Inverse problems of crack's theory research with asymptotic approach using

Authors

  • Vatulyan A.O. Southern Federal University, Rostov-on-Don, Российская Федерация
  • Yavruyan O.V. Vladikavkaz Science Center, Russian Academy of Science, Vladikavkaz, Российская Федерация

UDC

534.16

DOI:

https://doi.org/10.31429/vestnik-15-2-39-46

Abstract

The effective approach for inverse problems of cracks identification in the layer is proposed. The scheme is based on asymptotic analysis of the problem, taking into account the small relative size of the defect. The crack identification is realized from the acoustic data - displacement fields wich on the part of upper bound measured. Asymptotic analysis of displacement fields in the layer and on the boundary is carried out. In the case of a crack, that allows parametrization by a finite number of parameters, for example, a straight-line crack, the identification problem is solved, the transcendental equations are obtained in regard to the corresponding defect's characteristics in the frequency sensing mode. The proposed approach is tested for a model inverse problem of a vertical crack, located on the boundary between two semi-layers. The steady-state oscillations for anti-plane deformations are considered. The expressions for displacement fields calculation for each of the semi-layers are recieved, asymptotic estimates of these expressions are obtained. The inverse problem of crack identification by amplitude characteristics of running waves is resolved. Transcendental expressions for crack's parameters identification are presented. The results of numerical experiments of characteristics' reconstruction are represented. The proposed approach effectiveness is conducted.

Keywords:

crack, layer, identification, asymptotic approach, oscillations, acoustic sensing

Author Infos

Aleksandr O. Vatulyan

д-р физ.-мат. наук, профессор кафедры теории упругости института математики, механики и компьютерных наук им.Воровича И.И. Южного федерального университета

e-mail: vatulyan@math.rsu.ru

Oksana V. Yavruyan

канд. физ.-мат. наук, научный сотрудник отдела дифференциальных уравнений Южного математического института Владикавказского научного центра РАН

e-mail: yavruyan@mail.ru

References

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Issue

2018. Vol. 15. No. 2

Section

Mechanics

Pages

39-46

Submitted

2018-04-23

Published

2018-06-27

How to Cite

Vatulyan A.O., Yavruyan O.V. Inverse problems of crack's theory research with asymptotic approach using. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2018, vol. 15, no. 2, pp. 39-46. DOI: https://doi.org/10.31429/vestnik-15-2-39-46 (In Russian)

Copyright (c) 2018 Vatulyan A.O., Yavruyan O.V.

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