On the reconstruction of a two-dimensional density of a functionally graded elastic plate

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In this article, the in-plane vibrations of a rectangular plate within the framework of a plane stress is formulated based on the general formulation of steady-state vibrations of an inhomogeneous elastic isotropic body. The left side of the plate is rigidly fixed, vibrations are forced by tensile load applied at the right side. The properties of the functionally graded material are described by two-dimensional variation laws (Young’s modulus, Poisson’s ratio and density). A dimensionless problem formulation is given. The direct problem solution of the displacement field determination is obtained using the finite element method. The effect of material characteristics on the displacement field and the value of the first resonance are shown. An analysis of the obtained results is carried out. The inverse problem of density determination from displacement field data for a fixed frequency is considered. To reduce the error in calculating two-variable table functions derivatives, an approach based on spline approximation and a locally weighted regression algorithm is proposed. Reconstruction examples of different laws are presented to demonstrate the possibility of using this approach.

Sobre autores

V. Dudarev

Institute of Mathematics, Mechanics and Computer Sciences named after I.I. Vorovich, Southern Federal University

Autor responsável pela correspondência
Email: dudarev_vv@mail.ru
Rússia, Rostov-on-Don

R. Mnukhin

Institute of Mathematics, Mechanics and Computer Sciences named after I.I. Vorovich, Southern Federal University

Email: romamnuhin@yandex.ru
Rússia, Rostov-on-Don

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