On inverse coefficient problems of poroelasticity

Vatul’yan, A. O.; Lyapin, A. A.

doi:10.3103/s0025654413020131

Cited by 4 publications

(7 citation statements)

References 6 publications

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“…In the second stage, to reconstruct the shear modulus at each step of the iterative process, it is necessary to solve the integral Fredholm equation of the first kind (10). As a rule, such ill-posed problems are solved using the Tikhonov regularization method [3].…”

Section: Numerical Implementationmentioning

confidence: 99%

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One method of determining the elastic properties of inhomogeneous solids

Vatul’yan

Денина

2012

J Appl Mech Tech Phy

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This paper considers the inverse problem of reconstructing three inhomogeneous characteristics of a rod (Young's modulus, shear modulus, and density) from amplitude-frequency characteristics for the regime of steady-state longitudinal, flexural, and torsional vibrations. The unknown characteristics are identified by constructing iterative processes based on the apparatus of the Fredholm integral equations of the first and the second kind. Results of numerical experiments are presented.

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Section: Numerical Implementationmentioning

confidence: 99%

“…General aspects of the solution of inverse and ill-posed probelms are considered in detail in [1][2][3][4][5]. One of the most efficient methods for solving ill-posed problems is the principle of iterative regularization.…”

Section: Introductionmentioning

confidence: 99%

One method of determining the elastic properties of inhomogeneous solids

Vatul’yan

Денина

2012

J Appl Mech Tech Phy

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“…Let us assume that the displacement field in a certain section of the upper surface [c, d] (c > 0) is known, and it is required to determine the law of the distribution of the mechanical characteristics μ(x 2 ) and ρ(x 2 ). It is known that such problems are essentially nonlinear and one of the methods of their study is the method of linearization [11].…”

Section: Inverse Problemmentioning

confidence: 99%

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

Vatul’yan

Uglich

2014

J Appl Mech Tech Phy

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Direct and inverse problems of forced antiplane vibrations of a transverse inhomogeneous elastic layer are considered. The mechanical characteristics of the layer (density and shear modulus) are considered to be functions of the transverse coordinate. A method for solving the direct problem, based on using the integral Fourier transform and solving the boundary problem by the shooting method, is proposed. The inverse problem of determining the distributions of the mechanical parameters based on the known information on the wave field on some part of the upper surface is considered. Iterative sequences of integral equations are constructed. Results of numerical experiments and recommendations on the optimal choice of the vibration frequency and the interval, on which the displacements are determined, are given.

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“…Investigations in this field are actively conducted at present. Among the works in this area let us mention the works by Zimmerman R.W., Berryman J.G., Cowin S.C., Schanz M., Vatulyan A.O., Vasilyeva M., Igumnov L.A…”

Section: Introductionmentioning

confidence: 99%

“…This substance is a system of mutually intersecting bone septa with the bone marrow. Taking into account such a structure, one may use models of the poroelasticity theory to describe the deformation of bone tissues …”

Section: Introductionmentioning

confidence: 99%

On the determination of the Biot modulus of poroelastic cylinder

et al. 2019

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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.

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On inverse coefficient problems of poroelasticity

Cited by 4 publications

References 6 publications

One method of determining the elastic properties of inhomogeneous solids

One method of determining the elastic properties of inhomogeneous solids

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

On the determination of the Biot modulus of poroelastic cylinder

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