Long wave motion in layered elastic media

Lutianov, Michael; Rogerson, G. A.

doi:10.1016/j.ijengsci.2010.07.003

Cited by 10 publications

(5 citation statements)

References 13 publications

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“…This is clear also in figure 2a, where the start of the straight-line segment indicates where the bending regime ends and the stretching regime begins. These results extend those in Liu & Bhattacharya [4] and Lutianov & Rogerson [18].…”

Section: Limiting Forms Of the Dispersion Relationsupporting

confidence: 90%

An asymptotic decoupling method for waves in layered media

Chapman

2013

Proc. R. Soc. A.

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This paper presents a technique, asymptotic decoupling, for analysing wave propagation in multilayered media. The technique leads to a hierarchy of approximations to the exact dispersion relation, obtained from finite-product approximations to loworder dispersion relations appearing as factors in the asymptotically decoupled limits. Levels of refinement may be added or removed according to the frequency range of interest, the degree of accuracy required, and the material and geometrical parameters of the different layers. This is shown to be particularly useful in stiff problems, because unlimited accuracy is obtainable without redundancy even when Young's moduli and the thicknesses of the layers differ by many orders of magnitude, for example in a stiff sandwich plate with a very soft core. Full details are presented for a non-trivial example, that of antisymmetric waves in a three-layered planar elastic waveguide. Comparisons are made with two widely used approximations, Tiersten's thinskin approximation and the composite Timoshenko approximation. The mathematical basis of the paper is the asymptotic decoupling of the wave motion in different layers in the limit of indefinitely large or small density ratio.

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Section: Limiting Forms Of the Dispersion Relationsupporting

confidence: 90%

An asymptotic decoupling method for waves in layered media

Chapman

2013

Proc. R. Soc. A.

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“…It has a potential to be extended for a more sophis-40 ticated setup. In particular the obtained results could be applied to analysis of the lowest cut-off frequencies [10,11] of sandwich plates and shells and also have some more general implications to 2D and 3D dynamic problems for elastic structures with contrast material parameters. In the latter case the perturbation scheme presented in this paper may need to be amended by including numerical 45 routines.…”

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confidence: 95%

Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods

Kaplunov

Приказчиков

Sergushova

2016

Journal of Sound and Vibration

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The results of a multi-parametric analysis of the near-rigid body motions of a three-component strongly inhomogeneous elastic rod are presented. It is demonstrated that the values of the associated lowest natural frequencies tend to zero at large/small ratios of material and geometric parameters. The low-frequency behavior is classified into global and local regimes and the general conditions supporting global low-frequency regimes are derived. As an example, a rod with piecewise uniform properties is considered. A perturbation procedure oriented to a more general setup is developed.

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“…The conventional AHM seems to be a counterpart of the classical theories for thin plates, shells and rods. A theoretical framework for the asymptotic theories of long wave motion in plates and layered media was developed by Rogerson et al (2006Rogerson et al ( , 2007Rogerson et al ( , 2009), Lutianov and Rogerson (2010), Mukhomodyarov and Rogerson (2012). Homogenization of nonlinear dynamic problems was considered by Andrianov et al (2011Andrianov et al ( , 2013.…”

Section: Measuring the Characteristics Of Nonlinear Waves Enables Detmentioning

confidence: 99%

Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface

Danishevskyy

Kaplunov

Rogerson

2015

International Journal of Non-Linear Mechanics

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Abstract. The propagation of nonlinear elastic anti-plane shear waves in a unidirectional fibre-reinforced composite material is studied. A model of structural nonlinearity is considered, for which the nonlinear behaviour of the composite solid is caused by imperfect bonding at the "fibre-matrix" interface. A macroscopic wave equation accounting for the effects of nonlinearity and dispersion is derived using the higher-order asymptotic homogenization method.Explicit analytical solutions for stationary nonlinear strain waves are obtained.This type of nonlinearity has a crucial influence on the wave propagation mode: for soft nonlinearity, localised shock (kink) waves are developed, while for hard nonlinearity localised bell-shaped waves appear. Numerical results are presented and the areas of practical applicability of linear and nonlinear, long-and shortwave approaches discussed.

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Long wave motion in layered elastic media

Cited by 10 publications

References 13 publications

An asymptotic decoupling method for waves in layered media

An asymptotic decoupling method for waves in layered media

Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods

Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface

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