Introduction

Svanadze, Merab

doi:10.1007/978-3-030-28022-2_1

Cited by 2 publications

(4 citation statements)

References 165 publications

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“…Obviously, Theorems 2 and 3 imply that K (1) , K (2) and K (3) are the singular integral operators. Therewith, the operator K (j) is of the normal type with an index equal to zero.…”

Section: Surface Potentials and Singular Integral Operatorsmentioning

confidence: 99%

“…are given in the book by Kupradze et al [24]. In addition, an extensive review and a historical information on the potential method are presented in the book by Svanadze [2].…”

Section: Surface Potentials and Singular Integral Operatorsmentioning

confidence: 99%

“…The mathematical models for single and multiple porosity media have found applications in many branches of civil and geotechnical engineering, technology and biomechanics. The intended applications of the mathematical theories for elastic materials with a triple porosity structure are to geological materials such as rocks and soils, manufactured porous materials such as ceramics and pressed powders, and biomaterials such as bone (for details, see the books by Straughan [1] and Svanadze [2], and the references therein).…”

Section: Introductionmentioning

confidence: 99%

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External problems of steady vibrations in the theory of elastic materials with a triple porosity structure

Svanadze

2023

Proc Appl Math and Mech

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In this paper, the linear theory of elasticity for materials with a triple porosity (macro, meso and micro levels of porosities) structure based on the volume fraction concept is considered. The external boundary value problems (BVPs) of steady vibrations of this theory are investigated. Namely, the uniqueness theorem for classical solutions of these BVPs is established. Then, the basic properties of the surface (single‐layer and double‐layer) potentials are given. Finally, on the basis of the properties of potentials, the existence theorems for classical solutions of the above mentioned BVPs of steady vibrations are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.

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“…Obviously, Theorems 2 and 3 imply that K (1) , K (2) and K (3) are the singular integral operators. Therewith, the operator K (j) is of the normal type with an index equal to zero.…”

Section: Surface Potentials and Singular Integral Operatorsmentioning

confidence: 99%

“…are given in the book by Kupradze et al [24]. In addition, an extensive review and a historical information on the potential method are presented in the book by Svanadze [2].…”

Section: Surface Potentials and Singular Integral Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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External problems of steady vibrations in the theory of elastic materials with a triple porosity structure

Svanadze

2023

Proc Appl Math and Mech

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“…Based on Darcy’s law, and considering a single porosity structure, Biot [2–5] formulated the first deformation theory involving a porous elastic solid and a viscous compressible fluid. For the basic results, as well as for historical information about this founding theory, the reader can refer to the books by Cheng [6], Straughan [7], and Svanadze [8]. However, thinking about geological formations—for instance—it is easy to realize that they often show a variety of heterogeneous levels of porosity: fractures, fissures, cracks, and so on.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh waves in thermoelasticity: Triple porous media in local thermal non-equilibrium

Zampoli

Chiriţă

2022

Mathematics and Mechanics of Solids

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Assuming the hypothesis of local thermal non-equilibrium, this work investigates the propagation of Rayleigh surface waves in a thermoelastic half-space, isotropic, homogeneous and structured with a triple level of porosity. Its surface is supposed to be stress-free, thermally insulated and characterized by null pressure boundary conditions. A class of wave solutions is highlighted for the differential system of the model, each solution satisfying suitable asymptotic conditions in the depth of the considered half-space. Then, the Rayleigh wave solution is sought as a linear combination of the elements of this class, and, moreover, by means of the selected boundary conditions, the associated secular equation is found. By solving the secular equation, the characteristics of the wave solution are determined: the propagation speed as well as the damping in time. With the purpose of clearly highlighting the characteristics of the model, the secular equation is solved numerically and significant graphical representations are provided, using the software packages Mathematica and MATLAB. This suggests an increase of the Rayleigh wave propagation speed, corroborated with the appearance of the damping in time of its amplitude.

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Introduction

Cited by 2 publications

References 165 publications

External problems of steady vibrations in the theory of elastic materials with a triple porosity structure

External problems of steady vibrations in the theory of elastic materials with a triple porosity structure

Rayleigh waves in thermoelasticity: Triple porous media in local thermal non-equilibrium

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