Shear Critical Angles Research Articles

Analysis of the Directivity of Glass-Etalon Fabry-Pérot Ultrasound Sensors.

Planar glass-etalon Fabry-Pérot (FP) optical ultrasound sensors offer an alternative to piezoelectric sensors for the measurements of high-intensity focused ultrasound (HIFU) fields and other metrological applications. In this work, a model of the frequency-dependent directional response of the FP sensor was developed using the global matrix method, treating the sensor as a multilayered elastic structure. The model was validated against the experimentally measured directional response of an air-backed cover-slip FP sensor with well-known material properties. In addition, the model was compared with the measurements of an all-hard-dielectric sensor suitable for HIFU measurements. The model was then used to calculate modal dispersion curves for both glass-etalon sensors, allowing the features of the directional response to be linked to specific wave phenomena. The features in the directivity of the air-backed cover-slip sensor are due to guided Lamb waves. Symmetric Lamb modes give rise to regions of high sensitivity, whereas anti-symmetric modes cause regions of low sensitivity. For the all-hard-dielectric sensor, two features correspond to the water-substrate and water-spacer compressional and shear critical angles. A region of high sensitivity close to the shear critical angle is associated with a leaky-Rayleigh wave, which has a frequency-dependent phase speed. At higher frequencies, this feature is counteracted by a region of low sensitivity, which occurs when there is no difference in the vertical displacement of the mirrors forming the FP cavity. The model may be used to improve and optimize the design of FP sensors or could be used to assist with the accurate deconvolution of the directional response from array measurements in metrological and imaging applications.

Determination of Sound Velocities by High Frequency Complex V(z) Measurement in Acoustic Microscopy

An amplitude-and-phase-measuring acoustic microscope operating at frequencies higher than 100 MHz has been developed. Complex V(z) curves of fused silica and aluminum were measured at 400 MHz with high accuracy. Inverse Fourier transform of each V(z) curve was achieved to give the reflectance function of the specimens. The Rayleigh, longitudinal and shear critical angles were obtained from the results. These were in good agreement with the theoretical predictions.

Resonances of Scholte‐Stoneley waves propagating on cylindrical shells at oblique incidence

This paper deals with the oblique scattering of an incident monochromatic plane wave by a circular cylindrical shell immersed in water. The propagation direction of the incident wave makes an angle α with a normal to the longitudinal axis of the shell. Experiments are carried out over the broad reduced frequency range 0 < ka > 35, involving the method of isolation of resonances, for two targets: (1) an air‐filled aluminum shell with b/a = 0.94 (b = inner radius of the shell: a = outer radius of the shell) whose length is infinite with regard to the incident acoustic beam cross section; and (2) the same shell of the finite length: In this case, the incident beam insonifies the entire target. With α varying from 0° to 35°, the backscattered spectra—obtained from the signals scattered by both targets—exhibit wide minima which are due to the reemission of Scholte‐Stoneley waves. Resonance peaks are located at the same frequencies on the corresponding resonance spectra. The frequency position of these peaks slowly increases with the increasing values of α. Follow‐up of these frequencies is easy, especially beyond the shear critical angle, which confirms that these resonances are related to external waves. These new experimental results are similar to theoretical ones obtained for an infinite pipe by Kaplunov et al.

Elements of a geoacoustic model of the upper crust

Elements of a geoacoustic model of the geologically young (&amp;lt; 10 million years) upper crust, the top few hundred meters of the basalt subbottom, are described. The model is based on analysis of low-frequency reflectivity versus angle data at a 1 million-year-old sediment-free site, as well as limited Deep Sea Drilling Project downhole logging results, and extrapolated seismic refraction measurements. The upper crust at this site, which is in close proximity to the crest of the East Pacific Rise, may be characterized by low interfacial velocities (Vp∼2800 m/s and Vs∼800 m/s), large gradients (3–5 s−1), and substantial rms roughness (∼5 m). The low-inferred shear speed implies no shear critical angle. Hence, low-frequency energy incident on the bottom at small grazing angles is in large part transmitted into the rock, refracted by the gradient, and reradiated into the water. Scattering loss occurs at both the initial incidence and the interaction of the refracted energy at the boundary. Low interfacial shear speeds lead to large grazing angles at the boundary for the transmitted shear waves, large wavenumbers and, hence, large boundary-scattering losses; small changes in interfacial shear speed produce large changes in subsurface boundary-scattering loss, and hence in the reflection coefficient. A summary of logging and extrapolated seismic refraction measurements in the young crust, below 10 million years, suggests that the range of interfacial shear speeds is between about 800 and 2400 m/s. In older crust, the range of shear speeds is projected to be significantly different. Ramifications of the site dependence of upper crustal properties, particularly shear speed, on sound propagation are discussed.

