Semi-infinite Isotropic Medium Research Articles

On the Excitation of Time Harmonic Cylindrical Surface Acoustic Waves

Reciprocity theorem is used to study the excitation of time harmonic cylindrical surface acoustic waves in a semi-infinite isotropic medium. Excitations by point and partial ring sources with applica- tions to laser generated ultrasound are investigated. It is verified that the ablation and thermoelastic cylindrical SAW signals in a CW op- eration are 180 out of phase provided that the sources of excitation are in phase. Asymptotic expressions for acoustic fields, excited by par- tial ring sources, near and far from the ring center are calculated. The asymptotic solutions show that far from the focal region, the fields are essentially converging, diverging, or standing waves. Furthermore, it is established that there is a 90 phase difference between the converg- ing and diverging SAW's.

Green functions and fluctuation spectra for coupled acoustic-thermal modes in semi-infinite isotropic media

Linear response functions or Green functions are derived for the coupled acoustic-thermal vibrations which propagate perpendicular to the surface of a semi-infinite medium. The authors consider an isotropic thermally isolated medium with a stress-free surface and the fluctuations are described by macroscopic hydrodynamic and thermodynamic equations. The power spectra and the cross section for inelastic light scattering are derived from the Green functions. The results are illustrated with numerical calculations for silicon and compared with those obtained for uncoupled acoustic and thermal modes.

Elastic interactions between defects and interfaces

We determine the elastic interaction between a point defect and the plane interface between two different isotropic elastic media. We also determine the elastic energy of interaction between two point defects in the vicinity of such an interface. In the latter case the two defects can either both be on the same side of the interface, or they can be on opposite sides of it. The results obtained are compared with previously obtained results for the elastic interactions of point defects in a semi-infinite isotropic elastic medium. The results of this study should be useful in understanding phenomena such as solute segregation, or its absence, near interface.

The computed piezomagnetic anomaly field for Kilauea volcuano, Hawaii.

A volcano containing a pressurized magma chamber is approximated by a centre of dilatation embedded in a semi-infinite isotropic elastic medium. Stresses corresponding to a given surface strain are used to compute the associated piezomagnetic surface anomaly field. Comparison with results taken from a proton precession magnetometer array on Kilauea volcano, Hawaii indicates that stresses associated with shallow centres of inflation beneath the volcano are less than those expected from an elastic model. The most plausible explanation appears to be anelastic deformation of the volcano, leading to an effective crustal rigidity an order of magnitude less than that for competent basalt.

Electrolytic tank solution of electric field associated with two circular disks on the surface of an isotropic homogeneous medium.

The electric field associated with two disks on the surface of a semi-infinite isotropic homogeneous medium is found on a plane perpendicular to the disks and passing through their centers. To an accuracy which is primarily determined by the finite dimensions of the electrolytic tank, the solution is presented as families of curves. In this presentation, the magnitude of the electric field (normalized in terms of the distance of the field point from the surface, conductivity of the medium, and applied power) and the angular orientation of the field vector are plotted as functions of the ratios of the linear dimensions which characterize the geometry of the system to the distance of the field point from the surface.

Thermal stress singularities at tips of a crack in a semi-infinite medium under uniform heat flow

In the framework of plane thermoelastic problems is discussed the thermal stress field near the tips of an arbitrarily inclined crack in an isotropic semi-infinite medium with the thermally insulated edge surface under uniform heat flow. The crack is replaced by continuous distributions of quasi-Volterra dislocations corresponding to line heat sources and edge dislocations, and we obtain a set of simultaneous singular integral equations for dislocation density functions, whose solution is given in the forms of series in terms of Tchebycheff polynomials of the first kind. By means of this method, the thermal stress singularities at the crack tips are estimated exactly and the stress intensity factors can be readily evaluated. Numerical results are given for the particular case where the surface of the inclined crack is maintained at constant temperature and the heat supplied across the surface of the crack vanishes as a whole. The effects of the distance from the crack tip to the edge surface of the semi-infinite medium and the angle of inclination of the crack on the stress intensity factors and the initial direction of crack extension are shown graphically.

