Scattering of an Ostrovsky wave packet in a delaminated waveguide

Tamber, J.S.; Tranter, Matthew R.

doi:10.1016/j.wavemoti.2022.103023

Cited by 5 publications

(14 citation statements)

References 34 publications

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“…In this study we examine the scenario when the difference in characteristic speeds is significant. In particular, we are considering the case from [21], where we take the limit of zero displacement in the lower layer, corresponding to a much denser material. We assume that we have a delaminated region between x 0 and x 1 before entering the soft bonded region from x 1 to x 2 , then a delaminated region between x 2 and x 3 , and finally another bonded region between x 3 and x 4 .…”

Section: Problem Formulationmentioning

confidence: 99%

“…for i = 1, 2, 3. As in [11,21], we adopt the approach of expressing our system in terms of longitudinal strains rather than displacements. By differentiating (1) and setting u…”

Section: Problem Formulationmentioning

confidence: 99%

“…The Ostrovsky equation originally arose in the context of shallow water waves where the rotation of the Earth is taken into account [17] and the evolution of wave packets generated from an initial pulse has been extensively studied [18,19,20]. The scattering of such wave packets in the delaminated region of a waveguide has recently been studied [21]. This paper presents further results from this problem.…”

Section: Introductionmentioning

confidence: 99%

“…The material of the lower layer is taken to be significantly denser than the upper layer, so that the displacements in the lower layer can be assumed to be zero, and the strains are described by BKG equations, rather than coupled Boussinesq equations. In Section 2, the problem formulation is presented and, following the work in [21], the weakly-nonlinear solution is constructed using an asymptotic multiple-scales expansion, which can be used in a semi-analytical method for the solution of the problem. We consider the case of delamination "sandwiched" between soft bonded regions.…”

Section: Introductionmentioning

confidence: 99%

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Studying the effect of delamination on Ostrovsky wave packet propagation in waveguides

Tranter,

Tamber

2024

J. Phys.: Conf. Ser.

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This paper considers the scattering of Ostrovsky wave packets in a delaminated two-layer waveguide with a soft bonding between the layers. The lower layer is significantly denser than the upper layer, so the displacements are described by Boussinesq-Klein-Gordon (BKG) equations in bonded regions or Boussinesq equations in the delaminated regions. A semi-analytical approach is developed using asymptotic multiple-scales expansions, which is less expensive than direct numerical modeling, and good agreement is shown between the two methods. In delaminated regions, the Ostrovsky wave packet evolves into a series of rank ordered solitons with dispersive radiation, and when these solitons re-enter a bonded region, they each evolve into Ostrovsky wave packets, with the lead Ostrovsky wave packet being most distinct. The numerical results are then linked to material parameters, which can motivate physical experiments with a wide range of materials to determine if this measure can be used to control delamination.

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Section: Problem Formulationmentioning

confidence: 99%

“…for i = 1, 2, 3. As in [11,21], we adopt the approach of expressing our system in terms of longitudinal strains rather than displacements. By differentiating (1) and setting u…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Studying the effect of delamination on Ostrovsky wave packet propagation in waveguides

Tranter,

Tamber

2024

J. Phys.: Conf. Ser.

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“…The constructed solution can find useful applications in the studies of the scattering of radiating solitary waves by delamination, 11,24 where the previous considerations were restricted to the initial conditions with either small or zero mean value because of the zero-mass contradiction. The propagation of cnoidal waves and undular bores 25,26 in structures with defects is an interesting area for future research.…”

Section: Please Cite This Article Asmentioning

confidence: 99%

Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction

Хуснутдинова

Tranter

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Coupled Boussinesq equations are used to describe long weakly nonlinear longitudinal strain waves in a bi-layer with soft bonding between the layers (e.g., a soft adhesive). From a mathematical viewpoint, a particularly difficult case appears when the linear long-wave speeds in the layers are significantly different (high-contrast case). The traditional derivation of the uni-directional models leads to four uncoupled Ostrovsky equations for the right- and left-propagating waves in each layer. However, the models impose a “zero-mass constraint”; i.e., the initial conditions should necessarily have zero mean, restricting the applicability of that description. Here, we bypass the contradiction in this high-contrast case by constructing the solution for the deviation from the evolving mean value, using asymptotic multiple-scale expansions involving two pairs of fast characteristic variables and two slow time variables. By construction, the Ostrovsky equations emerging within the scope of this derivation 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 apply the models to the description of counter-propagating waves generated by solitary wave initial conditions, or co-propagating waves generated by cnoidal wave initial conditions, as well as the resulting wave interactions, and contrast with the behavior of the waves in bi-layers when the linear long-wave speeds in the layers are close (low-contrast case). One local (classical) and two non-local (generalized) conservation laws of the coupled Boussinesq equations for strains are derived and used to control the accuracy of the numerical simulations.

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Detecting delamination via nonlinear wave scattering in a bonded elastic bar

Tamber,

Chappell,

Poore

et al. 2023

Nonlinear Dyn

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In this paper we examine the effect of delamination on wave scattering, with the aim of creating a control measure for layered waveguides of various bonding types. Previous works have considered specific widths of solitary waves for the simulations, without analysing the effect of changing the soliton parameters. We consider two multi-layered structures: one containing delamination ‘sandwiched’ by perfect bonding and one containing delamination but ‘sandwiched’ by soft bonding. These structures are modelled by coupled Boussinesq-type equations. Matched asymptotic multiple-scale expansions lead to coupled Ostrovsky equations in soft bonded regions and Korteweg-de Vries equations in the perfectly bonded and delaminated region. We use the Inverse Scattering Transform to predict the behaviour in the delaminated regions. In both cases, numerical analysis shows that we can predict the delamination length by changes in the wave structure, and that these changes depend upon the Full Width at Half Magnitude (FWHM) of the incident soliton. In the case of perfect bonding, we derive a theoretical prediction for the change and confirm this numerically. For the soft bonding case, we numerically identify a similar relationship using the change in amplitude. Therefore we only need to compute one curve to determine the behaviour for any incident solitary wave, creating a framework for designing measurement campaigns for rigorously testing the integrity of layered structures.

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Scattering of an Ostrovsky wave packet in a delaminated waveguide

Cited by 5 publications

References 34 publications

Studying the effect of delamination on Ostrovsky wave packet propagation in waveguides

Studying the effect of delamination on Ostrovsky wave packet propagation in waveguides

Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction

Detecting delamination via nonlinear wave scattering in a bonded elastic bar

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