A unified approach to the study of reflection and refraction of elastic waves in general anisotropic media is presented. Christoffel equations and boundary conditions for both anisotropic media in coordinate systems formed by incident and interface planes, rather than in crystallographic coordinates, are considered. Consideration of wave propagation in an acoustic-axis direction is included in the general algorithm, so results can be obtained both generally and for planes of symmetry, including planes of isotropy. General features of the numerical results are discussed. Energy conversion coefficients are shown to satisfy reciprocity relations which are formulated. It is much more natural to consider intensity–conversion ratios, rather than amplitude–conversion ratios, showing the important role of ray (rather than wave-vector) directions in describing phenomena such as grazing angles. In particular, it is shown that the incident wave vector for grazing incidence may be greater or less than 90°: The domain of incident wave-vector angles can actually split into disjoint pieces. The reflection coefficient at grazing incidence is shown to be unity, as in the isotropic case. Critical-angle phenomena are described naturally by this approach.
Based on the classical work of Biot [ J. Acoust. Soc. Am. 28, 168 (1956) ] which predicts that three different kinds of bulk waves may propagate in the fluid-saturated porous solid, the wave equation is solved to determine the energy reflection and transmission coefficients of plane elastic waves at oblique incidence on an interface between a fluid and a fluid-saturated porous solid. For this purpose, the necessary formalism of the energy equation, the Poynting energy flux vector, and the sound intensity of elastic waves in fluid-saturated porous media are presented. Two general cases of mode conversion have been investigated: ( 1 ) The initial wave is incident from the fluid to the interface and generates three transmitted bulk waves in the fluid-saturated porous solid, and (2) the initial wave is incident from the fluid-saturated porous solid to the interface and generates three reflected bulk waves in the same medium. Furthermore, the transmission of sound through a fluid-saturated porous solid plate immersed in fluid is calculated. Measurement of sound transmission through a porous plate was carried out using experimental techniques suggested by Plona [ Appl. Phys. Lett. 36, 259 (1980) ]. Good correlation between measured and calculated values of the angular behavior of the transmission coefficients for fast, shear, and slow waves was obtained after adjusting the theory for experimentally obtained attenuation.
The problem of ultrasonic transmission and reflection at a randomly rough interface is considered in connection with ultrasonic NDE of rough surface samples by immersion method. A simple first-order phase perturbation technique is used to calculate both transmitted and reflected components for comparison with experimental results. The transmitted wave is shown to be attenuated in a similar way to the reflected one, and their attenuation ratio is found to be independent of frequency in the considered cases of slight surface roughness. For instance, the surface roughness induced attenuation of the wave reflected from a water-aluminum interface is about seven times higher than that of the transmitted component, Experimental results are presented to show good agreement with calculated predictions of the suggested simple technique.
The behavior of a Gaussian ultrasonic beam incident on a liquid-solid interface at the Rayleigh angle, the angle at which surface waves are excited on the interface, has been studied in some detail. The reflected beam is displaced in the manner predicted by Schoch; however, the ’’Schoch displacement’’ in general is too large. Good agreement is obtained between experimental results and the theory of Bertoni and Tamir, which assumes that the incident beam couples resonantly into a leaky surface wave at the Rayleigh angle and that the energy reradiated from this leaky surface wave interferes with specularly reflected energy. The propagation distance of the ultrasonic beam is explicitly included in describing the ultrasonic wave reflection at the Rayleigh angle.
The characterization of porosity in solids using the frequency dependence of the ultrasonic attenuation is discussed both from the theoretical and experimental viewpoint. The major thrust of our work is the determination of the volume fraction and size of the voids for the case of dilute porosity (<6%) in structural materials. An aluminum alloy (A357) was chosen for study due to its economic importance in large-scale casting and the particular suitability of aluminum for this type of study. Following recent papers the attenuation is described by an independent scatterer model for spherical voids. Numerical results are presented in a form suitable for use with a range of materials. A method for determining the volume fraction and pore size is given. Specific tabular results are given for stainless steel, IN-100, Ti, Si3N4, as well as aluminum. Figures of merit which partially describe those situations in which the method is usable are also presented. In the experimental work a digitized spectrum analysis system was used to measure the frequency dependence of the attenuation coefficient in A357 aluminum cast alloys. In the cast materials the average pore size was in the order of 100 μm and the pore concentration varied from essentially 0 to 6%. It was found that experimental measurement of the attenuation could be fit by the theoretical model. The resulting parameters yield a good estimate of the pore volume fraction.
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