Abstract
The frequency equation giving the phase velocity of a wave at the edge of a thick plate under initial stress is obtained. Some particular cases are discussed to derive (a) the velocity of edge waves in a thin plate and (b) the velocity of Rayleigh waves in a plate of infinite thickness under initial stress.
The results are compared with those for zero initial stress.
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Abbreviations
- P=−T 11 :
-
initial stress along x direction
- s ij :
-
incremental stress components, i, j=1, 2
- u, v :
-
displacement components along x and y directions, respectively
- ρ :
-
density of the material
- μ :
-
rigidity of the material at initial stress
- λ 1 :
-
extension ratio in length in x direction due to initial stress
- e ij :
-
strain components with respect to rotated axes, i, j=x, y
- β :
-
velocity of shear wave under initial stress
- α :
-
frequency of oscillation
- λ :
-
2π/wavelength
- C E :
-
velocity of edge wave
- C R :
-
velocity of Rayleigh wave
- \(w = \frac{1}{2}\left( {\frac{{\partial \upsilon }}{{\partial x}} - \frac{{\partial u}}{{\partial y}}} \right)\) :
-
rotational component about z axis
References
Ewing, W. M., W. S. Jardetzky and F. Press, Elastic Waves in Layered Media, McGraw-Hill, New York 1957.
Miklowitz, J., Appl. Mech. Rev. 13 (1960) 865.
Kumar, S., Edge Waves in Plates, Int. Symp. on Stress Wave Propagation in Materials, Pennsylvania State University (Penn.), U.S.A. 1959.
Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Dover, New York 1944.
Biot, M. A., Mechanics of Incremental Deformations Wiley, New York 1965.
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Das, S.C., Dey, S. Edge waves under initial stress. Appl. Sci. Res. 22, 382–389 (1970). https://doi.org/10.1007/BF00400543
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DOI: https://doi.org/10.1007/BF00400543