Scattering of an elastic wave by a rigid sphere in a semi-bounded domain: Fìz.-mat. model. ìnf. tehnol. 2020, 28:81-91 - Selezov, Ihor (PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, 2020)
The problem of scattering of plane elastic waves by a rigid sphere near a rigid boundary is considered. This leads to the appearance of multiply re-reflected dilatation and shear waves, which generate strong oscillations of the wave field. The problem for a vector operator of the shear waves is reduced to the definition of scalar functions as a consequence of symmetry. Approximate formulas for the far field and the long-wave Rayleigh approximation are presented. The construction of multiply re-reflected waves by the image method is presented and analyzed. Calculations of the scattered wave fields are plotted in the form of scattering diagrams. References Selezov, I. T., Kryvonos, Yu. G., Gandzha, I. S. (2018). Wave propagation and diffraction. Mathematical methods and applications. Springer. Selezov, I. T. (1993). Diffraction of waves by radially inhomogeneous inclusions. Physical Express, March., 1(2), 104 — 115. Jackson, J. D. (1962). Classic electrodynamics. John Wiley & Sons. Kratzer, A., Franz W. (1963). Transzendente Funktionen. Leipzig: Geest & Portig. Watson, G. N. (1945). A treatise of the theory of Bessel functions. Cambride, New York:Macmillan. Friedman, B., Russek, J. (1954). Addition theorem for spherical waves. Quart. Appl. Math., 12(1), 13-23. DOI https://doi.org/10.1090/qam/60649 Knopoff, L. (1959). Scattering of compression waves by spherical obstacles. Geophysics, 24(1), 30-39. DOI http://dx.doi.org/10.1190/1.1438562 Ying, C. F., Truell, R. (1956). Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid. J. Appl. Physics, 27, 1086-1097. DOI https://doi.org/10.1063/1.1722545 Jain, D. L., Kanwal, R. P. (1980). Scattering of elastic waves by an elastic sphere. Int. J. Eng. Sci., 18(9), 1117-1127. DOI https://doi.org/10.1016/0020-7225(80)90113-5 Morse, Ph. M., Feshbach, H. (1953). Methods of theoretical physics. New York, Mc Gray Hill Book Company. Yale, S. (2016). Seismic diffraction. SEG Geophysics reprint series. Society of Exploration Geopgycists, 30.