Abstract
In the present paper, a radiation condition for time-harmonic elastic waves in a homogeneous, isotropic, perfectly elastic medium is presented. It is based upon certain physical considerations pertaining to the elastodynamic radiation generated by a source of finite extent. In it, the particle displacement on and the traction across a spherical surface around the source occur. Separate conditions are imposed on the radial and the angular parts of these quantities. It is shown that the resulting far-field radiation characteristics for the particle displacement are in accordance with the properties that could be expected from the physical considerations we have started with.
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Sommerfeld, A., Jber. Deutsch. Math. Verein 21 (1912) 309.
Sommerfeld, A., Verlesungen über Theoretische Physik, Band VI, Dieterich'sche Verlagsbuchhandlung Inh. W. Klemm, Wiesbaden, 1947, p. 191–202.
Silver, S., Microwave Antenna Theory and Design, McGraw-Hill Book Company Inc., New York, 1949, p. 73–90.
Müller, C., Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen, Springer-Verlag OHG., Berlin-Göttingen-Heidelberg, 1957, p. 136.
Wilcox, C. H., Arch. Rat. Mech. and Analysis 3 (1959) 133.
Stoker, J. J., Water Waves, Interscience Publishers Inc., New York, 1957, p. 174–181.
Auld, B. A., Acoustic Fields and Waves in Solids, Vol. I, John Wiley & Sons, New York, 1973, p. 45.
Achenbach, J. D., Wave Propagation in Elastic Solids, North-Holland Publ. Co., Amsterdam, 1973, p. 53.
Tan, T. H., Appl. Sci. Res. 31 (1975) 29.
Rellich, F., Jber. Deutsch. Math. Verein 53 (1943) 57.
Wilcox, C. H., Proc. Amer. Math. Soc. 7 (1956) 271.
Wilcox, C. H., Comm. Pure Appl. Math. 9 (1956) 115.
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The research reported in this paper has been supported by the Netherlands organization for the advancement of pure research (Z.W.O.).
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Tan, T.H. Far-field radiation characteristics of elastic waves and the elastodynamic radiation condition. Appl. sci. Res. 31, 363–375 (1975). https://doi.org/10.1007/BF00418047
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DOI: https://doi.org/10.1007/BF00418047