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THE SHAPE OF THE TALLEST COLUMN.
- Source :
-
SIAM Journal on Mathematical Analysis . 1998, Vol. 29 Issue 3, p547-554. 8p. - Publication Year :
- 1998
-
Abstract
- The height at which an unloaded column will buckle under its own weight is the fourth root of the least eigenvalue of a certain Sturm-Liouville operator. We show that the operator associated with the column proposed by Keller and Niordson [J. Math. Mech., 16 (1966), pp. 433-446] does not possess a discrete spectrum. This calls into question their formal use of perturbation theory, so we consider a class of designs that permits a tapered summit yet still guarantees a discrete spectrum. Within this class we prove that the least eigenvalue increases when one replaces a design with its decreasing rearrangement. This leads to a very simple proof of the existence of a tallest column. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361410
- Volume :
- 29
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Mathematical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 13207800
- Full Text :
- https://doi.org/10.1137/S0036141097314537