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Abstract <p> We consider shallow elastic shells with a given circular boundary and seekan axisymmetric shell shape minimizing the weight at a given fundamental shell vibrationfrequency. Using the obtained formula for the gradients of the components of the eigenfunctioncorresponding to the minimum eigenvalue, the second Fréchet differentiability of thefrequency functional is established. It is proved that if the necessary conditions are satisfied, thenso are the sufficient conditions.</p>

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

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • M. H. Arabyan

摘要

Abstract

We consider shallow elastic shells with a given circular boundary and seekan axisymmetric shell shape minimizing the weight at a given fundamental shell vibrationfrequency. Using the obtained formula for the gradients of the components of the eigenfunctioncorresponding to the minimum eigenvalue, the second Fréchet differentiability of thefrequency functional is established. It is proved that if the necessary conditions are satisfied, thenso are the sufficient conditions.