Propagation of axisymmetric waves in an initially twisted circular compound bimaterial cylinder with a soft inner and a stiff outer constituents

Akbarov, S. D.; Guliev, M.; Kepceler, Tamer

doi:10.1007/s11029-011-9176-z

Cited by 9 publications

(4 citation statements)

References 13 publications

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“…While determining the diffusive and dissipative properties in sheared layers of pulsing filtration, let's consider the self-oscillations and behavior of the structure in the area of basic frequencies (Popkov et al 2000, Akbarov et al 2011. Basing upon the root analysis of dispersion equ'n we have considered the character of wave advancement versus the function of losses in material and type of its fixing.…”

Section: Basic Frequencies In Resonant Out-flows With Restricted Densmentioning

confidence: 99%

“…9; in the process of lithogenesis to depart into zones of compaction and de-compaction. The same abnormal filtration of HC cannot be described by parabolic equ's like thermal conductivity, and this required systematic integrated conjugation equ's for mass and energy transfer (Demyanov et al 2004, Kulesh et al 2005, Akbarov et al 2011, Berdnikov et al 2014, Astafiev et al 2015. Modification of differential equ's (DE) in view on their instant micro-structure is described in papers of Koser Е.…”

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confidence: 99%

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Global Hydrocarbon Energy Potential of Euro-Asia or Solution of Navier-Stokes Equation for Deformed Micro-Structure of the Earth’s Porous Space

Popkov¹,

Astafiev²,

Shterenberg³

et al. 2015

MAS

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The authors present the hydro-geological basin-type model of global energetics with hydro-dynamic potential showing the interaction of inland platforms of the Earth. The authors propose the new cluster-type approach towards the asymmetric multi-scaled modeling at the basis of integral solution within the quadrature of Navier-Stokes equation for deformed micro-structure of Earth's porous space. We have studied the effect of poor local tectonic faults upon the arrangement of hydrocarbon traps in lithosphere, shale tight fields, that is based upon the interconnected methods in geophysics, hydro-geology and geo-mechanics, tectono-physics and structural geology. The authors also present the scientific concept of new principles to increase the level of geo-informatics while searching exploring and developing the hydro-carbon reserves, geo-physical studies of seismic emissions, micro-seismic and seismology of mega-scales in geological ages of stresses with transition to predictable man-induced time for geological/technological events. Basing upon the conjugation of Navier-Stokes equation and due consideration of deforming relaxation we have built the energy self-arranged model of Earth's lithosphere de-fluidization, have found inherent energy delayed spectra for the dynamic contacts of stratified structure. We have obtained the energy conjugated solution of micro-structure porous media interaction for hydro-geological decompression of subduction channel in seabed and saturation of generalized Middle Oceanic Ridge with self-organization of classic sedimentological hydro-carbon traps and complexly organized shale reservoirs with compacted depositions of Allochthon structures in Domanik and Bazhenov formations. The authors present the energy stable mean filtration profile as per Darcy, conjugated with stress-deformed status of porous geo-media micro-structure at various boundary conditions: closed-type or capillary jammed boundaries of filtration blocks and free-type -with phase filtration front and diffusive displacement of fluids by saturated porous media and smart technologies of multi-stage hydro-fracture in dense shale reservoirs. Analytically, in quadrature, there is the dissipation velocity, potential and kinetic energy potentials of mean outflow and shear layer of filtration dissipative structure, like a generalized model of viscous elasticity that depends upon the wave number, phase velocity, thickness of the layer and geo-mechanical parameters that reflect the geo-media heterogeneity.

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Section: Basic Frequencies In Resonant Out-flows With Restricted Densmentioning

confidence: 99%

mentioning

confidence: 99%

Global Hydrocarbon Energy Potential of Euro-Asia or Solution of Navier-Stokes Equation for Deformed Micro-Structure of the Earth’s Porous Space

Popkov¹,

Astafiev²,

Shterenberg³

et al. 2015

MAS

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“…Equations (4), presented in a form of Helmholtz, in a cylindrical system of coordinates [20][21][22][23]26] has the type of Bessels' differential equation. Ther solution of the resulted system is written down in a form of longitudinal and transversal waves with complex wave number of k=α+iβ:…”

Section: Natural Properties Of Mixed Deformed Viscous-elastic Layermentioning

confidence: 99%

“…The profile of mean velocity U(η) is set on the basis of a principle of maximal stability for mean characteristics received after resolution of a system of linear differential equations (21)(22)(23)(24)(25)(26), proceeding from approximation in viscous sub-layer U(η)= η.…”

Section: Stability Of Interaction Of Mean Characteristics Of Mass Tramentioning

confidence: 99%

Geo-informatics of multi-scale solutions in Navier-Stokes equations for deformed porous space

Popkov¹,

Zatsepina²,

Shakshin³

2014

imf

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Within the framework of block self-organizing of geological bodies with use of deformation theory the mathematical solution of a problem for effective final speed is proposed. The analytical and numerical integrated solutions of Navier-Stokes equation for deformable porous space were obtained. The decisions of multi-scaled regional problems «on a flow basis» were also presented: from lithology of rock space -to a well and from a well -to petro-physics. The evolutionary transformation of the linear solution of the equation on mass conservation up to the energetically stable non-linear solution of the equation on preserving the number of movements is also offered.

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Axisymmetric Longitudinal and Flexural Wave Propagation in Pre-strained Bi-material Compound Circular Cylinders

Akbarov

2015

Dynamics of Pre-Strained Bi-Material Elastic Systems

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Propagation of axisymmetric waves in an initially twisted circular compound bimaterial cylinder with a soft inner and a stiff outer constituents

Cited by 9 publications

References 13 publications

Global Hydrocarbon Energy Potential of Euro-Asia or Solution of Navier-Stokes Equation for Deformed Micro-Structure of the Earth’s Porous Space

Global Hydrocarbon Energy Potential of Euro-Asia or Solution of Navier-Stokes Equation for Deformed Micro-Structure of the Earth’s Porous Space

Geo-informatics of multi-scale solutions in Navier-Stokes equations for deformed porous space

Axisymmetric Longitudinal and Flexural Wave Propagation in Pre-strained Bi-material Compound Circular Cylinders

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