The schlieren technique can be used to visualize the two-dimensional ultrasonic standing wave fields associated with circular cylindrical shells under resonance conditions. However, the interpretation of the schlieren image is not simple due to the complex relationship between the acoustic and optical fields. A model for predicting the optical image in an ideal schlieren system is presented and used to investigate the influence of the acoustic pressure and optical spatial filtering on the resultant image, demonstrating the conditions under which the image is a meaningful representation of the acoustic wave field. A low-frequency ͑Ͼ100 kHz͒, wide-aperture, laboratory schlieren system is used to image the fluid column resonances of a circular cylindrical shell. Experimental results agree well with the predictions, validating the theory. Although the schlieren image is two-dimensional, limiting investigations to targets having translational symmetry, the technique is noninvasive and can potentially provide greater insight into the acoustic resonance behavior of more complex scattering geometries.
The acoustic resonances of a submerged fluid-filled cylindrical shell are analyzed as the shell cross section is deformed from circular to elliptical geometry. A schlieren visualization system is used to image standing wave fields within insonified water-filled shells of different eccentricities, and to locate the resonance frequencies of the fluid column. The acoustic behavior of elliptical cavities with infinite and finite surface impedances are modeled and the theory used to predict the resonance frequencies of the fluid column and calculate the pressure distribution in the acoustic field. As the symmetry of the circular shell is broken by deforming it to the more general ellipse the resonance spectrum changes; mode splittings and level crossings are observed as the eccentricity increases. The experimental observations of resonance patterns and frequency variation are in good agreement with the theoretical predictions.
The acoustic backscattering from a submerged metal (iron) cube has been investigated as a function of frequency and angle of incidence in the low-frequency regime ka<5, where k is the acoustic wave number and a is a characteristic dimension of the cube. The experimental measurements were made in the laboratory using a parametric array as an acoustic source at frequencies between 8 and 120 kHz and a cube of side length 20 mm. The backscattered field is expressed as a dimensionless “form function” and normalized in terms of the average projected cross-sectional area of the cube. The scattered field is seen to vary considerably with the orientation of the cube. The scattering behavior of a rigid cube is modeled numerically using a boundary element code. The results for a cube are compared with calculations of the form function for an elastic sphere. When averaged over cube orientations the form function has characteristics reminiscent of a spherical scatterer, suggesting the propagation of creeping waves.
A schlieren technique is used to visualize the fluid cavity resonances of an insonified fluid-filled (brass) cylindrical shell in the high-frequency overlapping resonance regime, kb>30, where b is the inner radius of the shell. Hybridization of modes occurs at frequencies where resonances interfere and the resulting dissymetrization of the wave fields are evident in the experimental images. Similar behavior is seen in theoretical predictions obtained using the normal mode series solution for a shell excited by a plane wave. At very high frequencies (kb>100) the field in the cavity has characteristics that can be associated with a ray description of acoustic propagation; in these cases caustics are observed in the acoustic field.
The acoustic backscattering behavior of both nonmetallic (glass) and metallic (steel) cubes has been investigated over a wide frequency range where elastic resonances are important in determining the acoustic response of the cubes. A laboratory system incorporating a parametric array was used to make measurements between 20 and 200 kHz using cubes of side (l) 20 mm, and a combined finite element/boundary element code was used to numerically model scattering by the cubes. The frequency range covered corresponds to ka values up to 10, where a=l(3/4π)1/3 is a characteristic dimension of the cube. Results are presented for three scattering geometries involving incidence on to a face, an edge, and a corner. The backscattered form function differs greatly for the different geometries and is seen to depart significantly from that of a rigid cube when ka>5 due to the elastic resonances of the cube. The resonance contributions are clearly seen when the rigid background is subtracted from the elastic predictions.
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