 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 49, Issue 4 / 2014 | Next article >> |
| R.V. Goldstein, V.A. Gorodtsov, and D.S. Lisovenko, "Rayleigh and Love Surface Waves in Isotropic Media with Negative Poisson's Ratio," Mech. Solids. 49 (4), 422-434 (2014) |
| Year |
2014 |
Volume |
49 |
Number |
4 |
Pages |
422-434 |
| DOI |
10.3103/S0025654414040074 |
| Title |
Rayleigh and Love Surface Waves in Isotropic Media with Negative Poisson's Ratio |
| Author(s) |
R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, goldst@ipmnet.ru)
V.A. Gorodtsov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, gorod@ipmnet.ru)
D.S. Lisovenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, lisovenk@ipmnet.ru) |
| Abstract |
The behavior of Rayleigh surface waves and the first mode of the Love waves in isotropic media with positive and negative Poisson's ratio is compared. It is shown that the Rayleigh wave velocity increases with decreasing Poisson's ratio, and it increases especially rapidly for negative Poisson's ratios less than −0.75. It is demonstrated that, for positive Poisson's ratios, the vertical component of the Rayleigh wave displacements decays with depth after some initial increase, while for negative Poisson's ratios, there is a monotone decrease. The Rayleigh waves are characterized by elliptic trajectories of the particle motion with the change of the rotation direction at critical depths and by the linear vertical polarization at these depths. It is found that the elliptic orbits are less elongated and the critical depths are greater for negative Poisson's ratios. It is shown that the stress distribution in the Rayleigh waves varies nonmonotonically with the dimensionless depth as (positive or negative) Poisson's ratio varies. The stresses increase strongly only as Poisson's ratio tends to −1.
It is shown that, in the case of an incompressible thin covering layer, the velocity of the first mode of the Love waves strongly increases for negative Poisson's ratios of the half-space material. If the thickness of the incompressible layer is large, then the wave very weakly penetrates into the half-space for any value of its Poisson's ratio. For negative Poisson's ratios, the Love wave in a layer and a half-space is mainly localized in the covering layer for any values of its thickness and weakly penetrates into the half-space. For the first mode of the Love waves, it was discovered that there is a strong increase in the maximum of one of the shear stresses on the interface between the covering layer and the half-space as Poisson's ratios of both materials decrease. For the other shear stress, there is a stress jump on the interface and a more complicated dependence of the stress on Poisson's ratio on both sides of the interface. |
| Keywords |
surface wave, Rayleigh wave, Love wave, Poisson's ratio, dispersion equation, thin covering layer, thick layer, displacement, shear stresses, normal stresses |
| References |
| 1. | L. D. Landau and E. M. Lifshits,
Theoretical Physics. Vol. 7: Theory of Elasticity
(Nauka, Moscow, 1967, 1987; Pergamon Press, Oxford, 1970). |
| 2. | I. A. Viktorov,
Sonic Surface Waves in Solids
(Nauka, Moscow, 1981)
[in Russian]. |
| 3. | R. S. Lakes,
"Foam Structures with a Negative Poisson's Ratio,"
Science
235 (4792), 1038-1040 (1987). |
| 4. | R. V. Goldstein, V. A. Gorodtsov, and D. S. Lisovenko,
"Auxetic Mechanics of Crystalline Materials,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 43-62 (2010)
[Mech. Solids (Engl. Transl.)
45 (4), 529-545 (2010)]. |
| 5. | T.-C. Lim, P. Cheang, and F. Scarpa,
"Wave Motion in Auxetic Solid,"
Phys. Status Solidi. Ser. B
251 (2), 388-396 (2013). |
| 6. | A. W. Lipsett and A. I. Beltzer,
"Reexamination of Dynamic Problems of Elasticity for Negative Poisson Ratio,"
J. Acoust. Soc. Amer.
84 (6), 2179-2186 (1988). |
|
| Received |
26 December 2013 |
| Link to Fulltext |
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