Green’s function and its non-wave nature for SH-wave in inhomogeneous elastic solid. (English) Zbl 1211.74123
Summary: Impulsive and time-harmonic Green’s functions are obtained for SH waves in an inhomogeneous elastic solid. The velocity variation is assumed to be a power function of one space variable. A parametric expression for wave fronts and rays are derived from the exact Green’s function. Time development of wave front shape and the ray trajectory are also illustrated. It is found that a material singular point, where the wave velocity is infinite, generates a new wave which has a finite jump at its front. A time-harmonic Green’s function is also derived from the impulsive Green’s function. A critical frequency that distinguishes the wave nature of the response is found in the case of a linear velocity variation, and we found that a time-harmonic source with lower frequency than the critical one cannot produce any waves in the inhomogeneous solid. This is a very interesting result for the dynamic behavior of inhomogeneous media.
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