Diffraction of flexural waves by cracks in orthotropic thin elastic plates. Part II. Far field analysis

The scattered field arising from diffraction of a plane flexural wave by a semi-infinite crack in an orthotropic Kirchhoff thin plate is analysed. The crack is aligned with a principal direction of the material, so that two of the plate's three planes of symmetry are preserved. An asymptotic approximation is derived via the method of steepest descents, and explicit expressions are given for the most significant contributions. The effects of anisotropy upon the scattered field are made clear, and numerical results are presented for several typical engineering materials.

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Flexural wave filtering and platonic polarisers in thin elastic plates

The Quarterly Journal of Mechanics and Applied Mathematics ◽

10.1093/qjmam/hbt013 ◽

2013 ◽

Vol 66 (4) ◽

pp. 437-463 ◽

Cited By ~ 8

Author(s):

M. J. A. Smith ◽

M. H. Meylan ◽

R. C. McPhedran

Keyword(s):

Flexural Wave ◽

Elastic Plates ◽

Thin Elastic Plates

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Active cloaking of inclusions for flexural waves in thin elastic plates

The Quarterly Journal of Mechanics and Applied Mathematics ◽

10.1093/qjmam/hbv007 ◽

2015 ◽

Vol 68 (3) ◽

pp. 263-288 ◽

Cited By ~ 18

Author(s):

J. O'Neill ◽

Ö. Selsil ◽

R.C. McPhedran ◽

A.B. Movchan ◽

N.V. Movchan

Keyword(s):

Elastic Plates ◽

Flexural Waves ◽

Thin Elastic Plates

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Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I Formal solution

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2004.1418 ◽

2005 ◽

Vol 461 (2063) ◽

pp. 3413-3436 ◽

Cited By ~ 7

Author(s):

Ian Thompson ◽

I. David Abrahams

Keyword(s):

Formal Solution ◽

Plane Waves ◽

Flexural Wave ◽

Elastic Plates ◽

Flexural Waves ◽

Incident Plane ◽

Principal Directions ◽

Orthotropic Thin Plate ◽

Non Destructive ◽

Kirchhoff Theory

The problem of flexural wave diffraction by a semi-infinite crack in an infinite orthotropic thin plate is considered. Such models have application to the ultrasonic non-destructive inspection of thin components, such as aeroplane wings. For simplicity, the plate is modelled using Kirchhoff theory, and the crack is chosen to be aligned along one of the principal directions of material orthotropy. For incident plane waves, an exact analytical expression for the scattered field is derived by means of the Wiener–Hopf technique. In this model problem, the Wiener–Hopf kernel is scalar and its factorization is expressed in terms of simple, definite, non-singular contour integrals. A detailed numerical evaluation of the solution will be provided in the second part of this work.

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Scattering Reduction and Resonant Trapping of Flexural Waves: Two Rings to Rule Them

Applied Sciences ◽

10.3390/app11104462 ◽

2021 ◽

Vol 11 (10) ◽

pp. 4462

Author(s):

Alexander B. Movchan ◽

Ross C. McPhedran ◽

Giorgio Carta

Keyword(s):

Thin Plate ◽

High Frequency ◽

Finite Element Models ◽

Vibration Modes ◽

Elastic Plates ◽

Flexural Waves ◽

Double Ring ◽

Elastic Thin Plate ◽

Equivalent Mass ◽

Single Mass

In this paper, we discuss two problems concerning scattering and localisation of flexural waves in structured elastic plates. Firstly, we compare the scattering amplitudes of waves in a thin plate, generated by a point source, due to a single mass and to a large number of smaller masses, having the same equivalent mass and located around a circle. We show that in the second case, the scattering can be reduced, in particular in the medium- and high-frequency regimes. Secondly, we develop a homogenised model for a double-ring cluster of spring-mass resonators, connected to an elastic thin plate. We determine the conditions for which the plate exhibits vibration modes trapped between the two rings. Further, we show that the frequencies of the localised modes can be tuned by varying the geometry of the two rings and the characteristics of the resonators. The analytical results are corroborated by numerical simulations performed with independent finite element models.

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