Rayleigh-type Surface Waves Research Articles

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano’s and Ferrari’s methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.

Effect of surface wave propagation in a four-layered oceanic crust model

Dispersion of Rayleigh type surface wave propagation has been discussed in four-layered oceanic crust. It includes a sandy layer over a crystalline elastic half-space and over it there are two more layers—on the top inhomogeneous liquid layer and under it a liquid-saturated porous layer. Frequency equation is obtained in the form of determinant. The effects of the width of different layers as well as the inhomogeneity of liquid layer, sandiness of sandy layer on surface waves are depicted and shown graphically by considering all possible case of the particular model. Some special cases have been deduced, few special cases give the dispersion equation of Scholte wave and Stoneley wave, some of which have already been discussed elsewhere.

Study of Rayleigh type surface wave in the initial stressed irregular bottom of ocean due to point source

Rayleigh type surface wave propagation in the irregular bottom of ocean model which is the interface of homogeneous liquid layer over laying an irregular boundary of homogeneous orthotropic half space under initial stresses has been discussed in this paper. Three different dispersion equations are obtained in the form of simple equation using and not using Perturbation technique. Some special cases have been considered. The effect of irregularity, initial stressed, point source, and depth of liquid layer on the propagation of Rayleigh waves has been analyzed and results of numerical discussion have been presented graphically for three different dispersion equations. Mainly the graphs are shown the variation of phase velocity with wave number in different cases.

A fluid-saturated porous medium under the action of a moving concentrated load

The problem of motion of a concentrated load along the surface of a fluid-saturated porous medium is studied for a subsonic range of speeds. An analytical solution is found. It is shown that there exists a critical speed equal to the speed of the Rayleigh-type surface waves in a porous elastic medium. If this critical speed is exceeded, then the behavior of the solution and the free surface shape are changed. The free surface shape is analyzed at different speeds.

Influence of prestress and periodic corrugated boundary surfaces on Rayleigh waves in an orthotropic medium over a transversely isotropic dissipative semi-infinite substrate

The paper environs the study of Rayleigh-type surface waves in an orthotropic crustal layer over a transversely isotropic dissipative semi-infinite medium under the effect of prestress and corrugated boundary surfaces. Separate displacement components for both media have been derived in order to characterize the dynamics of individual materials. Suitable boundary conditions have been employed upon the surface wave solutions of the elasto-dynamical equations that are taken into consideration in the light of corrugated boundary surfaces. From the real part of the sixth-order complex determinantal expression, we obtain the frequency equation for Rayleigh waves concerning the proposed earth model. Possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. Numerical computations have been performed in order to graphically demonstrate the role of the thickness of layer, prestress, corrugation parameters and dissipation on Rayleigh wave velocity. The study may be regarded as important due to its possible applications in delay line services and investigating deformation characteristics of solids as well as typical rock formations.

Rayleigh-type waves in nonlocal micropolar solid half-space

Propagation of Rayleigh type surface waves in nonlocal micropolar elastic solid half-space has been investigated. Two modes of Rayleigh-type waves are found to propagate under certain approximations. Frequency equations of these Rayleigh type modes and their conditions of existence have been derived. These frequency equations are found to be dispersive in character due to the presence of micropolarity and nonlocality parameters in the medium. One of the frequency equations is a counterpart of the classical Rayleigh waves and the other is new and has appeared due to micropolarity of the medium. Phase speeds of these waves are computed numerically for Magnesium crystal and their variation against wavenumber are presented graphically. Comparisons have been made between the phase speeds of Rayleigh type waves through nonlocal micropolar, local micropolar and elastic solid half-spaces.

Surface Waves in a Viscoelastic Liquid Half-Space Under Initial Stress in Presence of Thermal and Magnetic Field

In this paper propagation of Rayleigh-type surface waves in a homogeneous, isotropic, perfectly conducting viscoelastic liquid half-space under initial stress in presence of thermal and magnetic field has been discussed, in the context of generalized thermoelasticity using Green–Lindsay model. The frequency equation signifying the velocity of Rayleigh surface waves has been established. The velocity of Rayleigh surface waves is computed numerically for different values of initial stress parameter, magnetic pressure number, thermoelastic coupling parameter and viscosity. The results are shown graphically.

