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On the determination of the Biot modulus of poroelastic cylinder
Author(s) -
Dudarev Vladimir V.,
Mnukhin Roman M.,
Vatulyan Alexander O.,
Nedin Rostislav D.,
Gusakov Dmitriy V.
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800137
Subject(s) - biot number , poromechanics , mathematical analysis , cylinder , vibration , mathematics , depth sounding , amplitude , fredholm integral equation , inverse problem , inverse , integral equation , acoustics , physics , mechanics , geometry , materials science , porous medium , optics , geology , oceanography , porosity , composite material
The paper is concerned with a problem of radial vibrations of an inhomogeneous poroelastic cylinder by means of the acoustic sounding method. We have carried out the analysis of the amplitude‐frequency characteristic of the cylinder depending on the variation law of the Biot modulus and have considered the inverse problem on the determination of this law by the available data of the amplitude‐frequency characteristic measured in a given frequency range. The solution of the inverse problem has been obtained on the basis of the iterative process constructed, when the correction to the current form of the reconstructed function was defined by the derived Fredholm integral equation of the first kind. A number of examples of the reconstruction of the variation laws of the Biot modulus are presented. The reconstruction accuracy is estimated, and the recommendations on a successful implementation of the proposed approach are provided.