On the Optimality Conditions in the Weight Minimization Problem for a Shell of Revolution at a Given Vibration Frequency

We consider shallow elastic shells with a given circular boundary and seek an axisymmetric shell shape minimizing the weight at a given fundamental frequency of shell vibrations. Using the resulting formula for the linear part of the increment of the frequency functional, the multiplicity of the min...

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Bibliographic Details
Published in:Differential equations 2023-09, Vol.59 (9), p.1262-1279
Main Author: Arabyan, M. H.
Format: Article
Language:English
Subjects:
Control Theory
Difference and Functional Equations
Elastic shells
Mathematics
Mathematics and Statistics
Optimization
Ordinary Differential Equations
Partial Differential Equations
Resonant frequencies
Shells of revolution
Vibration
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Summary:We consider shallow elastic shells with a given circular boundary and seek an axisymmetric shell shape minimizing the weight at a given fundamental frequency of shell vibrations. Using the resulting formula for the linear part of the increment of the frequency functional, the multiplicity of the minimum natural frequency of vibrations of the shell is estimated. The Fréchet differentiability of the frequency functional is also established, and optimal conditions for minimizing the weight of the shell at a given fundamental vibration frequency are obtained.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266123090112