) it is shown that the linear relationship is reasonably valid when the modes are approximately close to each other. However, for a simply supported rectangular plate of aspect ratio two or more, the fundamental vibration mode and the lowest buckling mode are usually different to each other. It is observed that the apparent non-linear curve in this situation consists of a few linear segments depending on the aspect ratio. The buckling load could be accurately predicted by measuring the first few frequencies, instead of just one.

Key words

Buckling load Frequency Rectangular plates 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bokian, A. (1988) Natural frequencies of beams under compressive axial loads, Journal of Sound and Vibration, 126(1), 49–65.CrossRefGoogle Scholar
  2. Costley, A. C., Mourad, S. A., Kazanjy, R. P. and Pardoen, G. C. (1991) Determination of critical buckling load of thin-walled cylinders using modal analysis, Proc. Ninth International Modal Analysis Conference, Florence, IT Union College, N.Y., Pt 1, 542–548.Google Scholar
  3. Galef, A. E. (1967) Bending frequencies of compressed beams, The Journal of the Acoustical Society of America, 44(8), 643.Google Scholar
  4. Jubb, J. E. M., Philips, I. G. and Becker, H. (1975) Interrelation of structural stability, stiffness, residual stress and natural frequency, Journal of Sound and Vibration, 39(1), 121–134.CrossRefGoogle Scholar
  5. Lee, J. A. N., Hope, B. B. and MacGowan, J. P. (1965) The Prediction of the Buckling Load of Columns by Non-destructive Testing Methods, Ontario Joint Highway Research Programme, Report No. 41; Department of Civil Engineering (C.E. Report no. 50), Queen’s University, Kingston, Ontario, Canada.Google Scholar
  6. Leissa, A. (1993) Vibration of shells, Acoustical Society of America.Google Scholar
  7. Lurie, H. (1952) Lateral vibrations as related to structural stability, Journal of Applied Mechanics, 19, 195–204.MATHGoogle Scholar
  8. Melan, H. (1917) Kritische Drehzahlen von Wellen mit Langsbelastung, Zeitschrift der Österr Ingenieur- und Architekten- Vereines, 69, 610–612, 619–621.Google Scholar
  9. Ovunc, B. A. (1980) Effect of axial force on framework dynamics, Computers and Structures, 11, 389–395.MATHCrossRefGoogle Scholar
  10. Plaut, R. H. and Virgin, L. N. (1990) Use of frequency data to predict buckling, Journal of Engineering Mechanics, 116(10), 2330–2335.CrossRefGoogle Scholar
  11. Rao, G. V. (2001) A simple formula to predict the fundamental frequency of initially stressed square plates, Journal of Sound and Vibration, 246(1), 185–189.CrossRefGoogle Scholar
  12. Shastry, B. P. and Rao, G. V. (1986) Vibration of partially stressed beam, Journal of Vibration, Acoustics, Stress and Reliability in Design, 108, 474–475.CrossRefGoogle Scholar
  13. Singer, J. (1982) Vibration correlation techniques for improved buckling predictions of imperfect stiffened shells, in Buckling of Shells in Off-shore Structures, edited by Harding J. E., Dowling P. J. and Agelidis N., Granada Publishing, London, England, 285–329.Google Scholar
  14. Souza, M. A. and Assaid, L. M. B. (1991) A new technique for the prediction of buckling loads from nondestructive vibration tests, Experimental Mechanics, 31(2), 93–97.CrossRefGoogle Scholar
  15. Sundararajan, C. (1992) Frequency analysis of axially loaded structures, AIAA Journal, 30(4), 1139–1141.CrossRefGoogle Scholar
  16. Tarnai, T. (1995) The Southwell and the Dunkerley theorems, in Summation Theorems in Structural Stability, edited by Tarnai, T., CISM Courses and Lectures no. 354, Springer-Verlag, New York.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • P. Mandal
    • 1
  1. 1.Manchester Centre for Civil & Construction EngineeringUMISTManchesterUK

Personalised recommendations