Rayleigh-Type Surface Waves in a Swelling Porous Half-Space

The present work deals with the propagation of Rayleigh-type surface waves in a swelling porous elastic half-space consisting of three phases, namely solid matrix, liquid (viscous) and gas (inviscid). Using Eringen’s theory of swelling porous media, the governing equations are first solved by potential method. Frequency equation of Rayleigh-type waves has been derived, which is found to be irrational due to the presence of radicals in it. This irrational equation has been rationalized into a polynomial, which is then solved numerically for a specific porous model consisting of sandstone, water (viscous) and carbon dioxide as solid, liquid and gas phases, respectively. The nature of Rayleigh-type surface waves in the considered swelling porous medium is found to be inhomogeneous. Two modes of Rayleigh-type surface waves are noticed: One of them is the counterpart of the classical Rayleigh wave, while the second mode of Rayleigh-type surface waves arises due to the presence of either liquid or gas phases of the swelling porous medium. The variation of phase speeds and the corresponding attenuations of Rayleigh-type surface waves are depicted graphically against frequency parameter for the selected model. In the considered model, the swelling parameter has negligible effect on the propagation speeds of Rayleigh-type surface modes. It is also observed that in the absence of swelling, there still exist two modes of Rayleigh-type waves. The effect of the viscosity of the liquid constituent present in the pores is also examined on the phase speeds and attenuations. The results of Gales (Eur J Mech A Solids, 23:345–357 2004) for the cases of fluid saturation alone and gas saturation alone have also been deduced analytically as special cases from the present formulation.

Circular synthetic aperture sonar images of backscattering enhancements on solid elastic cubes due to Rayleigh waves and other mechanisms

Aspect dependent backscattering enhancement mechanisms aid in detecting and identifying underwater objects. This work examines enhancement mechanisms on a solid metal cube observed in acoustic images, emphasizing Rayleigh type surface waves that undergo retroreflection at the corners of the face of the cube [K. Gipson and P. L. Marston, J. Acoust. Soc. Am. 105, 700–710 (1998)]. Backscattering from a steel cube insonified in water was measured using a circular synthetic aperture sonar system. Image reconstruction was performed using Fourier based algorithms. Rayleigh waves are launched on a face of the cube when the local incident angle is equal to the Rayleigh coupling angle. The presence of four right-angle retroreflectors on each face means that multiple reverberations of this wave are observed. In reconstructed images of the cube, the Rayleigh wave mechanism is responsible for some of the brightest features. If the relative orientation of the circular aperture and the cube is such that specular glints are suppressed, edge and corner diffraction features are clearly observed. This relative orientation may be deduced from the reconstructed image. Discussions of both the spectral response and temporal response of the cube as a function of viewing angle will also be included. [Work supported by ONR.]

Effect of reinforcement, gravity and liquid loading on Rayleigh-type wave propagation

In the present time, self-reinforced materials are the basic requirement for civil engineering construction. These constructions encounter surface wave propagation during earthquakes and similar disturbances. Therefore, the study of surface wave propagation in such material is of great significance. The present paper, in the light of practical situation like dams, canals etc. aims to study the effect of gravity on the propagation of Rayleigh-type surface wave in a self-reinforced semi-infinite medium bounded and loaded by an inviscid liquid layer. Secular equation for the propagation of Rayleigh-type wave has been derived in closed form. The effect of gravity, reinforcement and liquid loading on phase velocity of Rayleigh-type wave has been distinctly observed. Numerical computation has been carried out and graphical illustration is provided for analysis of the presented study. Moreover, the effect of reinforced semi-infinite medium is compared to the effect of reinforced free semi-infinite medium on the phase velocity of Rayleigh-type surface wave to unravel the reinforcement effect. The effect of presence and absence of liquid loading on self-reinforced semi-infinite medium for Rayleigh-type wave propagation is also analysed and depicted by means of graphs.

