Critical Angles Of Incidence Research Articles

АНАЛІЗ ПАРАМЕТРІВ МОДЕЛІ ПРОХОДЖЕННЯ УЛЬТРАЗВУКОВИХ ХВИЛЬ ЧЕРЕЗ ЗАНУРЕНУ У РІДИНУ ПЛАСТИНУ

The physical-mathematical model of the fall of an ultrasonic wave falling on the surface of a plate immersed in a liquid has been considered. The parameters of the model are the angle of incidence of the ultrasonic wave, the reflection and transparency coefficients for the incident wave and the thickness of the plate.This model is a theoretical basis for the practical implementation of the immersion method for measuring the velocities of propagation of longitudinal and transverse waves in samples of different materials. According to the experimental results of the propagation velocities of the longitudinal and transverse waves, the Poisson’s ratio of the material is determined. The materials of a typical plate are polymers that have different Poisson ratio in sign and magnitude. If the angle of incidence does not exceed the corners of the total internal reflection on the boundary of the liquid – solid for the longitudinal and transverse waves propagation in the plate, then the reflection and transparency coefficients are the real numbers. In this case, the squares of the modules of these quantities are the reflection and transparency coefficients of the energy of the wave. For the incident ultrasonic wave, reflection and transparency coefficients are calculated, depending on the angle of the incidence, the thickness of the plate and the material of the plate The analysis of the obtained results shows that the functional dependences of the energy coefficients of reflection and transparency are clearly expressed maxima and minima at different angles and plate thickness. For this purpose, the conditions for full reflection for incident waves and transparency for a transverse wave at critical angles of incidence are analyzed. The critical angles of fall of an ultrasonic wave from a liquid are calculated, under which in a plate only a transverse wave propagates. Determined thickness of the plate for polymeric materials, in which there is a complete reflection and full passage of the incident wave.

Superprism effect in a deformed triangular sonic crystal

The superprism effect in a two-dimensional sonic crystal composed of lead cylinders in water aligned on a lattice obtained by varying the angle between the primitive vectors of triangular lattice is numerically investigated. Symmetry breaking influences the equi-frequency contours to reflect the lattice symmetry, so that compression along a direction leads to smaller critical angles of incidence. The whole 0°–90° range is spanned by the refracted waves at the water/sonic crystal interface for frequencies between 165 and 183 kHz, in the third band, and angles of incidence between 0° and 15°. The studied superprism behaviour can be used to achieve both spectral and angular resolution. The refraction angle varies linearly for small angles of incidence below 3° at a constant frequency, while its frequency dependence at a given angle of incidence is quadratic for small frequencies. Finite-element computations reveal that waves are refracted into the angles calculated from the equi-frequency contours with small beam divergence at any frequencies and angles of incidence.

Acoustic reflectivity goniometry of bounded ultrasonic pulses: Experimental verification of numerical models

The angle of incidence reflectivity of a bounded acoustic pulse from water loaded elastic solids is tested using an experimental configuration with a large transmitter and a small pointlike receiver. The experimental response, affected by well-known nonspecular effects near critical angles, is modeled fully by propagation of the full bounded pulse using a phase advance technique. This allows for visualization of the evolution of the bounded pulse with time and upon reflection. The modeled and the observed reflectivities and phase rotations, as measured along the specular path, agree well with observations even at post Rayleigh critical angles of incidence. Moreover, small amplitude deviations are accurately reproduced. The longitudinal and Rayleigh critical angles are obtained from the observed reflectivity curves and used to calculate the material elastic wave speeds, which are in good agreement with those measured directly. The density is also obtained by inversion of portions of the reflectivity curves where they do not significantly differ from the plane wave response. These tests validate use of the full phase propagation method to study such reflection problems.

Stress field in a crack on the interface of materials irradiated with SH-waves

On the basis of the solution of the problem of diffraction of a field of plane SH-waves on a crack located on the interface of materials obtained by the authors earlier, we deduce asymptotic expressions for the stress intensity factors at the crack tips. The dependences of the stress intensity factors on the dimensionless crack length, the angle of incidence of the plane wave, and the mechanical and physical properties of the materials are investigated. The possibility of appearance of singularities of the stress intensity factors near the remote crack tip (relative to the source of radiation) for the tangential and critical angles of irradiation is demonstrated. It is shown that, for the critical angles of incidence, these singularities can appear only in perfect materials and that, in the presence of losses, the increase in the stress intensity factors is bounded. It is also demonstrated that the indicated effects are caused by the diffraction interaction of SH-waves with the crack tips.

