Solitary waves in an inhomogeneous cylindrical shell interacting with an elastic medium

Бочкарев, А. В.; Zemlyanukhin, A. I.; Mogilevich, L. I.

doi:10.1134/s1063771017020026

Cited by 14 publications

(3 citation statements)

References 13 publications

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“…( ) , ( ) -продольное перемещение и прогиб, положительный к центру кривизны, -продольная координата; -время; , -напряжения со стороны жидкости, находящейся между оболочками;˜,˜-напряжения со стороны жидкости, заполняющей внутреннюю оболочку; реакция упругой среды в нормальном и продольном направлениях [5,6,[15][16][17][18]:…”

Section: рис 1 бесконечно длинные соосные цилиндрические оболочкиunclassified

Wave Processes Modeling in Two Coaxial Shells Filled with a Viscous Liquid and Surrounded by Elastic Medium

Blinkov¹,

Евдокимова²,

Mogilevich³

et al. 2018

Vestn. Ross. univ. družby nar., Ser. Mat. inform. fiz

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Section: рис 1 бесконечно длинные соосные цилиндрические оболочкиunclassified

Wave Processes Modeling in Two Coaxial Shells Filled with a Viscous Liquid and Surrounded by Elastic Medium

Blinkov¹,

Евдокимова²,

Mogilevich³

et al. 2018

Vestn. Ross. univ. družby nar., Ser. Mat. inform. fiz

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“…Equation (1) was, in particular, derived for waves at interfaces in a three-layer fluid flow that is symmetrical relative to the half-depth [13,14]. It also naturally arises in modeling the propagation of longitudinal waves in thin rods, plates and shells when the dependence of the stress intensity on the strain intensity has the form of a fifth-degree polynomial [15,16]. The classification of its exact solitary-wave and periodic solutions is given in [17].…”

Section: Introductionmentioning

confidence: 99%

Modulational Instability of Nonlinear Wave Packets within (2+4) Korteweg–de Vries Equation

Kurkina,

Pelinovsky,

Kurkin

2024

Water

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The higher-order nonlinear Schrödinger equation with combined nonlinearities is derived by an asymptotic reduction from the (2+4) Korteweg–de Vries model for weakly nonlinear wave packets for the context of interfacial waves in a three-layer symmetric media. Focusing properties and modulation instability effects are discussed for the considered physical context. Instability growth rate, maximum of the increment and the boundaries of the instability interval are derived in terms of three-layer density stratification, their structure on the parameter planes of relative layer depth, carrier wavenumber and envelope amplitude, are considered in detail.

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“…The study of the wave process in elastic shells is widely applied in various technical fields. The propagation of deformation waves in elastic, viscoelastic, and nonlinear viscoelastic shells and plates was considered in [7][8][9][10][11]. In those papers, the case of interaction of shells and a viscous incompressible fluid is not considered.…”

Section: Introductionmentioning

confidence: 99%

The Study of Wave Propagation in a Shell with Soft Nonlinearity and with a Viscous Liquid Inside

Mogilevich¹,

Иванов²

2019

Nelin. Dinam.

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This article is devoted to studying longitudinal deformation waves in physically nonlinear elastic shells with a viscous incompressible fluid inside them. The impact of construction damping on deformation waves in longitudinal and normal directions in a shell, and in the presence of surrounding medium are considered. The presence of a viscous incompressible fluid inside the shell and the impact of fluid movement inertia on the wave velocity and amplitude are taken into consideration. In the case of a shell filled with a viscous incompressible fluid, it is impossible to study deformation wave models by qualitative analysis methods. This makes it necessary to apply numerical methods. The numerical study of the constructed model is carried out by means of a difference scheme analogous to the Crank-Nickolson scheme for the heat conduction equation. The amplitude and velocity do not change in the absence of surrounding medium impact, construction damping in longitudinal and normal directions, as well as in the absence of fluid impact. The movement occurs in the negative direction, which means that the movement velocity is subsonic. The numerical experiment results coincide with the exact solution, therefore, the difference scheme and the modified Korteweg-de Vries-Burgers equation are adequate.

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Solitary waves in an inhomogeneous cylindrical shell interacting with an elastic medium

Cited by 14 publications

References 13 publications

Wave Processes Modeling in Two Coaxial Shells Filled with a Viscous Liquid and Surrounded by Elastic Medium

Wave Processes Modeling in Two Coaxial Shells Filled with a Viscous Liquid and Surrounded by Elastic Medium

Modulational Instability of Nonlinear Wave Packets within (2+4) Korteweg–de Vries Equation

The Study of Wave Propagation in a Shell with Soft Nonlinearity and with a Viscous Liquid Inside

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