On Propagation of Rayleigh Type Surface Wave in a Micropolar Piezoelectric Medium

In the present paper, the governing equations of a linear transversely isotropic micropolar piezoelectric medium are specialized for x-z plane after using symmetry relations in constitutive coefficients. These equations are solved for the general surface wave solutions in the medium. Following radiation conditions in the half-space, the particular solutions are obtained, which satisfy the appropriate boundary conditions at the stress-free surface of the half-space. A secular equation for Rayleigh type surface wave is obtained. An iteration method is applied to compute the non-dimensional wave speed of the Rayleigh surface wave for specific material parameters. The effects of piezoelectricity, non-dimensional frequency and non-dimensional material constant, charge free surface and electrically shorted surface are shown graphically on the wave speed of Rayleigh wave.

Improved model of a layered medium with slip on the contact boundaries

The continuum equations of a layered medium with slip taking into account second-order terms with respect to a small parameter of the layer thickness are obtained on the basis of the asymptotic homogenization method. A linear slip condition is used that relates the jumps in the tangential displacements at the interlayer boundaries to the shear stresses. The equations obtained are also an asymptotically complete unification of several models of a layered media based on engineering approaches or approximate hypotheses on the nature of the layers deformation's, The wave properties of the system of equations obtained are investigated and dispersion relations are written out for harmonic waves. The solution of a problem of a Rayleigh-type surface wave on the boundary of an elastic layered half-space is constructed.

Surface wave propagation in sandy layer overlying a liquid saturated porous half-space and lying under a uniform liquid layer

ABSTRACTDispersion of Rayleigh-type surface waves is studied in a sandy layer under a uniform layer of homogeneous liquid lying over liquid-saturated porous solid half-space. The frequency equation in the form of a ninth-order determinant is obtained and evaluated. Special cases have been deduced and dispersion curves for the phase velocity and wave number have been plotted for a particular model.

Cylindrical Rayleigh surface waves on a layer-coated cylinder measured by PVDF transducer and defocusing measurement method

This paper develops a measurement method for accurately determining dispersion curves of Rayleigh-type surface waves propagating on layer-coated elastic cylinders. It utilizes PVDF acoustic transducers and a defocusing measurement system. To deal with the cylindrically curved surface, a new cross-correlation waveform processing approach is proposed and verified. Cylindrical Rayleigh wave velocities of layered cylindrical solid samples have been successfully measured over a frequency range from 3 to 20MHz. The measured dispersion curves are in good agreement with their theoretical counterparts. It demonstrates the potential application for non-destructive evaluation of coating layers deposited on cylindrical solids.

Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre.

Brillouin scattering in optical fibres is a fundamental interaction between light and sound with important implications ranging from optical sensors to slow and fast light. In usual optical fibres, light both excites and feels shear and longitudinal bulk elastic waves, giving rise to forward-guided acoustic wave Brillouin scattering and backward-stimulated Brillouin scattering. In a subwavelength-diameter optical fibre, the situation changes dramatically, as we here report with the first experimental observation of Brillouin light scattering from surface acoustic waves. These Rayleigh-type surface waves travel the wire surface at a specific velocity of 3,400 m s−1 and backscatter the light with a Doppler shift of about 6 GHz. As these acoustic resonances are sensitive to surface defects or features, surface acoustic wave Brillouin scattering opens new opportunities for various sensing applications, but also in other domains such as microwave photonics and nonlinear plasmonics.

Surface Wave Propagation in a Microstretch Thermoelastic Diffusion Material under an Inviscid Liquid Layer

The present investigation deals with the propagation of Rayleigh type surface waves in an isotropic microstretch thermoelastic diffusion solid half space under a layer of inviscid liquid. The secular equation for surface waves in compact form is derived after developing the mathematical model. The dispersion curves giving the phase velocity and attenuation coefficients with wave number are plotted graphically to depict the effect of an imperfect boundary alongwith the relaxation times in a microstretch thermoelastic diffusion solid half space under a homogeneous inviscid liquid layer for thermally insulated, impermeable boundaries and isothermal, isoconcentrated boundaries, respectively. In addition, normal velocity component is also plotted in the liquid layer. Several cases of interest under different conditions are also deduced and discussed.

