Effect of surface stresses on surface waves in elastic solids

This paper deals with the propagation of surface waves in homogeneous, elastic solid media whose free surfaces or interfaces of separation are capable of supporting their own stress fields. The general theory for the propagation of surface waves in a medium which supports surface stresses is first deduced, and then this theory is employed to investigate the particular cases of surface waves, viz. (a) Rayleigh waves, (b) Love waves and (c) Stoneley waves. It is seen that the Rayleigh waves become dispersive in nature; and, in case of low frequency with residual surface tension, a critical wavelength exists, below which the propagation of Rayleigh waves is not possible. This critical wave length is directly proportional to the surface tension. Some numerical calculations have been made in the case of Love waves and conclusions have been drawn.     

Behavior of Rayleigh surface waves in an anisotropic media lying over a prestressed orthotropic half-space

The present paper discusses the propagation of Rayleigh waves in an anisotropic layer with finite thickness lying over a prestressed orthotropic half-space. An anisotropic media and orthotropic media are supposed for the upper layer and lower half-space, respectively. Dispersion equation and displacement components are computed in a compact form considering the case that the displacement and stress are continuous at the interface and stress vanishes on a free surface. Graphs are sketched to represent the effect of density, initial stress and height of the layer on wave velocity. The graphs are also configured to exhibit the mode of propagation of Rayleigh waves. This paper is an attempt to explain the nature of Rayleigh waves mathematically.     

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.     

Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium

The propagation of plane waves in fibre-reinforced media is discussed. The expressions of phase velocities of quasi-P (qP) and quasi-SV (qSV) waves propagating in plane symmetry are obtained in terms of propagation vectors. We have established a relation from which the displacement vector can be obtained in terms of the propagation vector. Expressions for the reflection coefficients of qP and qSV waves are obtained. Numerical results of reflection coefficients are obtained and presented graphically. The partition of energy between qP and qSV waves reflected on free and rigid boundaries due to incident qP and qSV waves are also obtained and presented graphically.     

Application of metal single crystal wedges to high frequency rayleigh wave propagation

Techniques for propagating Rayleigh waves with frequencies varying from <1 to 270 MHz were developed for the purpose of nondestructive evaluation of composition or defect gradients near the surface of nonpiezoelectric solids. The surface waves with frequencies greater than 15 MHz were obtained from a novel technique using single crystal wedges, whereas the low frequency waves were produced by a previously used high voltage impulse. Measurements of Rayleigh wave velocities on single crystals of Ge and Al were performed as a test of accuracy and precision and are compared with calculated values.     

Effects of inhomogeneity on surface waves in anisotropic media

This paper investigates the effects of anisotropy and inhomogeneity on surface waves in elastic media. Exponential variation in properties are assumed for the elastic parameters and material density. The classical equations of motion for propagation of waves in an inhomogeneous transversely isotropic elastic solid are deduced. The equations of motion for surface waves are derived and general surface waves are investigated. This general theory is then utilized to investigate Rayleigh, Love and Stoneley waves. Results obtained in the above cases reduce to the corresponding well-known classical results when inhomogeneity and anisotropy are not present. It is seen that inhomogeneity has significant effects on dispersion characteristics. Numerical calculations are included for Love waves and some conclusions have been drawn from the above calculations.     

Rayleigh Wave Propagation for the Detection of Near Surface Discontinuities: Finite Element Modeling

The paper presents a finite element study designed to gain physical insight into the effect of surface discontinuities on Rayleigh wave propagation in structural elements. In particular, a series of array measurements at various locations within a plate are simulated and compared with experimental measurements. Conversion of array measurements into the frequency-wavenumber domain reveals propagating Lamb modes, which are used to define Rayleigh wave motion. Numerical results show that Rayleigh waves measured after passing a fracture are composed of long wavelength Rayleigh wave energy propagating past the slot and short wavelength Rayleigh wave energy formed behind the slot.     

Ultrasonic leaky interface waves for composite-metal adhesive bond characterization

Highly stressed or damaged regions in aircraft structures are increasingly being reinforced by adhesively bonding an overlay of a unidirectional boron fiber-epoxy composite to the aircraft metallic substrate. While conventional C-scan ultrasonics can be used to detect disbonding of the overlay, nondestructive methods are also required to detect weak adhesive bonding. This paper describes a preliminary experimental investigation of the existence of ultrasonic leaky interface waves between overlays and 2024-T351 aluminum alloy and D6ac steel substrates, and their possible use for detection of weak bonds. The approach used was to excite these leaky waves using Rayleigh waves generated by a laser line-source on the substrate. The existence of the leaky waves, traveling normal to the composite fibers, between boron-epoxy overlays and either an aluminum or steel substrate, was confirmed by observations of the quasishear pulses leaked to the top of the overlay, and of the Rayleigh wave transmitted to the free surface beyond the overlay. When quantitative measurements were possible, measured values of the complex interface wave speed agreed satisfactorily with predicted values. This paper also demonstrates one case for which leaky interface waves are sensitive to weak bonding caused by the presence of a contaminant on the substrate surface prior to bonding: application of a low-concentration aqueous solution of hydraulic oil to the aluminum substrate prior to bonding of the overlay caused a marked increase, over that for the well-bonded case, in the observed amplitude of the quasi-shear pulses leaked to the top of the overlay by decay of the interface wave. More experiments are needed to establish whether leaky interface waves are sensitive to bond condition for various other combinations of substrate, overlay and contaminant.     

