Reconstruction of inhomogeneous characteristics of a transverse inhomogeneous layer in antiplane vibrations

Vatul’yan, A. O.; Uglich, P. S.

doi:10.1134/s0021894414030122

Cited by 7 publications

(16 citation statements)

References 7 publications

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“…The initial conditions coincide with the corresponding initial conditions , the remaining initial conditions are homogeneous. The formula for the integral equation kernels calculation using the residue theory in the case of double pole is proposed in [].…”

Section: Analysis Of the Wave Field And Kernels Of Integral Equationmentioning

confidence: 99%

Inverse coefficient problem of the variable properties reconstruction for the viscoelastic cylindrical waveguide

2020

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PresentAddress 344090, Russian Federation, Rostov-on-don, Milchakova St. 8A Funding informationModels, algorithms, and software for multiscale analysis of new materials and physically active media, Grant/Award Number: 075-15-2019-1928 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. K E Y W O R D Scylindrical waveguide, inhomogeneity, inverse problem, mechanical properties, oscillations, reconstruction

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Section: Analysis Of the Wave Field And Kernels Of Integral Equationmentioning

confidence: 99%

Inverse coefficient problem of the variable properties reconstruction for the viscoelastic cylindrical waveguide

2020

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“…Therefore, our aim in this section is to estimate the Green's function for an elastic layer with Neumann homogeneous conditions over straight boundaries. This means that we must solve the boundary value problem given by equations (10) and (11).…”

Section: Green's Function For Elastic Layermentioning

confidence: 99%

“…where the quantities A(s) , B(s) should be determined from the boundary conditions of equation (11). The solution is constructed in the following form:…”

Section: Green's Function For Elastic Layermentioning

confidence: 99%

“…These scattered waves, in both types, may be considered as elastic waves, depending on the composition and the structure of the considered medium. Most problems involving the first type of wave are investigated using high-frequency approximations, such as ray theory, the Born approximation, and Kirchhoff’s theory [9–11], while problems involving the second type of wave are studied in the low-frequency range.…”

Section: Introductionmentioning

confidence: 99%

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Diffraction of elastic waves from object in layer with slightly corrugated surface

Elmorabie

Yahya

2017

Mathematics and Mechanics of Solids

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This work is concerned with the influence of corrugated surfaces on waves diffracted from an object in an elastic layer. A boundary value problem is formulated to simulate an anti-plane problem for a harmonic load acting on the upper surface of the layer. By using the boundary integral equation method and the perturbation technique, the considered problem is reduced to a pair of integral equations. By constructing the Green’s function, the scattering problem in a one-mode frequency range is solved. To check the validity of the proposed technique, several numerical examples for different geometrical shapes of the corrugated bottom are presented.

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“…Here, we note a number of works aimed at creating effective algorithms for reconstruction of variable properties of structures and their numerical implementation 1–9 . A much larger number of works is devoted to the reconstruction of constant properties.…”

Section: Introductionmentioning

confidence: 99%

On the reconstruction of material properties of a radially inhomogeneous cylindrical waveguide

Vatul’yan

Yurov

2021

Math Methods in App Sciences

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The scheme of solving the inverse problem (IP) for reconstructing three functions characterizing the radial change in the Lamé parameters and in the density in a cylindrical waveguide is presented. The displacement fields corresponding to three types of loading are used as an additional information for solving the IP. An iterative process is constructed, at each step of which a direct problem is solved for the radially inhomogeneous waveguide, and the corrections to the restored functions are determined. The corrections are identified by solving the system of three Fredholm integral equations of the first kind with smooth kernels. The solution is constructed by the A. N. Tikhonov regularization method. A series of computational experiments was carried out. The role of the initial approximation and the frequency range is discussed.

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Reconstruction of inhomogeneous characteristics of a transverse inhomogeneous layer in antiplane vibrations

Cited by 7 publications

References 7 publications

Inverse coefficient problem of the variable properties reconstruction for the viscoelastic cylindrical waveguide

Inverse coefficient problem of the variable properties reconstruction for the viscoelastic cylindrical waveguide

Diffraction of elastic waves from object in layer with slightly corrugated surface

On the reconstruction of material properties of a radially inhomogeneous cylindrical waveguide

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