Some special solutions of Rayleigh’s equation and the reflections of body waves at a free surface
Contenido principal del artículo
Resumen
A partir de una nueva representación de las raíces de la ecuación de Rayleigh para todos los valores de la relación de Poisson v, se deriva una nueva expresión analítica para la raíz doble. Esta relaciona de una manera simple a los ángulos especiales de Brewster, que aparecen para ondas longitudinales o transversales incidentes en una superficie libre. Al mismo tiempo las peculiaridades de los coeficientes de reflexión RPS y RSP son investigadas.
Detalles del artículo
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
Citas
ACHENBACH, J. D., 1984. Wave Propagation in Elastic Solids, Elsevier, New York.
ARENBERG, D. L., 1948. Ultrasonic Solid Delay Lines, J. Acoust. Soc. America, 20, 1-26. DOI: https://doi.org/10.1121/1.1906343
EWING, W. M., W. S. JARDETZKY and F. PRESS, 1957. Elastic Waves in Layered Media, Mc Graw-Hill Inc., New York. DOI: https://doi.org/10.1063/1.3060203
HAYES, M. and R. S. RIVLIN, 1962. A Note on the Secular Equation for Rayleigh Waves. Z. Angew. Math. Phys., 13, 80-83. DOI: https://doi.org/10.1007/BF01600759
KAMEL, A. and L. B. FELSEN, 1981. Hybrid Ray-Mode Formulation of SH-Motion in a Two-Layer Half-Space. Bull. Seism. Soc. Am., 71, 1763-1781. DOI: https://doi.org/10.1785/BSSA0710061763
LAKES, R. S., 1987. Negative Poisson’s Ratio Materials. Science, 238, 551. DOI: https://doi.org/10.1126/science.238.4826.551-a
MALISCHEWSKY, P., 1971. Consideration of Certain Singularities in Haskell’s Matrix Method. Gerl. Beitr. Geophys., 80, 457-462.
MALISCHEWSKY, P., 1985. A Semi-Analytical Method for the Calculation of Leaking Love-Wave Modes. Wave Motion, 7, 253-262. DOI: https://doi.org/10.1016/0165-2125(85)90011-3
MALISCHEWSKY, P., 1987. Surface Waves and Discontinuities, Elsevier, Amsterdam. DOI: https://doi.org/10.1515/9783112756676
MALISCHEWSKY, P. G., 2000. Comment to “A New Formula for the Velocity of Rayleigh Waves” by D. Nkemzi. Wave Motion, 31, 93-96. DOI: https://doi.org/10.1016/S0165-2125(99)00025-6
MARCUSE, D., 1974. Theory of Dielectric Optical Waveguides, Academic Press, New York.
MAUPIN, V., 1996. The Radiation Modes of a Vertically Varying Half-Space: a New Representation of the Complete Green’s Function in Terms of Modes. Geophys. J. Int., 126, 762-780. DOI: https://doi.org/10.1111/j.1365-246X.1996.tb04701.x
NARASIMHAN, M. N. L., 1993. Principles of Continuum Mechanics, John Wiley & Sons, New York.
NKEMZI, D., 1997. A New Formula for the Velocity of Rayleigh Waves. Wave Motion, 26, 199-205. DOI: https://doi.org/10.1016/S0165-2125(97)00004-8
PAPAZACHOS, B., 1964. Angle of Incidence and Amplitude Ratio of P and PP Waves. Bull. Seism. Soc. Am., 54, 105-121. DOI: https://doi.org/10.1785/BSSA0540010105
RAHMAN, M. and J. R. BARBER, 1995. Exact Expressions for the Roots of the Secular Equation for Rayleigh Waves. ASME J. Appl. Mech., 62, 250-252. DOI: https://doi.org/10.1115/1.2895917
RAYLEIGH, J. W. S., 1885. On Waves Propagating along the Plane Surface of an Elastic Solid. Proc. London Math. Soc., 17, 4-11. DOI: https://doi.org/10.1112/plms/s1-17.1.4