Choice of kernels in solving problems involving creep and relaxation

Koltunov, M. A.

doi:10.1007/bf00860064

Cited by 9 publications

(8 citation statements)

References 2 publications

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“…We consider the visco elastic waveguide as an infinite axial х 1 Based on the geometric relationships and relations of the generalized Hooke's law, taking into account the kinematic hypotheses (2), the expressions for the components of the strain and stress tensor has the form [7] ( ) ( ) ω -real constant. Then, we replace of (6) approximate species [8] ( ) ( ) Introducing the notation for points 2 2 2 2 11 22 2 2 2 2 1 2 2 1 ; ;…”

Section: The Mathematical Formulation Of the Problemmentioning

confidence: 99%

Propagation of Natural Waves on Plates of a Variable Cross Section

Safarov¹,

Boltaev²

2018

OALib

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In this paper, a conjugate spectral problem and biorthogonality conditions for the problem of extended plates of variable thickness are constructed. A technique for solving problems and numerical results on the propagation of waves in infinite extended viscoelastic plates of variable thickness is described. The viscous properties of the material are taken into account using the Voltaire integral operator. The investigation is carried out within the framework of the spatial theory of viscoelasticity. The technique is based on the separation of spatial variables and the formulation of a boundary value problem for Eigen values which are solved by the Godunov orthogonal sweep method and the Muller method. Numerical values of the real and imaginary parts of the phase velocity are obtained depending on the wave numbers. In this case, the coincidence of numerical results with known data is obtained.

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Section: The Mathematical Formulation Of the Problemmentioning

confidence: 99%

Propagation of Natural Waves on Plates of a Variable Cross Section

Safarov¹,

Boltaev²

2018

OALib

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“…Äëÿ îïðåäåëåííîñòè ïîëîaeèì, ÷òî ÿäðî ðåëàêñàöèè ÿâëÿåòñÿ ÿäðîì Êîëòóíîâà [18]. Åãî áåçðàçìåðíàÿ ôîðìà èìååò âèä M(τ) = aτ α−1 exp (−ϑτ)/Γ(α), ãäå Γ(α) − ãàììà-ôóíêöèÿ, ϑ = βL/c, a = 4LA/(3ρc 3 ), à A, β è α − ôèçè÷åñêèå ïàðàìåòðû (α ≤ 1).…”

Section: êîíòàêòíàÿ ñèëàunclassified

“…îáåñïå÷èâàþùåãî îãðàíè÷åííóþ ïîëçó÷åñòü ìàòåðèàëà [18]. Â ðàñ÷åòàõ ïðèíèìàëèñü a = 1, ν = 0,3, çíà÷åíèå α âàðüèðîâàëîñü â ïðåäåëàõ 0 < α ≤ 1, à ïàðàìåòð ϑ âûáèðàëñÿ èç óñëîâèÿ (21).…”

Section: ïðèìåðmentioning

confidence: 99%

Symmetric Contact Problem for Viscoelastic Half-Plane and Absolutely Rigid Striker at Supersonic Stage of Interaction

Korovaytseva¹,

Тарлаковский²

2018

PSP

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“…+ |/x is a constant. To describe shearing strain, the Rzhanitsyn-Koltunov's relaxation kernel has been used [7] as the most common one in mechanics of polymers:…”

Section: -7mentioning

confidence: 99%

Synthesis of layered shells from a finite set of viscoelastic materials

Бондарев

Budugaeva

Gusev

1999

J. Aust. Math. Soc. Series B, Appl. Math

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The method suggested earlier for solving the problems of optimal design from a limited set of elastic materials is generalized to a viscoelasticity case. The computational experiment for the problem of free oscillations of a spherical shell shows that characteristics of a viscoelastic layered structure may be improved due to peculiarities of wave propagation through the boundaries of layers made of different materials.

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Choice of kernels in solving problems involving creep and relaxation

Cited by 9 publications

References 2 publications

Propagation of Natural Waves on Plates of a Variable Cross Section

Propagation of Natural Waves on Plates of a Variable Cross Section

Symmetric Contact Problem for Viscoelastic Half-Plane and Absolutely Rigid Striker at Supersonic Stage of Interaction

Synthesis of layered shells from a finite set of viscoelastic materials

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