Reciprocal Relations for Transmission Coefficients: Theory and Application

The paper presents a rigorous proof of certain intuitively plausible reciprocal relations for time harmonic plane-wave transmission and reflection at the interface between a fluid and an anisotropic elastic solid. Precise forms of the reciprocity relations for the transmission coefficients, and for the transmitted energy fluxes are derived, based on the reciprocity theorem of elastodynamics. It is shown that the reciprocity relations can be used in conjunction with measured values of peak amplitudes for transmission through a slab of the solid (water-solid-water), to obtain the water-solid coefficients. Experiments were performed for a slab of a unidirectional fiber-reinforced composite. Good agreement of the experimentally measured transmission coefficients with theoretical values was obtained.