On the inverse problem for the mechanical parameters reconstruction of a viscoelastic layer

Authors

UDC

534.1

DOI:

https://doi.org/10.31429/vestnik-20-4-53-62

Abstract

The problem of forced steady vibrations of a transversely inhomogeneous viscoelastic layer is considered. After the Fourier integral transform applying, the problem is reduced to a boundary value problem for the canonical system of ordinary differential equations, solved by the shooting method. Then the displacement field is found using the inverse Fourier transform.

The problem of restoring the distribution law of mechanical parameters from wavefield data on the top surface of the layer is also considered. The inverse problem is reduced to the sequence of the Fredholm integral equations of the first kind with the smooth kernel. To solve the integral equations, the modified Voyevodin method, applicable in the case of complex-valued kernel and right-hand side, is used. The results of numerical experiments for solving the inverse problem at different oscillations frequencies for various laws of inhomogeneity are presented. It is also shown that the proposed method can also be used to recover the real parameter distribution law in the purely elastic case.

Keywords:

viscoelasticity, inverse coefficient problems, layered structures

Author Info

Pavel S. Uglich

Ph.D (Physical and Mathematical), Assistant professor of the Elasticity Theory Department of Southern Federal University

e-mail: puglich@inbox.ru

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Issue

2023. Vol. 20. No. 4

Section

Mechanics

Pages

53-62

Submitted

2023-07-19

Published

2023-12-31

How to Cite

Uglich P.S. On the inverse problem for the mechanical parameters reconstruction of a viscoelastic layer. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2023, vol. 20, no. 4, pp. 53-62. DOI: https://doi.org/10.31429/vestnik-20-4-53-62 (In Russian)

Copyright (c) 2024 Uglich P.S.

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