Subsonic Free Surface Waves in Linear Elasticity

For general anisotropic linear elastic solids with smooth boundaries, Rayleigh-type surface waves are studied. Using spectral factorizations of matrix polynomials, a self-contained exposition of the case of a homogeneous half-space is given first. The main result is about inhomogeneous anisotropic bodies with curved surfaces. The existence of subsonic free surface waves is shown by giving ray series asymptotic expansions, including formulas for the transport equation.

Characterization of micrometric and superficial residual stresses using high frequency surface acoustic waves generated by interdigital transducers

Controlling thin film deposition of materials and property gradients is a major challenge for the implementation of applications in microelectronics or glassmaking. It is essential to control the level of residual stress and thus important to have the right tools to characterize this stress in terms of scale and nature of the deposits. In this context, dispersion of ultrasound surface waves caused by the presence of a residual micrometric surface stress was studied in an amorphous medium for different superficial fields of residual stress. The design and implementation of SAW-IDT MEMS sensors enabled quasi-monochromatic Rayleigh-type surface waves to be generated and the dispersion phenomenon to be studied over a wide range of frequencies. The thicknesses of the stressed cortical zones as well as the level of stress were estimated with good accuracy using an inverse method.

Surface wave studies for shear wave velocity and bedrock depth estimation over basalts

Shear wave velocity (V S) estimation is of paramount importance in earthquake hazard assessment and other geotechnical/geo engineering studies. In our study, the shear wave velocity was estimated from ground roll using multichannel analysis of surface wave (MASW) technique making use of dispersive characteristics of Rayleigh type surface waves followed by imaging the shallow subsurface basaltic layers in an earthquake-prone region near Jabalpur, India. The reliability of MASW depends on the accurate determination of phase velocities for horizontally traveling fundamental mode Rayleigh waves. Inversion of data from surface waves resulted in a shear wave velocity (V S) in the range of 200–1,200 m/s covering the top soil to weathering and up to bedrock corresponding to a depth of 10–30 m. The P-wave velocity (V P) obtained from refraction seismic studies at these locations found to be comparable with V S at an assumed specific Poisson’s ratio. A pair of selected set of V S profiles over basalt which did not result in a hazardous situation in an earthquake of moderate magnitude are presented here as a case study; in other words, the shear wave velocity range of more than 200 m/s indicate that the area is highly unlikely prone to liquefaction during a moderate or strong earthquake. The estimated depth to basalt is found to be 10–12 m in both the cases which is also supported by refraction studies.

Site-specific shear wave velocity investigation for geotechnical engineering applications using seismic refraction and 2D multi-channel analysis of surface waves

In order to quantify the near-surface seismic properties (P- and S-wave velocities, and the dynamic elastic properties) with respect to the depth at a specific area (6th of October club), we conducted a non-invasive and low cost active seismic survey. The primary wave velocity is determined by conducting a P-wave shallow seismic refraction survey. The dispersive characteristics of Rayleigh type surface waves were utilized for imaging the shallow subsurface layers by estimating the 1D (depth) and 2D (depth and surface location) shear wave velocities. The reliability of the Multi-channel Analysis of Surface Waves (MASW) depends on the accurate determination of phase velocities for horizontally traveling fundamental mode Rayleigh waves. Consequently, the elastic properties are evaluated empirically. The Vs30 (average shear wave velocity down to 30m depth), which is obtained from the MASW technique, plays a critical role in evaluating the site response of the upper 30m depth. The distribution of the obtained values of Vs30 through the studied area demonstrates site classes of C and D, according to the NEHRP (National Earthquake Hazard Reduction Program) and IBC (International Building Code) standards.