Phase and Dispersion of Cylindrical Surface Waves

Most theoretical and experimental work on surface waves does not take into account dispersion. When propagating along a flat planar half space, surface waves are known as Rayleigh waves and are not dispersive. When the radii of curvature are large, surface waves behave like Rayleigh waves. However, when the radii are small, dispersion becomes a contributing factor. Experimental measurements indicate that along with dispersion, there appears to be a strong phase shift effect as the wave propagates along the circumferential path of cylindrical specimens. The phase shift effect is observed even under conditions where dispersion is not detected. Classical theories provide the velocity-frequency equations, which represent the dispersion relationships, for surface waves. An alternate theoretical approach is discussed in this article that demonstrates the phase-dispersion relationship for cylindrical surface waves. Experimental data support the theoretical conclusions and indicate phase shift is directly related to the radius of curvature to an extent much more sensitive than dispersion.     

Thermal effect on gravity waves in a compressible liquid layer over a solid half-space under initial hydrostatic stress

This paper deals with the effect of temperature on gravity waves in a compressible liquid layer over a solid half-space. It has been assumed that the liquid layer is under the action of gravity, while the solid half-space is under the influence of initial compressive hydrostatic stress. When the temperature of the half-space is altered, gravity waves propagate through the liquid layer along with sub-oceanic Rayleigh waves in the system. A new frequency equation has been derived here for gravity waves and sub-oceanic Rayleigh waves. It has been shown graphically that the phase velocity of gravity waves is influenced significantly by the initial compressive hydrostatic stress present in the solid half-space, for a particular value of the phase velocity of sub-oceanic Rayleigh waves and different coupling co-efficients of the temperature.     

Depth measurement for cracks in corners using ultrasonic Rayleigh waves

The scattering of ultrasonic Rayleigh waves incident normally on corners containing cracks is considered by using elastodynamic ray theory. Detailed calculations are presented for vertical and horizontal cracks in right-angle corners in aluminium. It is shown that crack depth can be measured simply from the spacing of interference fringes in the high-frequency spectra of either the back- or forward-scattered Rayleigh waves, given only a knowledge of the Rayleigh wave speed. Use of the back-scattered wave is preferable because its fringes show stronger modulation, and because an experiment requires a single transducer and access to only one face of the specimen. The technique is applicable without modification to the more general case of a crack at any angle in a corner of any angle.     

Quantitative use of Rayleigh waves to locate and size subsurface holes

An ultrasonic inspection method is used to obtain the circumference of a subsurface hole and the depth of the hole below the surface. A pitch-catch Rayleigh wave transducer set-up was used to launch a Rayleigh surface wave at the flaw and to capture and record the scattered waves. The frequency spectrum of the scattered waves can be used to obtain the depth of the hole. The ligament of material between the hole and the surface is sent into resonance, and this feature can be extracted from the scattered waves' frequency spectrum. The frequency is a function of the ligament length; thus the hole depth can be obtained. The circumference of the hole is found from a time of flight measurement. A Rayleigh wave is formed that travels around the hole's surface. The length of time required for the wave to travel around the hole is a measure of the circumference.     

Rayleigh waves in Cosserat elastic materials

The present paper gives explicit solutions for surface waves propagation in a homogeneous half space filled with an isotropic Cosserat elastic material. Such solutions are important in the study of seismic waves in an earthquake, supposing that the bottom land is modeled as having a microstructure. To construct explicit expressions for the possible surface waves under consideration, we use the Stroh formalism. These solutions are further used to study the Rayleigh waves and to give the explicit equation for the Rayleigh surface wave speed (secular equation). Numerical calculations and graphics corresponding to the analytical solution are given for aluminium-epoxy composite.     

Rayleigh wave interaction with inhomogeneities—Part 1: Near surface cavity and inclusion

The interaction of a Rayleigh pulse with a circular cavity and circular inclusion has been examined employing dynamic photoelasticity. The explosively generated R-pulse travels along the free boundary and is trapped in the ligament between the cavity and the free boundary with little energy propagating around the cavity. For cavities and inclusions at shallow depth below the free surface failure of the ligament occurs and most of the energy associated with the incident R-wave is converted by diffraction into body and surface waves. The existence of a shadow zone on the downstream side of the circular cavity provides a means of identifying the location of the cavity which is nearly tangent to the surface by e.g. ultrasonic inspection.     

