SOME WAVE PROPAGATION PROBLEMS IN A BOUNDED, HETEROGENEOUS, ELASTIC MEDIUM.
STANFORD UNIV CALIF DEPT OF AERONAUTICS AND ASTRONAUTICS
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This report is a study of the relationships existing between the frequency, phase velocity, group velocity, and wave number of mechanical waves propagating in bounded, heterogeneous, linearly elastic media. For single wave systems, which include the Love and pressure waves and are governed by a single second-order ordinary differential equation, Sturmian theory is applicable. Due to the inapplicability of Sturmian theory to two or three coupled, second-order ordinary differential equations, general results of double wave systems, comprised of the pressure and shear-vertical waves and described by these two or three equations, are unobtainable. The analysis is directed towards either very short or very long wavelength waves and proceeds by perturbation or asymptotic methods. For both wave systems, the emphasis is on determining the way in which the phase velocity varies with the wave number. From this relationship, the frequency and group velocity can be found as functions of the wave number.