In the present paper, formulas for the velocity of Rayleigh waves in incompressible isotropic solids subject to a general pure homogeneous prestrain are derived using the theory of cubic equation. They have simple algebraic form and hold for a general strain-energy function. The formulas are concretized for some specific forms of strain-energy function. They then become totally explicit in terms of parameters characterizing the material and the prestrains. These formulas recover the (exact) value of the dimensionless speed of Rayleigh wave in incompressible isotropic elastic materials (without prestrain). Interestingly that, for the case of hydrostatic stress, the formula for the Rayleigh wave velocity does not depend on the type of strain-energy function.
Issue Section:
Research Papers
1.
Rayleigh
, L.
, 1885, “On Waves Propagating Along the Plane Surface of an Elastic Solid
,” Proc. R. Soc. London
0370-1662, 17
, pp. 4
–11
.2.
Adams
, S. D. M.
, Craster
, R. V.
, Williams
, D. P.
, 2007, “Rayleigh Waves Guided by Topography
,” Proc. R. Soc. London, Ser. A
0950-1207, 463
, pp. 531
–550
.3.
Rahman
, M.
, and Barber
, J. R.
, 1995, “Exact Expression for the Roots of the Secular Equation for Rayleigh Waves
,” ASME J. Appl. Mech.
0021-8936, 62
, pp. 250
–252
.4.
Nkemzi
, D.
, 1997, “A New Formula for the Velocity of Rayleigh Waves
,” Wave Motion
0165-2125, 26
, pp. 199
–205
.5.
Destrade
, M.
, 2003, “Rayleigh Waves in Symmetry Planes of Crystals: Explicit Secular Equations and Some Explicit Wave Speeds
,” Mech. Mater.
0167-6636, 35
, pp. 931
–939
.6.
Malischewsky
, P. G.
, 2000, “Comment to ‘A New Formula for Velocity of Rayleigh Waves’ by D. Nkemzi [Wave Motion 26 (1997) 199–205]
,” Wave Motion
0165-2125, 31
, pp. 93
–96
.7.
Pham
, C. V.
, and Ogden
, R. W.
, 2004, “On Formulas for the Rayleigh Wave Speed
,” Wave Motion
0165-2125, 39
, pp. 191
–197
.8.
Ting
, T. C. T.
, 2002, “A Unified Formalism for Elastostatics or Steady State Motion of Compressible or Incompressible Anisotropic Elastic Materials
,” Int. J. Solids Struct.
0020-7683, 39
, pp. 5427
–5445
.9.
Ogden
, R. W.
, and Pham
, C. V.
, 2004, “On Rayleigh Waves in Incompressible Orthotropic Elastic Solids
,” J. Acoust. Soc. Am.
0001-4966, 115
(2
), pp. 530
–533
.10.
Pham
, C. V.
, and Ogden
, R. W.
, 2004, “Formulas for the Rayleigh Wave Speed in Orthotropic Elastic Solids
,” Arch. Mech.
0373-2029, 56
(3
), pp. 247
–265
.11.
Pham
, C. V.
, and Ogden
, R. W.
, 2005, “On a General Formula for the Rayleigh Wave Speed in Orthotropic Elastic Solids
,” Meccanica
0025-6455, 40
, pp. 147
–161
.12.
Hirao
, M.
, Fukuoka
, H.
, and Hori
, K.
, 1981, “Acoustoelastic Effect of Rayleigh Surface Wave in Isotropic Material
,” ASME J. Appl. Mech.
0021-8936, 48
, pp. 119
–124
.13.
Delsanto
, P. P.
, and Clark
, A. V.
, 1987, “Rayleigh Wave Propagation in Deformed Orthotropic Materials
,” J. Acoust. Soc. Am.
0001-4966, 81
(4
), pp. 952
–960
.14.
Duquennoy
, M.
, Ouaftouh
, M.
, and Ourak
, M.
, 1999, “Ultrasonic Evaluation of Stresses in Orthotropic Materials Using Rayleigh Waves
,” NDT & E Int.
0963-8695, 32
, pp. 189
–199
.15.
Duquennoy
, M.
, Devos
, D.
, Ouaftouh
, M.
, Lochegnies
, D.
, and Roméro
, E.
, 2006, “Ultrasonic Evaluation of Residual Stresses in Flat Glass Tempering: Comparing Experimental Investigation and Numerical Modeling
,” J. Acoust. Soc. Am.
0001-4966, 119
(6
), pp. 3773
–3781
.16.
Tanuma
, K.
, and Man
, C. -S.
, 2006, “Pertubation Formula for Phase Velocity of Rayleigh Waves in Prestressed Anisotropic Media
,” J. Elast.
0374-3535, 85
, pp. 21
–37
.17.
Song
, Y. Q.
, and Fu
, Y. B.
, 2007, “A Note on Perturbation Formulae for the Surface-Wave Speed Due to Perturbations in Material Properties
,” J. Elast.
0374-3535, 88
, pp. 187
–192
.18.
Dowaikh
, M. A.
, and Ogden
, R. W.
, 1990, “On Surface Waves and Deformations in a Pre-Stressed Incompressible Elastic Solids
,” IMA J. Appl. Math.
0272-4960, 44
, pp. 261
–284
.19.
Cowles
, W. H.
, and Thompson
, J. E.
, 1947, Algebra
, Van Nostrand
, New York
.20.
Ewing
, W. M.
, Jardetzky
, W. S.
, and Press
, F.
, 1957, Elastic Waves in Layered Media
, McGraw-Hill
, New York
.21.
Malischewsky
, P. G.
, 2000, “Some Special Solutions of Rayleigh’s Equation and the Reflections of Body Waves at a Free Surface
,” Geofis. Int.
0016-7169, 39
, pp. 155
–160
.22.
Novozhilov
, V. V.
, 1961, Theory of Elasticity
, Pergamon
, Oxford
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
