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In this paper we shall study elastic mixed or initial-interface value problems and give an inner estimate of the location of singularities of the reflected and refracted Riemann functions by making use of the localization method.

Elastic waveguides are often applied in the acoustic nondestructive evaluation systems. Even though elastic waves in the waveguides are studied in the literature rather in detail, the very important problem of the incident wave interaction with the waveguide and its re-emission into the waveguide practically hasn’t been studied.

The technique of artificial absorbing boundaries is often applied in the numerical modelling of wave propagation and other related numerical studies of ultrasonic NDE. For a physical problem with an unbounded spatial domain, the introduction of artificial boundaries to bound the computational domain can be vital for a successful numerical solution. Even for problems with bounded spatial domains, the introduction of artificial absorbing boundaries that localize the area of interest can reduce the computing cost and allow limited computer resources to achieve more. It is particularly so in ultrasonic NDE where the field near the scatterers or transducers is normally of interest.

A theoretical study of correlation phenomena in an optical Fabry-Perot Interferometer (FPI) containing random elastic scatterers between the mirrors is presented. Among the correlation effects, we find a Lorentzian shaped correlation function between incident waves of different frequencies. For an FPI which contains moving scatterers between the mirrors (for example, scatterers embedded in a liquid), we calculated the intensity correlations between different times. Generally, the calculated intensity correlations are much broader than the corresponding correlations for bulk systems.

A number of imaging techniques rely on digital computation in order to recover a mapping of the interaction parameters from the measured data. These techniques all proceed from fundamental algorithms which are, essentially, the expression of the inverse (scattering) problem for the particular measurement configuration associated with that imaging technique. Even the more conventional pulse-echo techniques, widely used in medical applications, may be seen as a subset of these methods, relying, as they do, on backscattered waves only. In a similar way, computerised ultrasound tomographic (“CUT”) methods comprise the subset of techniques which rely on forward scattered waves.

Acoustic barriers can be made with arrays of inclusions periodically spaced and embedded in a plate (Alberich). Their frequency behavior conditions their use as reflectors or absorbing coatings. Generally the study of reflection and transmission coefficients when the structure is insonified by an incident wave, allows to characterize the barrier.

A new photoelastic visualization of ultrasonics proportional to the intensity of ultrasonics has been done by Date. The results obtained by this means and by numerical visualization are in very good agreement, thus verifying the reliability of the two methods.

We consider the transmission and reflection of ultrasonic waves at the interface between a real periodic solid and a continuum liquid. If the sound velocity in the liquid is considerably smaller (as e.g. in He) than that of the solid then at sufficiently high frequencies the wavelength in the liquid can be smaller than a lattice spacing of the solid. In that case the periodicities in the boundary plane become important and there is an additional transmission with the modified Snell’s law, $$\overrightarrow {{{\text{k}}_T}} = \overrightarrow {{{\text{k}}_i}} + \overrightarrow G$$ where \(\overrightarrow {{k_T}}\) and \(\overrightarrow {{\user2{k}_i}}\) are the projections on the boundary plane of the transmitted and incident wave vectors, respectively, and \(\overrightarrow G\) is a reciprocal lattice vector in the boundary plane.

Transformation-toughening of ceramics has attracted considerable attention [1,2,3] in recent years. The key mechanism in this toughening is the stress-induced phase transformation of the partially stabilized zirconia (PSZ) inhomogeneities, which accompanies volumetric expansion. Due to this expansion, the composite material consisting of PSZ inhomogeneities in a brittle matrix becomes more resistant to fracturing. While this problem has been studied for guasi-static loadings [4,5], the corresponding dynamic case has remained relatively unexplored.

This paper presents results of a study on an inversion transformation ℐA for backscattering of ultrasonic waves from an obstacle embedded in a solid. For a rigid sphere the resulting function A(t) is derived which is related to the cross-sectional area intercepted at any given time by a transverse plane moving across the obstacle in the same direction as the incident wave. The maximum value of A(t) is the total backscattering cross section. From this study emerges a proposed inversion algorithm for cavities. The use of the inversion algorithm is demonstrated for “exact” theoretical data obtained from Opsal as well as experimental data collected on an ellipsoidal cavity and a double cavity. Associated with the inversion of the experimental data is an iterative technique which optimizes the construction of A(t) and therefore the estimates for the size and shape of the scatterer.

The specific action of the sound field in the degassing of liquids originates in the vibrations of gas bubbles. An analysis of the interaction of the sound field and single bubble is considerably simplified if we assume that the bubble radius is small in comparison with the acoustic wavelength in the liquid. The pressure in the incident wave, varying periodically with time, excites forced vibrations of the bubble, which are radiated into the surrounding liquid, where they result in the formation of secondary sound waves (acoustic scattering effect). Part of the incident wave energy in this case is used up in overcoming the internal losses in the bubble — liquid system and is released in the form of heat.

Currents induce additional forces (drag and lift) on ocean structures that on occasion may be of far greater magnitude than is initially suspected. This occurs when the currents and surface gravity water waves have components which coincide directionally. Thus, since the drag force is usually taken to be proportional to the square (rather than the first power) of the fluid particle velocity, the resulting force, due in part to the coupling (cross-multiplication products) terms, may be considerably enlarged. Currents also have another effect, namely that of refraction of surface waves which occurs at the boundary of an ocean current and still water. The end result is a change in the ‘apparent’ wave lengths and direction of the incident waves. The change in wave lengths also appears as a change in wave steepness. For details, the reader is referred to the paper by Johnson (1947).