Stress field of a dislocation segment perpendicular to a free surface

Abstract In an isotropic semi-infinite medium it is possible to compute the stress field of an angular dislocation, the arms of which are, respectively, parallel and perpendicular to the free surface. The contribution of each arm being separable, and the stress field of the parallel arm being known, the stress field of a dislocation segment perpendicular to a free surface is readily obtainable.

DIRECTIVITY PATTERNS OF ANGLE PROBES FOR ULTRASONIC BULK WAVES AND SURFACE WAVES

The directivity patterns of angle probes commonly used in ultrasonic material-testing are studied both theoretically and experimentally. Expressions are obtained for longitudinal waves and transverse waves radiating into the body under test and for surface waves propagating over the surface of the body, treated as a semi-infinite isotropic medium. Numerical computations are given in all three cases for a steel object. The theoretical deductions are partially checked by experiments for the case of longitudinal and surface waves. Some problems to be considered in ultrasonic testing are pointed out.

Transient stresses induced by heating a plane boundary

A closed-form solution to the plane strain problem of a semi-infinite isotropic elastic medium subjected to an instantaneous line heat source at the boundary is obtained in terms of tabulated functions. This solution is regarded as fundamental and is employed to derive solutions to transient thermal stress fields for several cases of practical interest.

Propagation of Stoneley waves along a perturbed interface

This paper investigates the two dimensional propagation of Stoneley waves along a perturbed interface between two semi infinite isotropic media. A perturbation technique is used to obtain the contribution due to the perturbation of the interface to the potential functions. Further, the expressions for the components of the total strain due to the perturbed and unperturbed contributions are obtained. Finally, the period equation for the case of the perturbed interface is also obtained.

The axisymmetric problem of propagation of a normal stress discontinuity in a semi-infinity elastic medium

The displacements at the free surface due to sudden creation of a normal stress discontinuity over a circular area which expands uniformly after creation, inside a semi-infinite isotropic elastic medium are studied. Applying Cagniard's method as modified by De Hoop, the displacement components are derived in the integral forms. Their approximate evaluations are carried out in order to obtain the displacement components at the time of their first arrival.

Reflection and Refraction Coefficients at a Fluid-Solid Interface

For an infinite plane elastic wave which strikes the plane interface separating two semiinfinite isotropic media, the calculation of the complex reflection coefficient, R*, for varying angles of incidence, θ, is not difficult. In the past, calculations have been made for a number of lossless media and, consequently, an important facet of the R*−θ curve for real materials has been overlooked. The total reflection, |R*|=1, which occurs at the longitudinal- and shear-wave critical angles is well known, but the appearance of a minimum (sometimes a zero) in R* is not and its existence defines a third critical angle, sometimes inappropriately called the Rayleigh-wave angle, at which a wave with large surface components is generated. During experiments with beams of acoustic waves, there is an apparent lateral displacement of the reflected beam at the third critical angle which manifests itself markedly only when there is a near-zero in |R*|. Notwithstanding the calculations of Schoch [Ergeb. Exakt. Naturw. 23, 127–234 (1950)] and the experimental measurements of others apparently to the contrary, it is strongly suggested that no actual lateral displacement occurs and that re-radiation from the region outside that ensonified by the incident beam gives rise to the apparent lateral displacement. Some outcomes of the investigation are discussed and of these the more important are: (1) Rayleigh and other interface and surface waves in real media are degenerate; (2) no interface wave can exist independently at the junction of two nonideal media; (3) Huyghens's principle in its elementary secondary-wavelet form does not apply to lossy media; (4) the usefulness of the sensitivity of R* to minute changes in elastic parameters at the Rayleigh angle as a measuring tool has a wide application; (5) elliptical polarization of both shear and longitudinal waves can occur, owing to boundary influences in lossy refracting media. The real part of the propagation vector lies in the plane of the ellipse.

