Spectral analysis of elastic pulses backscattered from two cylindrical cavities in a solid. Part I

A series solution for the scattering of plane harmonic pressure waves from two cylindrical cavities in an elastic solid is derived in terms of cylindrical wavefunctions. The scattered waves are expressed as an infinite sum of various orders of scattering, the first order being the scattering of the incident wave by each of the two cavities, and each successive order being expressed in terms of the single cylinder scattering coefficients. The exact steady-state solution for the scattered radial stress is derived, which is also the power spectra of the scattered pulse due to an incident pulse of delta function in time. These results are simplified further for the case of backscattering at farfields.

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