On the optimal design of a vibrating beam
- 1 April 1965
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 23 (1), 47-53
- https://doi.org/10.1090/qam/175392
Abstract
This paper deals with the problem of finding the best possible tapering of a simply supported beam, which for a given volume would have the highest possible value of the natural frequency for the lowest mode of lateral vibrations. The differential equation governing the deflection is given and a procedure to solve this non-linear equation by successive iterations is presented.Keywords
This publication has 5 references indexed in Scilit:
- Bounds for the principal frequency of nonuniformly loaded stringsIsrael Journal of Mathematics, 1963
- Some results on the frequencies of nonhomogeneous rodsJournal of Mathematical Analysis and Applications, 1962
- Strongest Columns and Isoperimetric Inequalities for EigenvaluesJournal of Applied Mechanics, 1962
- The shape of the strongest columnArchive for Rational Mechanics and Analysis, 1960
- Isoperimetric Inequalities for the Nonhomogeneous Clamped Rod and PlateIndiana University Mathematics Journal, 1959