Optical wave propagation in cholesteric liquid crystals with finite thickness

Theoretical analysis was performed on optical wave propagation along the helical axis of a cholesteric liquid crystal of a finite thickness bounded by two semi-infinite isotropic media. Some new effects involved in the selective reflection, circular dichroism and also optical rotatory dispersion were predicted by taking the boundary condition into account.

The dislocation loop near a free surface

Abstract The solution for the displacements due to a point force in a semi-infinite isotropic elastic medium is used to obtain the displacements of an infinitesimal dislocation loop of arbitrary orientation. By integration these can be used to give the elastic field of a dislocation of arbitrary shape, orientation and Burgers vector. The equations are used to study the stability of a prismatic dislocation loop on a glide prism of square cross section near a free surface. Results are presented for the forces on the loop sides and the changes in loop energy during rotation for cases in which b is normal or parallel to the surface. The width of the denuded zone is discussed, and the results on loop orientation indicate why the equilibrium orientations of polygonal loops in thin films should be stabilized away from the pure edge orientation.

Concentration-dependent diffusion in a semi-infinite medium

A variational formulation is presented which has as its Euler-Lagrange equation the fundamental partial differential equation of diffusion. This variational expression is applicable for both time-dependent and time-independent boundary conditions and for a diffusion coefficient which is a function of the concentration. This variational technique is applied to the problem of unidimensional diffusion in a semi-infinite isotropic medium where the diffusion coefficient is strongly dependent upon the concentration of the diffuser. To solve the extremum problem, a system of “natural” finite difference equations is established as a consequence of the variational expression. Curves of concentration ratio vs distance are calculated and compared with a formal exact solution for a specific diffusion coefficient.

Propagation of Love waves in a non-homogeneous stratum of finite depth sandwitched between two semi-infinite isotropic media

Propagation of Love waves in a non-homogeneous stratum of finite depth sandwitched between two semi-infinite isotropic media

Microseisms: Its dependence on the movement of the source

The displacements on the free surface of a homogeneous isotropic semi-infinite medium has been obtained assuming a moving normal stress on the surface. It has been studied how the displacements behave with (1) the direction of propagation of the source with respect to the recording station and (2) the velocity of the source.

Propagation of love waves in a non-homogeneous stratum of finite depth sandwitched between two semi-infinite isotropic media

The possibility of propagation of Love-waves in a non-homogeneous internal stratum internal stratum of finite depth sandwitched between two semi-infinite isotropic media has been studied in this paper. The density and rigidity both are considered to be variable, density being taken as $$\varrho 2 = \frac{{\varrho 0}}{{\left( {1 + \alpha z} \right)}} and rigidity \mu 2 = \frac{{\mu 0}}{{\left( {1 + \alpha z} \right)}},$$ ϱ0 and μ0 are constants. The velocity β=c2 is taken here as constant $$ = \surd \overline {\mu 2} /\varrho 2 = \surd \overline {\mu 0} /\varrho 0$$ . It is found that the phase velocityc exists between the limitc 2<c≦(1.121c 2). The variability ofKH (whereK, the wave number andH, the depth of the internal medium) with the change ofc/c 2 andC/c 2 (whereC is the group velocity) is shown graphically.

On the propagation of Love waves in a non-homogeneous internal stratum of finite depth lying between two semi-infinite isotropic media

The possibility of propagation of Love waves in a non-homogeneous internal stratum of finite depth lying between two semi-infinite isotropic media has been studied in this paper. The density and rigidity of the internal stratum are taken to vary exponentially with depth.

Disturbance due to Shearing-stress Discontinuity in a Semi-infinite Elastic Medium

Summary The displacements at the free surface due to sudden introduction of shearing-stress discontinuity which expands or moves uniformly after creation, inside a semi-infinite isotropic elastic medium have been obtained in exact forms for SH type of motion by the method due to Cagniard. Displacements at different points on the free surface have been calculated numerically and results are shown graphically for two particular cases.