On the maximum of the first resonance frequency for inhomogeneous elastic bodies

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The paper considers a non-classical optimization problem associated with the development of the production of new functionally graded materials. It is proposed to optimize the first natural frequency of oscillations by choosing the law of change in elastic moduli, and not the shape, as is done in most works devoted to optimization. This formulation of the problem becomes practically justified with the development of 3D printing and the production of FGM ceramics with specified properties. As an example, the problems of oscillations of a FGM rod and a FGM beam with spring boundary conditions at one of the ends are considered.

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作者简介

A. Vatulyan

Southern Federal University

编辑信件的主要联系方式.
Email: aovatulyan@sfedu.ru
俄罗斯联邦, Rostov-on-Don

V. Yurov

Southern Mathematical Institute, Vladikavkaz Scientific Center of Russian Academy of Sciences

Email: vitja.jurov@yandex.ru
俄罗斯联邦, Vladikavkaz

参考

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2. Fig. 1. Eigenvalue k: according to (4.10) – solid line, according to (4.15) – dotted line

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3. Fig. 2. Eigenvalue k: according to (4.12) – solid line, according to (4.16) – dotted line

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