Specific Features of the Influence of the Lower Boundary of a Waveguide on the Angular Structure of the Sound Field in the Shelf Zones in the Northwest Part of the Black Sea

We analyze the possibility of existence of critical angles of incidence of sound waves along two paths of propagation of sound typical of the northwest shelf of the Black Sea from the viewpoint of the characteristics of the lower boundary of a waveguide and the space and time structure of the field of sound velocity. The lower boundary of the waveguide may possess the property of acoustic transparency both in the case of a subsurface sound channel and under the conditions of negative refraction if the bottom is formed by fine-aleurite silts responsible for significant losses in the process of propagation of sound. The angles of total internal reflection exist for bottoms formed by shell rocks under all hydrological conditions typical of this region. At the same time, for bottoms formed by fine-aleurite silts, these angles exist only for a certain vertical structure of the field of sound velocity, which enables one to use the range of angles in which the losses caused by the reflections of sound waves from the bottom can be neglected.

Anomalous absorption of bulk shear sagittal acoustic waves in a layered structure with viscous fluid

It is demonstrated theoretically that the absorptivity of bulk shear sagittal waves by an ultra-thin layer of viscous fluid between two different elastic media has a strong maximum (in some cases as good as 100%) at an optimal layer thickness. This thickness is usually much smaller than the penetration depths and lengths of transverse and longitudinal waves in the fluid. The angular dependencies of the absorptivity are demonstrated to have significant and unusual structure near critical angles of incidence. The effect of non-Newtonian properties and non-uniformities of the fluid layer on the absorptivity is also investigated. In particular, it is shown that the absorption in a thin layer of viscous fluid is much more sensitive to non-zero relaxation time(s) in the fluid layer than the absorption at an isolated solid–fluid interface.

Acoustic scattering by transversely isotropic cylinders

We study the scattering of an acoustic wave incident on a transversely isotropic cylinder immersed in a fluid. Scalar potentials are expanded in series of normal modes. This expansion changes in character as the angle of incidence increases. There exist critical angles beyond which the angular pattern of scattering changes dramatically. The transversely isotropic materials are of two types. Materials of the first type have two critical angles of incidence whereas materials of the second type have an additional critical angle. Below the first critical angle the form function is rich in peaks whose number steadily goes down as the angle of incidence increases.

Scanning tomographic acoustic microscopy using shear waves

We propose to use shear waves instead of longitudinal waves in a novel scanning tomographic acoustic microscope (STAM) in which the specimens are solid. When a specimen with a shear modulus is immersed in the microscope's water bath, mode conversion takes place at the water-solid interface. The shear wave energy is detectable and can be used for image reconstruction. Although wave transmission in most solid specimens is limited to about 20 degrees for longitudinal waves, it is about twice that for shear waves. Also, velocities of shear waves are lower than those of longitudinal waves and hence the wavelengths at the same frequency are smaller. For these and other reasons we can expect that for many specimens the resolution of a shear-wave STAM to be substantially better than that of a longitudinal-wave STAM. We use computer simulation in order to compare the operation of a shear-wave STAM with that of the conventional longitudinal-wave STAM. We have simulated tomographic reconstruction for each. The corresponding critical angles of incidence are computed and tomographic reconstructions of a particular solid specimen is obtained by using the back-and-forth propagation algorithm (BFP). Our simulation results show that shear-wave STAM has better resolution than longitudinal-wave STAM.

