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.     

Propagation of Rayleigh, Scholte and Stoneley waves along random boundaries

The effect of boundary roughness on the propagation of Rayleigh, Scholte and Stoneley waves is analysed under the assumption of the wavelength being much larger than the roughness scale of the interface. The scattering of the fundamental interface waves is represented by systems of plane waves in both neighbouring half-spaces; the formulas for amplitudes of these waves are determined using the perturbation method. The phase velocity of the interface waves is analysed by an approximate technique and is found to increase with the growing boundary roughness for all three types of interface waves.     

Surface roughness induced attenuation and changes in the propagation velocity of long Rayleigh-type waves

Summary The propagation of long Rayleigh waves on a rough surface is studied theoretically by Rayleigh method and for the free rough surface of a homogeneous and isotropic elastic half-space. The frequency dependence of the propagation velocity and attenuation is analysed under the assumption that the frequency is real. Moreover, the changes in the propagation velocity induced by the surface roughness are expressed in terms of the square of the ratio of the root-mean-square departure of the surface from flatness to the correlation length of the distance between successive peaks and valleys in the rough-surface profile.     

Surface wave propagation in a fluid-saturated incompressible porous medium

A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.     

Propagation of pure shear surface waves in magnetostrictivepolycrystalline ferrites

The launching and propagation of pure shear surface waves (SSW) in magnetostrictive polycrystalline ferrite were studied. The results show that SSW have lower sensitivity to surface quality than Rayleigh waves, but the launching effectiveness by a meander-type transducer is lower than for Rayleigh waves. The variation in phase velocity of SSW on a magnetic field was 4.5%, which can be of interest in applications     

Transmitted scattered light from a thin film with shallow random rough interfaces

The transmitted scattered energy of plane electromagnetic waves from a thin metallic film with shallow rough interfaces bounded by two semi-infinite media is calculated. Both interfaces are modeled as independent stationary random processes with a Gaussian roughness spectrum. Scattering of light is calculated for both TM (p) or TE (s) polarizations for normal and oblique angles of incidence. An integral equation is obtained for the transmitted field based on the Rayleigh method and their solution involves Fourier coefficients, depending on the roughness profiles. We present some results for the case of a single thin metallic film in the attenuated total reflection configuration for s and p polarization around the angle of the excitation of surface-plasma waves θ(sp). The transmitted scattered intensity shows a maximum at the resonant angle θ(sp) in the case of p polarization.     

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.     

Elastic properties of proton exchanged lithium niobate

A method is demonstrated for determination of elastic constants of anisotropic layers on arbitrarily anisotropic and piezoelectric substrates only using the easily measured velocity of surface acoustic waves. By means of a detailed theoretical analysis it is shown that by use of the presented method, the elastic stiffness constants and propagation properties of any nonpiezoelectric isotropic, cubic, or even trigonal layer can be determined. The method is applied to proton-exchanged lithium niobate (PE:LiNbO(3)). Complete measurements of dispersion characteristics of Rayleigh waves on Y -cut PE:LiNbO(3) and calculated values of all elastic stiffness constants of the proton-exchanged film are reported.     

Love type waves in a porous layer with irregular interface

The dispersion equation is derived relating to the frequency and the phase velocity of propagation of Love waves in a nondissipative liquid filled porous solid underlain by an isotropic and homogeneous half space. The rectangular irregularity in the interface between the upper porous layer and the lower semi-infinite medium with a source in it is studied herein. The modified dispersion equation of Mal and the standard dispersion equation of Love waves are deduced as particular cases. In the present study, the frequency equation is obtained by applying the method of perturbation and the phase velocity curves have been drawn for different irregularities by using the numerical parameteric values as suggested by Biot.     

