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 axisymmetric waves on the surface of a cylindrical cavity in elastic medium

A nondamped axisymmetric mode that propagates in an elastic cylindrical waveguide representing an extended cavity with a circular cross section in an infinite homogeneous medium is described. The wave dispersion in this system is analyzed and the similarity with and differences from other elastic media with one boundary are considered, including an infinite round rod and the surface of a half-space (Rayleigh wave). It is shown that, for axisymmetric waves in the cavity, a boundary frequency dependent on the curvature radius always exists, below which the waves are evanescent. A physical interpretation of results is given.     

Calculation of the statistical characteristics of the light reflected by a rough random cylindrical homogeneous Gaussian surface

Statistical characteristics of light reflected by a rough random cylindrical homogeneous Gaussian surface are investigated using a modified method of specular points, as developed by Gardashov. In this proposed method, a special procedure for determining the light intensity near the caustics has been formulated. The probability distribution of the intensity of reflected light is expressed in terms of a special function, which is determined by the characteristic function of distribution of radii of curvature at the specular points and the distribution density of the number of specular points. The distribution of radii of curvature, derived by Gardashov, and expressed in terms of dimensionless radii of curvature, has a simple expression which does not contain any parameter of the surface (as a surface rms deviation, etc.). Consequently, it is universally valid and applicable to any cylindrical homogeneous Gaussian surface. After modification, the infinite dispersion of the reflected light intensity turns into a finite. The relationship between the distributions of reflected light intensity and the number of specular points, in the form of a Fredholm integral equation of the first kind is obtained. The kernel of the integral equation is expressed in terms of a characteristic function of the radii of curvature at specular points. The validity of formulae and relationships, thus derived, is tested by numerical simulations.     

Acoustic microscopy and dispersion of leaky Rayleigh waves onrandomly rough surfaces: a theoretical study

A theoretical investigation of the dispersion of leaky Rayleigh waves propagating along one-dimensional (1-D) rough fluid-solid interfaces was carried out by simulating the measurement process of a line-focus beam acoustic microscope. The interface profiles were described in terms of their rms, also known as the roughness of the profile, autocorrelation length, and autocorrelation function. The reflectivity of the interfaces was calculated by using a second-order perturbation approach in the profile roughness. Theoretical V(z) curves were generated and analyzed to yield values of the phase velocity of the Rayleigh waves. The dependence of the Rayleigh wave velocity on the profile and material parameters was examined. Significant variations of the phase velocity were found for values of the roughness which are small compared to the shortest of the wavelengths involved in the scattering. The dispersion relations also showed considerable sensitivity to changes in mechanical properties typical of materials of engineering interest. In the low-frequency range, simulations indicated the dispersion of Rayleigh waves to be rather insensitive to the spectral content of the profile     

Elastodynamic Doppler effects

Summary The Doppler effect is discussed for flexure waves in beam and plate, three body waves (P, SV, SH) in an infinite solid, modal SH waves in a thick plate and a Rayleigh wave on the surface of a semi-infinite solid. The exact closed form solution for each elasto-dynamic problem is obtained and the simple equation for the Doppler frequency shift is derived for all waves. It is shown that the Doppler frequency shift takes place continuously in the 2D plane problems, and that the most sensible wave for the Doppler frequency shift is the non-dispersion wave, such as the body wave and Rayleigh wave. The flexural and modal waves, which have the dispersion nature, are less sensible. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

Equivalence of Normalized Thermal-Wave Fields Between Curved and Flat Surfaces and Its Application in the Characterization of Curved Samples

Equivalence of the normalized thermal-wave fields between curved and flat surfaces under certain conditions is investigated based on theoretical models of cylindrical, spherical, and flat solids with multilayer structures. The principle and the physical mechanism of the elimination of the surface curvature effect from the overall photothermal signal of the curvilinear solid are suggested. The effects of the relative values of radii of curvature of the curvilinear solid, the thickness of the inhomogeneous surface layer, and the measurement azimuthal angle on the validity of the equivalence principle are discussed. Consistent experimental reconstructions of thermophysical depth profiles of hardened cylindrical steel rods of various diameters are performed and obtained based on both the curvilinear theory and the equivalent flat surface theory.     

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.     

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

In this study, a theoretical method is applied to investigate the multiple scattering of thermal waves and temperature field resulting from a subsurface cylindrical inclusion in a semi-infinite functionally graded material (FGM). The adiabatic boundary condition at the semi-infinite surface is considered. The thermal waves are excited at the surface of semi-infinite functionally graded materials by modulated optical beams. The model includes the multiple scattering effects of the cylindrical thermal wave generated by the line heat source. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented. Numerical calculations illustrate the effect of subsurface inclusion on the temperature and phase change at the sample surface under different physical and geometrical parameters. It is found that the temperature above the conducting cylindrical inclusion decreases because of the existence of the inclusion. The effect of the inclusion on the temperature and phase change at the surface is also related to the non-homogeneous parameter of FGMs, the wave frequency of thermal waves, and the distance between the inclusion and the semi-infinite surface. Finally, the effect of the relaxation time of buried inclusion on the temperature and phase change at the surface is examined.     

