Peraulis clâf
- Buckling loads, beams, Darboux Lemma, quasi-isospectral operators, inverse problems
Cemût citâ
[1]
MORASSI, A. 2014. Exact determination of beams with given buckling loads. Gjornâl Furlan des Siencis - Friulian Journal of Science. 18, 18 (Dec. 2014), 57–66.
Ristret
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
Riferiments
- Cali`o I., Gladwell G.M.L., Morassi A. (2011). Families of beams with the same buckling spectrum. Inverse Problems, 27, Paper 045006 (16pp).
- Darboux G. (1882). Sur la r´epresentation sph´erique des surfaces. Comptes Rendus de l’Acad´emie des Sciences, 94: 1343-1345.
- Love A.E.H. (1944). A Treatise on the Mathematical Theory of Elasticity. New York: Dover Publications Edition.
- Morassi A. (2015). Exact construction of beams with a finite number of given natural frequencies. Journal of Vibration and Control, 21: 591 600.
- P¨oschel J., Trubowitz E. (1987). Inverse Spectral Theory. London: Academic Press