Corrections for critical rays in 2-D seismic modelling

The usual high-frequency (ω) ray method of modelling reflections from smooth boundaries does not account for interference arising near critical angles of incidence. When the reflector is effectively convex towards the incident-wave side, the ray method fails (i) in a transition zone of width O(ω-1/2) separating regions of partial and total ray reflection, (ii) for the transmission in a zone along the reflector having thickness O(ω-1/2) and where a whispering-gallery is formed by multiply-reflected turning waves, and (iii) for turning rays refracted back into the first medium at distances from the critical point less than O(mω-1/4), where m is the number of turns. The interference is a local effect and approximate analytic waveforms can be found for laterally varying media. The 2-D acoustic case is described here. The fields near the point of critical incidence and about the critically reflected ray are found in a way similar to the grazing ray solution described in an earlier paper. However, through the critical ray problem the first two terms of the asymptotic expansion must be considered. The whispering-gallery is obtained by exploiting work on modes by Buldyrev, Lewis, Ludwig and others. The modal solution is then matched with the solution near the critical point to determine the initial modal amplitudes. The individual ray contributions separate from the modes as the waves progress along the boundary. The modal form of solution is needed, even if one wishes to demonstrate only the matching with ray theory for the primary refracted/turning wave near the critical point. This is because the transition zone for the refraction is much wider than that for the reflected wave. Though it is more complicated than the earlier grazing ray solution, the critical-ray diffracted wavefield is still continued way from the boundary using ray coordinates. Hence, it is not difficult to provide ray tracing programs with corrections to ray synthetics. Some preliminary numerical examples are presented to indicate the waveforms and potential significance of these corrections. They are small in comparison with the total reflection, but they are very significant in comparison with the weaker refracted waves. Even where ray theory is (just) valid, for practical reasons one may wish to avoid tracing multiple reflections close to a numerically specified boundary. The boundary-layer formulae provide a more ‘natural’ solution to both the theoretical and numerical problems for the refracted part of the field.

Critical angles of incidence for transmission of magnetohydrodynamic waves across shock surfaces

When an MHD wave impinges on a fast shock from its upstream side, in general it may excite six diverging waves on the downstream side when the angle of incidence, the angle between the normal direction of the incident wave and the shock normal, is less than a critical angle. The boundary conditions across the shock surface determine the perturbations excited on the downstream side of the shock. We introduce a wave function approach to study the interaction of an MHD wave with an fast shock. When the angles of incidence are greater than certain critical values, less than six diverging waves can be excited; the flow becomes unstable on the downstream side of the shock. The existence of critical angles of incidence infers that the conclusion obtained on the stability of fast MHD shock with respect to normal incidence of MHD disturbances does not hold true for oblique incidence of disturbances at large angles of incidence. We investigate the critical angles of incidence, which are calculated as functions of the mode of the incident wave and three upstream conditions of the shock: the fast Mach number, the plasma β value and the shock angle. Our numerical results show that the critical angles of incidence are of the order of 60°.

Snell's law for viscoelastic materials

The purpose of this note is to discuss a solution to the generalized Snell's law of viscoelasticity for a plane wave incident on a welded boundary, to present necessary and sufficient conditions for determining critical angles of incidence, and to present sufficient conditions for when a critical angle can exist given two media and the complex wave vector of the incident wave. These conditions affect how viscoelastic effects are included in existing elastic wavefield calculation methods.

Scattering of an acoustic Gaussian beam from a fluid-solid interface

The reflection and refraction of a three-dimensional acoustic beam, whose amplitude is Gaussian in cross section, at a fluid-solid interface is studied. The acoustic Gaussian beam is constructed by assigning complex values to the source coordinates of an acoustic monopole, a technique used in optics to model coherent light beams. The incident beam is specularly reflected except at certain critical angles of incidence of which the Rayleigh angle is the most important. Near this angle the incident beam excites both a leaky Rayleigh wave and a reflected beam, and the interference between these two disturbances produces a shifted and distorted reflected wavefield. The incident beam, near normal incidence, is refracted into a compressional beam and a shear beam, both of whose amplitudes are Gaussian in cross section. Whereas the incident beam has a circularly shaped cross section, both transmitted beams have elliptically shaped cross sections. [Work supported by NSF.]

Graphical method for reflection of plane waves in a micropolar half space

Analysis of reflection of plane waves from a flat boundary in a micropolar half space poses tedious calculations. In this paper, utilizing the concept of slowness surfaces, a simple and efficient method is proposed as an alternative to the previous analytical methods. Critical angles of incidence, the nature of the reflected body, and boundary waves corresponding to the incident longitudinal displacement and coupled transverse displacement microtational waves are studied. Subject Classification: [43]20.15, [43]20.30.

Ultrasonic scattering from polycrystalline solids and plates

Relative maxima in ultrasonic backscattering were observed at critical angles of incidence that correspond to Lamb modes on brass plates located between air and water. Critical angles were determined utilizing schlieren visualization of beam displacement. Results are compared to backscattering the Rayleigh angle at a brass bulk solid-water interface.