Rayleigh surface wave propagation in an orthotropic rotating magneto-thermoelastic medium subjected to gravity and initial stress

Abstract

The prime objective of the present article is to analyze the effects of rotation and initial stress on the propagation of Rayleigh surface waves in a homogeneous, orthotropic magneto-thermoelastic half space subjected to gravity field. The frequency equations in closed form are derived and the amplitude ratios of surface displacements, temperature change during the Rayleigh wave propagation on the surface of half space have been computed analytically. The highlights of this study are the effects of different parameters (rotation, magnetic field, initial stress, and gravity) on the velocity of Rayleigh waves. Variation in phase velocity of Rayleigh waves against a wave number is shown graphically. Some particular cases have been deduced. Also, the classical Rayleigh wave equation is obtained as a special case of the present study. Numerical example has been carried out and represented by the means of graphs. Impacts of various involved parameters appearing in the solutions are carefully analyzed. In fact, in the absence of various parameters, these equations are in agreement with the results for isotropic medium.     

On dispersion relations of Rayleigh waves in a functionally graded piezoelectric material (FGPM) half-space

For propagation of Rayleigh surface waves in a transversely isotropic graded piezoelectric half-space with material properties varying continuously along depth direction, the Wentzel–Kramers–Brillouin (WKB) technique is employed for the asymptotic analytical derivations. The phase velocity equations for both the electrically open and shorted cases at the free surface are obtained. Influences of piezoelectric material parameters graded variations on Rayleigh wave dispersion relations, particles’ displacements magnitude and corresponding decay properties are discussed. Results obtained indicate that coupled Rayleigh waves can propagate at the surface of the graded piezoelectric half-space, and their dispersion relations and the particles displacements ellipticity at the free surface are dependent upon the graded variation tendency of the material parameters. By the Rayleigh surface waves phase velocities relative changing values combined with the relationship between the wave number and the material graded coefficient, a theoretical foundation can be provided for the graded material characterization by experimental measurement.     

Waves Generated by a Moving Source in a Two-Layer Ocean of Finite Depth

The velocity potentials of a point source moving at a constant velocity in the upper layer of a two-layer fluid are obtained in a form amenable to numerical integration. Each fluid layer is of finite depth, and the density difference between the two layers is not necessarily small. The far-field asymptotic behavior of the surface waves and internal waves are also derived using the method of stationary phase. They show that the wave system at the free surface or at the interface each contains contributions from two different modes: a surface-wave mode and an internal-wave mode. When the density difference between the two layers is small or the depth of the upper layer is large, the surface-wave mode mainly affects the surface waves while the internal-wave mode mainly affects the internal waves. However, for large density difference, both modes contribute to the surface wave or internal wave system. For each mode, both divergent and transverse waves are present if the total depth Froude number is less than a certain critical Froude number which is mode-dependent. For depth Froude number greater than the critical Froude number, only divergent waves exist for that mode. This classification is similar to that of a uniform fluid of finite depth, where the critical Froude number is simply unity. The surface waves and internal waves are also calculated using the full expressions of the source potentials. They further confirm and illustrate the features observed in the asymptotic analysis.     

Electromagnetic effects on Rayleigh surface wave propagation in a homogeneous isotropic thermo-microstretch elastic half-space

This paper deals with the problem of electromagnetic effect on the propagation of Rayleigh surface waves in a homogeneous, isotropic, thermally-conducting microstretch elastic half-space. In this context, the generalized theory of thermoelasticity is considered. The governing equations for the Rayleigh surface waves in the cases of insulated as well as isothermal boundaries are derived. In the presence of the magnetic effect, the analytical expressions for the displacement, microrotation, microstretch, and temperature changes are obtained. The changes in the phase velocity, microrotation, and path of particles for aluminum epoxy material are presented graphically.     

Effect of gravity on visco-elastic surface waves in solids involving time rate of strain and stress of first order

The aim of the present paper is to study the effect of gravity on visco-elastic surface waves in solids. The wave velocity equations are deduced from Biot’s theory of initial stress on the assumption that gravity creates a type of initial stress — hydrostatic in nature. Resulting equations are used to investigate surface waves of the Rayleigh, Love and Stoneley types. Results are in good agreement with corresponding classical results when gravity and viscosity are neglected.     

Surface acoustic breathers of self-induced transparency in semiconductors

A theory of the nonlinear surface acoustic waves in semiconductors containing paramagnetic impurities is constructed. The formation of surface acoustic breathers under the conditions of self-induced transparency is considered. Explicit analytic expressions for the breathers of Rayleigh waves are obtained. It is shown that the interaction of an acoustic wave with conduction electrons leads to a weak damping of the wave amplitude and a change in the breather parameters.