Rayleigh waves for a discrete elastic paraxial equation

Journal Article · Wed Dec 01 04:00:00 EST 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.48.4815· OSTI ID:5740798

Hedstrom, G W ^[1]

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1. Lawrence Livermore National Laboratory, P.O. Box 808, L-321, Livermore, California 94550 (United States)

We investigate the effects of a free surface on the 45[degree] paraxial equation for linear elasticity in a half space. We show that the 45[degree] equation has no Rayleigh wave and that it has an exponentially growing instability. We also examine a standard finite-difference approximation to the elastic paraxial equation. We show that the discrete equation also has an exponential instability, but this may be removed by projection. We also find that the discrete elastic paraxial equation has no Rayleigh waves when the mesh size is small, but a coarse mesh gives two Rayleigh waves. Moreover, by a proper choice of the mesh sizes, we may select a discretization so that one of these discrete Rayleigh waves has the speed of a physical Rayleigh wave, and we may project out the nonphysical discrete Rayleigh wave.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5740798
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 48:6; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360606* -- Other Materials-- Physical Properties-- (1992-)
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
ELASTICITY
ELASTOMERS
EQUATIONS
FOURIER TRANSFORMATION
INSTABILITY
INTEGRAL TRANSFORMATIONS
MECHANICAL PROPERTIES
PARTIAL DIFFERENTIAL EQUATIONS
POLYMERS
RAYLEIGH WAVES
SEISMIC SURFACE WAVES
SEISMIC WAVES
SHEAR
TENSILE PROPERTIES
TRANSFORMATIONS
TWO-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS