Low-frequency wave propagation in an elastic plate floating on a two-layered fluid

Indejtsev, D. A.; Zhuchkova, Marina G.; Kouzov, D. P.; Sorokin, Sergey

doi:10.1016/j.wavemoti.2015.12.003

Cited by 3 publications

(5 citation statements)

References 15 publications

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“…Low-frequency wave propagation in solids is relevant to a large number of modern applications (see, for example, [1,2,3,4,5,6,7] and references therein). Long longitudinal bulk strain solitary waves in elastic waveguides can be modelled using Boussinesq-type equations [1,2,8] (see also [5,9,10,11,12]).…”

Section: Introductionmentioning

confidence: 99%

Weakly-Nonlinear Solution of Coupled Boussinesq Equations and Radiating Solitary Waves

Хуснутдинова

Tranter

2019

Advanced Structured Materials

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Weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the materials of the layers have close mechanical properties, in which case the system can support radiating solitary waves. We construct a weakly-nonlinear d'Alembert-type solution of this system, considering the problem in the class of periodic functions on an interval of finite length. The solution is constructed using a novel multiple-scales procedure involving fast characteristic variables and two slow time variables. Asymptotic validity of the solution is carefully examined numerically. We also discuss the limiting case of an infinite interval for localised initial conditions. The solution is applied to study interactions of radiating solitary waves.

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Section: Introductionmentioning

confidence: 99%

Weakly-Nonlinear Solution of Coupled Boussinesq Equations and Radiating Solitary Waves

Хуснутдинова

Tranter

2019

Advanced Structured Materials

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“…The plate density is ρ = 917 kg/m 3 , the Young's module is E = 4.2 · 10 9 N/m 2 , the Poisson ratio is ν = 0.3, the thickness of the plate is h = 1.6 m, the thickness of the upper layer is h 1 = 20 m, the depth of the main fluid is h 2 = 330 m, the density of the upper fluid is ρ 1 = 1000 kg/m 3 , the density of the main fluid is ρ 2 = 1024 kg/m 3 . Following the paper [1] we non-dimensionalize the problem. We introduce the non-dimensional wave number k, the non-dimensional wave frequency Ω, the acceleration due to gravity G by…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Interest in gravity waves propagation in a two-layer incompressible fluid covered by an elastic plate has been inspired by various technical activities in the polar regions, where the floating ice is subjected to wave motion, and the underlying water is stratified owing to salinity and temperature variations [1]. The paper continues our previous researches [2][3][4], and is devoted to finding the exact analytical solution of the problem.…”

Section: Introductionmentioning

confidence: 85%

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Transmission of a flexural-gravitational wave through an obstacle in an elastic plate floating atop a two-layer fluid. Thin-upper-layer approximation

Kouzov

Zhuchkova

2015

2015 Days on Diffraction (DD)

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Low-frequency time-harmonic waves in an infinite elastic plate floating atop a two-layer fluid of finite depth are considered. Transmission of a surface flexural-gravitational wave through and reflection from a straight-line obstacle in the plate are studied analytically. Under a thin-upper-layer assumption, two-layer fluid is approximately replaced by a single-layer fluid with a special boundary condition at its upper surface. In a low-frequency range, the approximate results are in an excellent agreement with those obtained in the exact statement.

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“…The stability of solitary waves has inspired research into their applicability for detection of delamination in some cases, in addition to existing methods [11,12,13,14,15]. Low-frequency wave propagation in solids is relevant to a large number of modern applications (see, for example, [3,4,7,16,17,18,19] and references therein).…”

Section: Introductionmentioning

confidence: 99%

On Coupled Boussinesq Equations and Ostrovsky equations free from zero-mass contradiction

Хуснутдинова¹,

Tranter²

2021

Preprint

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Long weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. Previously, we considered the case when the materials of the layers have close mechanical properties, and the system supports radiating solitary waves. Here we are concerned with a more challenging case, when the mechanical properties of the materials of the layers are significantly different, and the system supports wave packet solutions. We construct a weakly-nonlinear solution of the Cauchy problem for this system, considering the problem in the class of periodic functions on an interval of finite length. The solution is constructed for the deviation from the evolving mean value using a novel multiple-scales procedure involving fast characteristic variables and two slow time variables. By construction, the Ostrovsky equations emerging within the scope of this procedure are solved for initial conditions with zero mean while initial conditions for the original system may have non-zero mean values. Asymptotic validity of the solution is carefully examined numerically. We also discuss the application of the solution to the study of co-propagating waves generated by the solitary or cnoidal wave initial conditions, as well as the case of counter-propagating waves and the resulting wave interactions. One local and two nonlocal conservation laws ae obtained and used to control the accuracy of the numerical simulations.

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Low-frequency wave propagation in an elastic plate floating on a two-layered fluid

Cited by 3 publications

References 15 publications

Weakly-Nonlinear Solution of Coupled Boussinesq Equations and Radiating Solitary Waves

Weakly-Nonlinear Solution of Coupled Boussinesq Equations and Radiating Solitary Waves

Transmission of a flexural-gravitational wave through an obstacle in an elastic plate floating atop a two-layer fluid. Thin-upper-layer approximation

On Coupled Boussinesq Equations and Ostrovsky equations free from zero-mass contradiction

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