On the optimal design of a vibrating beam

Niordson, Frithiof I.

doi:10.1090/qam/175392

Author: Frithiof I. Niordson
Journal: Quart. Appl. Math. 23 (1965), 47-53
MSC: Primary 73.49
DOI: https://doi.org/10.1090/qam/175392
MathSciNet review: 175392
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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.

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