A simple scattering model for finite objects

A model for acoustic scattering from finite objects is described in terms of a three‐dimensional Fourier wave space. This wave space representation, adapted from x‐ray diffraction analysis, provides a convenient method for depicting aspect and frequency dependence simultaneously. Physical observables are interpreted by means of the Ewald construction. The method is illustrated for a rigid right circular cylinder. A procedure which eliminates mathematical difficulties which arise from surface discontinuities for finite objects when one‐dimensional models are employed is discussed. Incorporation of impedance boundary conditions can alter details of the cylinder's scattering cross section. Examples are discussed and illustrated for aluminum and brass cylinders in water. Dominant observed features are related to the large phase shift which occurs at the shear critical angle. The model provides a useful simulation tool and also suggests a method for analyzing experimental data in detail.

Ultrasonic reflection of a bounded beam at Rayleigh and critical angles for a plane liquid-solid interface

Limited beams of low MHz ultrasound are directed at plane interfaces between water and different solids. Reradiated energy is observed by means of schlieren visualization outside the region predicted by Schoch for incidence at the Rayleigh angle. Some of the solids have properties that would cause prediction of a beam displacement many times that for aluminum. Previous thoery would predict the reflected beam to emerge totally separated from the incident beam for several of the materials used, but no such separation is observed. It is concluded that the reradiated field is composed of specular reflection and Rayleigh-wave radiation at and near the Rayleigh angle. These two radiations are out of phase at low MHz frequencies, and where they coexist and are of equal amplitude, which occurs within the specular region, a null strip occurs. This strip is sharply defined at exactly the Rayleigh angle. Surface waves (sometimes called pseudosurface waves) are also generated at the longitudinal and shear critical angles. These are also shown to radiate into the fluid but are generated to a much lesser degree and are difficult to demonstrate by schlieren visualization.

Observations of Acoustic Radiation Resulting from Incidence at the Critical Angles and the Rayleigh Angle for Plane Surfaces

The resulting radiated field is observed by sehlieren methods for an ultrasonic beam generated in water incident on a solid interface. Radiation outside the specular region has been observed at the longitudinal and shear critical angles and at the Rayleigh angle. A periodic spatial variation in acoustic amplitude occurs in this radiated field at the Rayleigh angle. This effect will be discussed.

Schlieren Visualization of Radiation Caused by Illumination of Plates with Short Acoustical Pulses

Schlieren visualization of the radiated field in water above and below aluminum plates, illuminated by short acoustic pulses, is presented. At certain angles of incidence of the incoming pulse, radiated wavefronts are seen to progress along the plates with specific angles of inclination and associated speeds of progression. In particular, strong effects are observed near the longitudinal and shear critical angles. The measured angles of incidence, at which these effects were generated, are in good agreement with predictions of Lamb theory for plates whose thicknesses are 0.58 wavelengths and larger. For thinner plates, the effects of water loading appear to become significant. A path trace analysis gives good agreement with the group velocity of observed effects when obvious trapped propagation paths are suggested by the reflection coefficient curves for a water-aluminum boundary. Specific radiated wavefronts on plates are related to waves which were observed on cylindrical shells. Relationship of the shell results to Lamb modes is discussed. Plates with thicknesses from 0.002 to 0.241 cm, and frequencies of 5 and 7.2 MHz, are used.