ASYMPTOTIC APPROXIMATION FOR THE ELASTIC NORMAL MODES IN A STRATIFIED SOLID MEDIUM
AIR FORCE CAMBRIDGE RESEARCH LABS HANSCOM AFB MA
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The asymptotic approximation method was applied to the calculation of normal modes of elastic waves in a solid medium. The approximations were based on the assumption that the properties of the medium are slowly varying functions of one coordinate in the sense of a small relative variation within a wave length. A comparison of dispersion curves computed by the approximate theory with those computed by the exact theory for a medium of 2 or 3 homogeneous layers indicated that the approximate theory is fairly accurate for normal modes of higher order than the fifth or sixth. The approximation for the lower modes is considered of some value for rough estimations, provided the approximations are used in conjunction with the limiting forms of the exact theory.
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