 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| V.V. Dudarev and R.M. Mnukhin, "On the Reconstruction of a Two-Dimensional Density of a Functionally Graded Elastic Plate," Mech. Solids. 59 (3), 1201-1213 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
3 |
Pages |
1201-1213 |
| DOI |
10.1134/S0025654424602532 |
| Title |
On the Reconstruction of a Two-Dimensional Density of a Functionally Graded Elastic Plate |
| Author(s) |
V.V. Dudarev (Institute of Mathematics, Mechanics and Computer Sciences named after I. I. Vorovich, Southern Federal University, Rostov-on-Don, 344090 Russia, dudarev_vv@mail.ru)
R.M. Mnukhin (Institute of Mathematics, Mechanics and Computer Sciences named after I. I. Vorovich, Southern Federal University, Rostov-on-Don, 344090 Russia, romamnuhin@yandex.ru) |
| Abstract |
In this work, based on the general formulation of the problem of steady-state vibrations of
an inhomogeneous elastic isotropic body, a direct problem of planar vibrations of a rectangular plate
within the framework of a plane stress state is formulated. 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 laws of change in Young’s modulus, Poisson’s ratio and
density. For generality of consideration, a dimensionless formulation of the problem is given.
The solution to the direct problem of determining the displacement field was obtained using the finite
element method. The effect of material characteristics on the displacement field and the value of the
first resonant frequency are shown. An analysis of the obtained results was carried out. The inverse
problem of determining the law of density from data on the values of the displacement field components at a fixed frequency is considered. To reduce the error in calculating derivatives of table functions
of two variables, 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. |
| Keywords |
plate, functionally graded material, finite element method, inverse problem, identification, density |
| Received |
31 January 2023 | Revised |
03 November 2023 | Accepted |
12 November 2023 |
| Link to Fulltext |
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