Premium
Inverse coefficient problem of the variable properties reconstruction for the viscoelastic cylindrical waveguide
Author(s) -
Vatulyan Alexander O.,
Uglich Pavel S.,
Yavruyan Oksana V.
Publication year - 2020
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.201900170
Subject(s) - inverse problem , mathematical analysis , inverse , viscoelasticity , mathematics , fredholm integral equation , shear modulus , boundary value problem , displacement field , waveguide , integral equation , materials science , geometry , physics , optics , finite element method , composite material , thermodynamics
An effective technique for inverse coefficient problem solving of the shear modulus reconstruction for both inhomogeneous elastic and viscoelastic cylindrical waveguide is proposed. The identification is carried out using the displacement field data measured on the finite part of the outer boundary of the cylindrical waveguide in the torsional vibrations mode. An iterative scheme for solving the inverse problem is developed. At each iteration step, the correction to the shear modulus distribution function is calculated using the Fredholm integral equation of the first kind with a smooth kernel. Numerical results are obtained for both direct and inverse problems for different laws of the shear modulus variation.