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

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Abstract

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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About the authors

A. O. Vatulyan

Southern Federal University

Author for correspondence.
Email: aovatulyan@sfedu.ru
Russian Federation, Rostov-on-Don

V. O. Yurov

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

Email: vitja.jurov@yandex.ru
Russian Federation, Vladikavkaz

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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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