Propagation of Surface Acoustic Pulses Generated by a Femtosecond Laser in Thin Films on Solid Substrates

The technique of phase velocity dispersion measurements of surface acoustic waves in a thin film-substrate system was demonstrated. The excitation of surface acoustic waves (SAWs) was quite efficient with femtosecond laser pulses, and the damage of the surface was minimized. The measurements were performed with films of Al deposited on silicon wafers. The errors in the determination of the phase velocity and absorption were analyzed. The temperature changes in the propagation velocity on bare Si wafers were also measured. The data obtained permitted estimation of the accuracy of the temperature determination from measurements with SAW pulses.     

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.     

Dispersion and characteristic surfaces of waves in hybrid multilayered piezoelectric circular cylinders

The frequency and group velocity dispersion behaviors, and characteristic surfaces of waves in a hybrid multilayered piezoelectric circular cylinder are investigated. The associated frequency dispersion equation is developed using an analytical-numerical method. In this method, the cylinder is modeled using the three-nodal-line layer element; the coupling between the elastic field and the electric field is considered in each element. A system of governing differential equations of each layer element is obtained following the Hamilton Principle. The phase velocity and slowness as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces, e.g. the phase velocity, slowness and wave surfaces as well as the group velocity, slowness and wave surfaces, are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. A corresponding program code is developed and numerical examples are presented for hybrid multilayered piezoelectric circular cylinders with two ratios of radius to thickness.     

Coherence solution for bidirectional reflectance distributions of surfaces with wavelength-scale statistics

The scalar bidirectional reflectance distribution function (BRDF) due to a perfectly conducting surface with roughness and autocorrelation width comparable with the illumination wavelength is derived from coherence theory on the assumption of a random reflective phase screen and an expansion valid for large effective roughness. A general quadratic expansion of the two-dimensional isotropic surface autocorrelation function near the origin yields representative Cauchy and Gaussian BRDF solutions and an intermediate general solution as the sum of an incoherent component and a nonspecular coherent component proportional to an integral of the plasma dispersion function in the complex plane. Plots illustrate agreement of the derived general solution with original bistatic BRDF data due to a machined aluminum surface, and comparisons are drawn with previously published data in the examination of variations with incident angle, roughness, illumination wavelength, and autocorrelation coefficients in the bistatic and monostatic geometries. The general quadratic autocorrelation expansion provides a BRDF solution that smoothly interpolates between the well-known results of the linear and parabolic approximations.     

Generalized RayleighWave Dispersion Analysis in a Pre-stressed Elastic Stratified Half-space with Imperfectly Bonded Interfaces

Within the framework of the piecewise homogeneous body model the influence of the shear-spring type imperfect contact conditions on the dispersion relation of the generalized Rayleigh waves in the system consisting of the initially stressed covering layer and initially stressed half plane is investigated. The second version of the small initial deformation theory of the three-dimensional linearized theory of elastic waves in initially stressed bodies is applied and the elasticity relations of the materials of the constituents are described by the Murnaghan potential. The magnitude of the imperfectness of the contact conditions is estimated through the shear-spring type parameter. Consequently, the influence of the imperfectness of the contact conditions on the generalized Rayleigh wave propagation velocity is studied through the influence of the values of this parameter. Numerical results on the action of the imperfectness of the contact conditions and the influence of the initial stresses in the constituents on the wave dispersion curves are presented and discussed. In particular, it is established that the magnitude of action of the imperfectness of the contact conditions under the influence of the initial stresses on the wave propagation velocity cannot be limited with corresponding ones obtained in the case where the contact between the constituents is complete and in the case where this contact is full slipping one. The possible application of the obtained results on the geophysical and geotechnical engineering is also discussed.     

间隙波在功能梯度压电板和压电半空间结构中的传播

研究了间隙波在功能梯度压电板和压电半空间结构中的传播性质.功能梯度压电板的材料性能沿x2方向呈指数变化,首先推导了间隙波传播时的解析解,利用界面条件得到了间隙波的频散方程,基于推导的频散方程,结合数值算例分析了功能梯度压电材料的梯度、压电层厚度以及材料性能对间隙波相速度的影响,研究结果对功能梯度压电材料的覆层结构在声波器件中的应用具有重要的参考价值.     

