Gjornâl Furlan des SiencisFriulian Journal of Science

No. 18 (2014): GFS
RESEARCH ARTICLES

Exact determination of beams with given buckling loads

PDF
  • ANTONIO MORASSI
ANTONIO MORASSI
Department of Civil Engineering and Architecture, University of Udine, Udine, Italy

Keywords

  • Buckling loads, beams, Darboux Lemma, quasi-isospectral operators, inverse problems

How to Cite

[1]
MORASSI, A. 2014. Exact determination of beams with given buckling loads. Friulian Journal of Science. 18, 18 (Dec. 2014), 57–66.

Abstract

We present an analytical procedure for the determination of EulerBernoulli beams which have given values of the first N buckling loads. The result is valid for pinned-pinned end conditions and for beams with regular bending stiffness. The analysis is based on a reduction of the buckling problem to an eigenvalue problem for a vibrating string, and uses recent results on the exact construction of Sturm-Liouville operators with prescribed natural frequencies

PDF

References

  1. Cali`o I., Gladwell G.M.L., Morassi A. (2011). Families of beams with the same buckling spectrum. Inverse Problems, 27, Paper 045006 (16pp).
  2. Darboux G. (1882). Sur la r´epresentation sph´erique des surfaces. Comptes Rendus de l’Acad´emie des Sciences, 94: 1343-1345.
  3. Love A.E.H. (1944). A Treatise on the Mathematical Theory of Elasticity. New York: Dover Publications Edition.
  4. Morassi A. (2015). Exact construction of beams with a finite number of given natural frequencies. Journal of Vibration and Control, 21: 591 600.
  5. P¨oschel J., Trubowitz E. (1987). Inverse Spectral Theory. London: Academic Press