Edge waves and resonance on elastic structures: An overview

Lawrie, Jane B.; Kaplunov, Julius

doi:10.1177/1081286511412281

Cited by 72 publications

(65 citation statements)

References 59 publications

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“…The effect of geometric non-linearity also can be incorporated in order to justify the analogues adhoc non-linear equation in [22]. Finally, we mention applications dealing with localised vibrations, including those caused by shape imperfections as well as shell edge waves, see review article [25] and references therein.…”

Section: Discussionmentioning

confidence: 99%

Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

2016

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A new asymptotic approximation of the dynamic equations in the 2D classical theory of thin elastic shells is established for a circular cylindrical shell. It governs long wave vibrations in the vicinity of the lowest cut-off frequency. At a fixed circumferential wave number the latter corresponds to the eigen frequency of in-plane vibrations of a thin almost inextensible ring. It is stressed that the well-known semi-membrane theory of cylindrical shells is not suitable for tackling a near-cut-off behaviour. The dispersion relation within the framework of the developed formulation coincides with the asymptotic expansion of the dispersion relation originating from full 2D shell equations. Asymptotic analysis also enables refining the geometric hypotheses underlying various adhoc setups, including the assumption on vanishing of shear and circumferential midsurface deformations used in the semi-membrane theory. The obtained results may be of interest for dynamic modelling of elongated cylindrical thin walled structures, such as carbon nanotubes.

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Section: Discussionmentioning

confidence: 99%

Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

2016

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“…It is peculiar that this wave was rediscovered several times, for more detail see Norris et al (2000) and Lawrie & Kaplunov (2012).…”

Section: Bending Edge Wave On a Thin Platementioning

confidence: 99%

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

Kaplunov

Приказчиков

2017

Advances in Applied Mechanics

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Abstract:Explicit asymptotic formulations are derived for Rayleigh and Rayleigh-type interfacial and edge waves. The hyperbolic-elliptic duality of surface and interfacial waves is established, along with the parabolic-elliptic duality of the dispersive edge wave on a Kirchhoff plate. The effects of anisotropy, piezoelectricity, thin elastic coatings, and mixed boundary conditions are taken into consideration. The advantages of the developed approach are illustrated by steady-state and transient problems for a moving load on an elastic half-space.

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“…is a well-known constant for the bending edge wave, 1,3 depending on the Poisson's ratio only, note that c e < 1 for all 0 < 1. It may be now observed from the dispersion relation (14) that…”

Section: J¼1mentioning

confidence: 99%

The edge wave on an elastically supported Kirchhoff plate

Kaplunov

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Rogerson

et al. 2014

The Journal of the Acoustical Society of America

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This Letter deals with an analysis of bending edge waves propagating along the free edge of a Kirchhoff plate supported by a Winkler foundation. The presence of a foundation leads to a nonzero cut-off frequency for this wave, along with a local minimum of the associated phase velocity. This minimum phase velocity corresponds to a critical speed of an edge moving load and is analogous to that in the classical 1D moving load problem for an elastically supported beam.

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Edge waves and resonance on elastic structures: An overview

Cited by 72 publications

References 59 publications

Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

The edge wave on an elastically supported Kirchhoff plate

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