On the Optimality Conditions in the Weight Minimization Problem for a Shell of Revolution at a Given Vibration Frequency-Reference-Cited by-同舟云学术

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

Published:2023-12-15 Issue:9 Volume:59 Page:1266-1282
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Arabyan M. O.¹

Affiliation:

1. Yerevan State University, Yerevan, 0025, Armenia

Abstract

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.

Publisher

The Russian Academy of Sciences

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