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Identification of inhomogeneous elastic properties of isotropic cylinder
Author(s) -
Bogachev Ivan V.,
Nedin Rostislav D.,
Vatulyan Alexander O.,
Yavruyan Oksana V.
Publication year - 2017
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.201600179
Subject(s) - isotropy , inverse problem , mathematics , dimensionless quantity , inverse , fredholm integral equation , cylinder , mathematical analysis , mathematical optimization , integral equation , geometry , physics , mechanics , quantum mechanics
We propose a scheme of efficient solving an inverse coefficient problem on a reconstruction of unknown laws of variation of mechanical properties of inhomogeneous isotropic cylindrical region. The reconstruction is performed step‐by‐step by means of solving two problems on torsional and radial vibrations of the considered region that provides a formulation of two inverse problems on searching the unknown functions. We build iterative processes of solving the inverse problems stated; in frames of each process, we derive systems of the Fredholm integral equations of the 1st and the 2nd kind in order to find corrections to the unknown functions relative to the corresponding initial approximations. We conduct the computational experiments on a reconstruction of the unknown dimensionless functions.