Coupled Tamm waves guided by an isotropic and homogeneous dielectric layer in a rugate filter

The propagation of Tamm waves (also known as Bloch surface waves) guided by a layer of homogeneous dielectric material in a rugate filter was studied theoretically. A canonical boundary-value problem was set up and a dispersion equation was obtained. The solution of the dispersion equation indicated the existence of coupled modes of Tamm waves that were absent when the homogeneous dielectric material was taken to occupy a half space. The spatial profiles of the electric and magnetic fields of Tamm waves showed that Tamm waves propagate localized to either one or both interfaces. Multiple Tamm waves may lead to multi-analyte chemical sensors and multi-channel communication.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part I. Stochastic interface models

A theoretical model for ultrasonic wave scattering by geometrically irregular and imperfectly bonded interfaces is presented. In Part I, the normal stiffness of interfaces formed by the partial contact of solids with rough surfaces is estimated for two models of contacting surfaces with random roughness in one dimension only. The first model considers nonconforming surfaces with a single-scale of roughness, while double-scale roughness characterizes the surfaces of the second model, which are conforming at the large scale and nonconforming at the smaller scale. The surfaces' profiles are described by Gaussian probability and spectral densities. The surfaces at each contact are modeled by two cylinders under a compressive load and the normal stiffness per unit area of the interface is evaluated by averaging the stiffness of all the contacts, assuming they do not interact with each other. It is shown that the smaller the roughness, the softer the interface; the larger the autocorrelation length, the softer the interface; and the smaller the initial aperture, the stiffer the interface. Furthermore, interfaces described by the second model appear much stiffer than those described by the first model. The interface characterizations and normal stiffness models developed in Part I will be used in Part II to study the scattering of ultrasonic plane waves by such an interface.     

Finite element simulation and visualization of leaky Rayleigh wavesfor ultrasonic NDE

The generation and propagation properties of transient leaky Rayleigh waves are characterized by a two-dimensional finite element model. The displacement vector is used as the primary variable for the solid medium and a potential scalar, which is a replacement for the pressure, is taken as the fundamental variable for the fluid medium. The coupled system of finite element equations are solved in the time domain by direct integration through the central difference scheme. Three configurations are considered: the conversion of a Rayleigh surface wave into a leaky Rayleigh wave, a focused beam probing a fluid/solid interface at the Rayleigh angle, and the interaction of a defocused wave with the interface. The wave velocity in the fluid (water) is lower than the Rayleigh wave velocity in the solid (aluminum). The wave propagation profile in each case is predicted by the model. The finite element model proves to be an effective tool for surface acoustic device design and ultrasonic NDE     

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.     

Theoretical and Experimental Identification of Love Wave Frequency Peaks in Layered Structure ZnO/Quartz SAW Device

In this paper, the layered structure ZnO/Quartz (90^deg rotated ST-cut) is investigated theoretically and experimentally. Both waves, Rayleigh and Love, are analyzed. Dispersion curves of phase velocities, electromechanical coupling coefficient (K ²) and temperature coefficient of frequency (TCF) were calculated as a function of normalized thickness ZnO film (kh _ZnO = 2pih _ZnO /lambda) and the optimum value of h _ZnO was determined for experimental study. Experimental results combined with simulation lead to clearly identify the generated waves and their higher modes in this structure except the mode 0 that shows comparable velocity for both Rayleigh and Love waves. The identification of the wave type was performed by studying the frequency response of the device with or without a droplet of water in the wave path. We also demonstrate that the highest elastic velocity is obtained for the mode 1 of the Love wave. This Love wave mode exhibits very interesting electrical characteristics, good K ², high-frequency rejection, low TCF, and very low attenuation in liquid making it very attractive for gas and liquid sensor applications.