Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the existence of solutions to optimization problems with eigenvalue constraints

Author: Kosla Vepa
Journal: Quart. Appl. Math. 31 (1973), 329-341
MSC: Primary 73.49
DOI: https://doi.org/10.1090/qam/428893
MathSciNet review: 428893
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Abstract: The optimum tapering of Bernoulli--Euler beams, i.e. the shape for which a given total mass yields the highest possible value of the first fundamental frequency of harmonic transverse small oscillations, is determined. The question of the existence of a solution to the optimization problem is considered. It is shown that, irrespective of the relationship between the flexural rigidity and linear mass density of the cantilever beam, the necessary conditions for optimality lead to a contradiction. This result is in partial disagreement with that obtained by earlier investigators. By imposing additional constraints on the optimization variable, a numerical solution for the case of the cantilever beam is obtained, using the formulation of the maximum principle of Pontryagin.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/428893
Article copyright: © Copyright 1973 American Mathematical Society

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