Rayleigh-type wave propagation in an auxetic dielectric

Drzewiecki, Andrzej

doi:10.2140/jomms.2012.7.277

Cited by 4 publications

(3 citation statements)

References 8 publications

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“…For this reason investigations on wave propagation through auxetic solids in the past have not only been confined to isotropic auxetic bulk materials [11][12][13] and auxetic halfspace [14][15][16][17][18][19][20][21][22][23][24][25], but also extended to isotropic auxetic rods [26][27][28][29][30], and isotropic auxetic plates [28][29][30][31]. It should also be pointed out at this juncture that a number of auxetic structures are 2D or anisotropic [32][33][34][35][36], and are therefore not subjected to the analysis of 3D isotropy.…”

Section: Introductionmentioning

confidence: 99%

Longitudinal wave motion in width-constrained auxetic plates

Lim

2016

Smart Mater. Struct.

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This paper investigates the longitudinal wave velocity in auxetic plates in comparison to conventional ones, in which the plate is constrained from motion in the width direction. By taking into account the thickness change of the plate and its corresponding change in density, the developed wave velocity is casted not only as a function of Young's modulus and density, but also in terms of Poisson's ratio and longitudinal strain. Results show that density and thickness variations compensate for one another when the Poisson's ratio is positive, but add up when the Poisson's ratio is negative. Results also reveal that the classical model of longitudinal wave velocity for the plate is accurate when the Poisson's ratio is about 1/3; at this Poisson's ratio the influence from density and thickness variations cancel each other. Comparison between the current corrected model and the density-corrected Rayleigh-Lamb model reveals a number of consistent trends, while the discrepancies are elucidated. If the plate material possesses a negative Poisson's ratio, the deviation of the actual wave velocity from the classical model becomes significant; auxeticity suppresses and enhances the wave velocity in compressive and tensile impacts, respectively. Hence the use of the corrected model is proposed when predicting longitudinal waves in width-constrained auxetic plates, and auxetic materials can be harnessed for effectively controlling wave velocities in thin-walled structures.

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Section: Introductionmentioning

confidence: 99%

Longitudinal wave motion in width-constrained auxetic plates

Lim

2016

Smart Mater. Struct.

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“…Coating of such materials with a well‐designed outer layer has been shown to allow certain undamped surface waves to propagate at frequencies laying in radiative bands of bulk waves . In addition, the reader is referred to the investigations by Vinh and Malischewsky , Scarpa and Malischewsky , Maruszewski et al , Malischewsky et al , Drzewiecki , Zieliński et al , and Lim et al . It is also of interest to note a comparison between the Rayleigh and first mode of the Love surface waves in isotropic conventional and auxetic media by Goldstein et al .…”

Section: Introductionmentioning

confidence: 99%

Effect of longitudinal stress on wave propagation in width‐constrained elastic plates with arbitrary Poisson's ratio

Sobieszczyk

Majka

Kuźma

et al. 2015

Physica Status Solidi (b)

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The Helmholtz wave equation is derived for longitudinal waves in an elastic plate of arbitrary thickness placed in a rigid gantry ensuring a constant width. The whole range of Poisson's ratio allowed for isotropic elastic media constrained in this way is considered. The wave speed is shown to increase under a constant longitudinal compressive stress applied to the front face of the plate and to decrease when the applied stress is tensile. The effect is most pronounced for zero Poisson's ratio and it vanishes for the limiting permitted values, i.e., 1 or À1. The reported results also describe the combined effect of longitudinal stress and Poisson's ratio on the wave speed. These findings provide guidelines for designing devices aimed at a passive control of propagation of longitudinal waves in thin-walled structures.

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“…The dynamics of the subsonic leaky waves and that of the typical supersonic leaky waves is somewhat different [13], the formers being characterized by a strong reactive amplitude, i.e., shifted in phase by p=2 with respect to the external force, whereas the latters show a maximum in the local density of states. The literature on surface dynamics in auxetics has grown recently [14][15][16][17][18][19][20][21][22], but the problem of concave surfaces was not considered to the best of our knowledge.…”

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confidence: 99%

Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio – Part I: Clean inner surface

Sobieszczyk

Gałązka

Trzupek

et al. 2015

Physica Status Solidi (b)

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The dynamics of the inner surface of an infinitely long circular‐cylindrical cavity in an isotropic elastic medium is studied in the whole range of the Poisson's ratio including negative values characteristic of auxetic materials. The existence of the unique long‐lived propagation mode (true surface wave, TSW) has been confirmed on the clean surface with the following properties: (i) existence of a low frequency cut‐off for all the azimuthal indices n except for n = 1 (flexural mode), (ii) polarization tending to that of the Rayleigh wave in the short wavelength limit, (iii) Airy phases (inflection points of dispersion curves) for n < 6 that shift towards short wave region when the Poisson's ratio becomes negative. A number of propagation modes with complex frequencies, i.e., with finite life times (surface leaky waves, pseudo surface waves) are found. The torsional leaky mode transforms into the skimming shear‐horizontal wave (Love wave) in the short wavelength limit. An axial–radial leaky mode, similar to the Rayleigh wave but with reverse elliptical polarization turns out a physical solution except for extremely short wavelengths. A strong radial component of the longitudinal resonance occurs at wavelengths comparable to the cavity's radius especially in the incompressible limit.

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Rayleigh-type wave propagation in an auxetic dielectric

Abstract: The propagation of Rayleigh-type waves in an elastic, isotropic, dielectric half-space for some orientation of the external electric field is considered, with Poisson's ratio in the range −1 < ν < 0.5.

Cited by 4 publications

References 8 publications

Longitudinal wave motion in width-constrained auxetic plates

Longitudinal wave motion in width-constrained auxetic plates

Effect of longitudinal stress on wave propagation in width‐constrained elastic plates with arbitrary Poisson's ratio

Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio – Part I: Clean inner surface

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