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Formulas for the Rayleigh wave speed in orthotropic elastic solids

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Formulas for the speed of Rayleigh waves in orthotropic compressible elastic materials are obtained in explicit form by using the theory of cubic equations. Different formulas are obtained by using different forms of the (cubic) secular equation. Each formula is expressed as a continuous function of three dimensionless material parameters, which are the ratios of certain elastic constants. It is interesting to note that one of the formulas includes as a special case the formula obtained recently by Malischewsky for isotropic materials.
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Bibliogr. 17 poz.
  • Faculty of Mathematics, Mechanics and Informatics Hanoi National University 334, Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam
  • Department of Mathematics, University of Glasgow Glasgow G12 8QW, UK
  • 1. Lord Rayleigh, On waves propagated along the plane surface of an elastic solid, Proc. R. Soc. Lond., A 17, 4–11, 1885.
  • 2. M. Rahman and J.R. Barber, Exact expressions for the roots of the secular equation for Rayleigh waves, ASME J. Appl. Mech., 62, 250–252, 1995.
  • 3. D. Nkemzi, A new formula for the velocity of Rayleigh waves, Wave Motion, 26, 199–205, 1997.
  • 4. M. Destrade, Rayleigh waves in symmetry planes of crystals: explicit secular equations and some explicit wave speeds, Mech. Materials, 35, 931–939, 2003.
  • 5. P. G. Malischewsky, Comment to A new formula for the velocity of Rayleigh waves by D. Nkemzi [Wave Motion 26, 199–205, 1997], Wave Motion, 31, 93–96, 2000.
  • 6. M. Romeo, Rayleigh waves on a viscoelastic solid half-space, J. Acoust. Soc. Am., 110, 59–67, 2001.
  • 7. D. Royer, A study of the secular equation for Rayleigh waves using the root locus method, Ultrasonics, 39, 223–225, 2001.
  • 8. Pham Chi Vinh and R. W. Ogden, On formulas for the Rayleigh wave speed, Wave Motion, 39, 191–197, 2004.
  • 9. T. C. T. Ting, A unified formalism for elastostatics or steady state motion of compressible or incompressible anisotropic elastic materials, Int. J. Solids Structures, 39, 5427–5445, 2002.
  • 10. R. W. Ogden and Pham Chi Vinh, On Rayleigh waves in incompressible orthotropic elastic solids, J. Acoust. Soc. Am., 115, 530–533, 2004.
  • 11. M. Destrade, P.A. Martin and T. C. T. Ting, The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics, J. Mech. Phys. Solids, 50, 1453–1468, 2002.
  • 12. P. Chadwick, The existence of pure surface modes in elastic materials with orthorhombic symmetry, J. Sound. Vib., 47, 39–52, 1976.
  • 13. D. Royer and E. Dieulesaint, Rayleigh wave velocity and displacement in orthorhombic, tetragonal, hexagonal, and cubic crystals, J. Acoust. Soc. Am., 76, 1438–1444, 1984.
  • 14. P. Chadwick and N. J. Wilson, The behaviour of elastic surface waves polarized in a plane of material symmetry III, Orthorhombic and cubic media, Proc. R. Soc. Lond., A 438, 225–247, 1992.
  • 15. R. Stoneley, The propagation of surface waves in an elastic medium with orthorhombic symmetry, Geophys. J., 8, 176–186, 1963.
  • 16. W.H. Cowles and J.E. Thompson, Algebra, Van Nostrand, New York 1947.
  • 17. V. G. Mozhaev, Some new ideas in the theory of surface acoustic waves in anisotropic media, [in:] Proceedings of the IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solids, Kluwer, 455–462, 1995.
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