Rayleigh waves in a thermoelastic solid half space using dual-phase-lag model

The present paper deals with the study of Rayleigh waves in a thermoelastic homogeneous isotropic solid half space in the context of dual-phase-lag model. The medium is subjected to stress free, thermally insulated, boundary conditions. The equation for the phase velocity of Rayleigh waves and the analytical expressions for the amplitudes of the displacements, temperature and thermal stresses have been derived. The expressions are obtained for a wave traveling along the free surface. The results discussed numerically and illustrated graphically to show effect of the coupling parameter and phase-lags.     

Response of acoustic imaging systems using convergent leaky waves to cylindrical flaws

A theoretical study of imaging systems utilizing focused leaky surface acoustic waves (SAWs), and their response to certain kind of defects is presented. In particular, circular cylindrical inhomogeneities with axes perpendicular to the surface are considered. The scattering of the SAW from this cylinder is formulated with some approximations. The surface wave incident on the inhomogeneity is initially found as an angular spectrum of plane waves. However, to apply the boundary conditions at the cylindrical surface, the incident field has to be transformed into a superposition of cylindrical waves. Similarly, the scattered field, which is found in the form of outgoing cylindrical SAWs, is converted back to a plane wave spectrum. A formula is obtained for the transducer output voltage in terms of the position and the radius of the cylinder, and it is suitable for computer evaluation. By considering various locations for the cylinder, the sensitivity of the system around the focal point is studied. By comparing the output voltages for cylinders of different radii, the sensitivity of the system to the size of the inhomogeneity is examined. The numerical results are in agreement with the experimental observations.     

On the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half space

In this paper, we consider the propagation of surface waves in half spaces made of anisotropic homogeneous thermoelastic materials. When the thermal dissipative properties of a half space are taken into consideration, the undamped characteristic features of Rayleigh waves do not remain valid. Then, the process is irreversible and the Rayleigh waves are damped in time and dispersive. Here, we show that the Stroh formulation of the problem leads to a first-order linear partial differential system with constant coefficients. The associated characteristic equation (the propagation condition) is an eight degree equation with complex coefficients and, therefore, its solutions are complex numbers. Consequently, the secular equation results to be with complex coefficients, and therefore, the surface wave is damped in time and dispersed. The results are illustrated for the case of an orthotropic homogeneous thermoelastic half space, when an explicit bicubic form of the characteristic equation with complex coefficients is obtained. The analysis of these Rayleigh waves in a homogeneous orthotropic half space is numerically exemplified. Further, in the case of an isotropic homogeneous thermoelastic material, the characteristic equation is solved exactly and the general solution of the first-order differential system follows. On this basis, the Rayleigh-type surface waves are studied, and the dispersion condition is found.     

Effects of surface stresses and voids on rayleigh waves in an elastic solid

Rayleigh waves propagating at the plane material boundary of an elastic half-space containing a distribution of voids (vacuous pores) are considered. It is found that the waves are generally dispersive and that the dispersion is caused by both the surface stresses exerted by the boundary and the voids inside. If the body is incompressible, voids have no influence on the motion. In the case of small frequency, the effect of the voids is just to modify the speed of propagation. If the frequency is small and surface stresses are due to a residual surface tension, there exists a critical wavelength at which waves propagate with the speed of pure shear waves and below which the motion is not possible. The critical wave length varies directly with the surface tension and the effect of the voids is to widen the range of wavelengths for which the waves exist.     

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.     

管桩屏障在柱面波源下近场隔振效应的解析求解

基于波函数展开法表示柱面波源自由场,首次提出了一种求解柱面波源下管桩屏障对弹性波隔振效应的解析方法。方法首先考虑柱面波源与管桩屏障的位置关系,采用波函数展开法对入射柱面波进行了0阶Hankel展开表示,并采用任意坐标系间变换的Graf加法定理在任意桩体坐标系中表示,将入射波场和散射波场叠加后通过满足所有桩体的边界条件以求解所有桩体的散射波场。该解析方法分析了柱面波源入射下群桩屏障的隔振效果,首次在排桩隔振问题中考虑了入射波曲率的影响,为柱面波的散射问题提供了理论解答。该文重点讨论了入射波曲率、管桩个数和桩排数等因素对管桩隔振效果的影响,结果表明：整体上管桩屏障对柱面P波的隔振效果优于柱面SV波;柱面波源距离管桩屏障更近时排桩后场地的位移反应显著增大;相比平面波,柱面波源作用下排桩数量的提升对隔振效果的影响较小;三排管桩屏障比两排管桩屏障隔振效果更强,更宜采用三排管桩屏障进行柱面波源的隔振。     

Theory of curved, clamped, piezoelectric film, air-borne transducers

Differential equations in the cylindrical coordinate system have been solved to calculate vibration mode of a curved, clamped, piezoelectric multilayer film. Type I has two clamps at straight ends with uniform film curvature, and Type II has the same two clamps with nonuniform curvature in which the radii are different for the central region and for side regions. The solutions include a uniform displacement term, flexural waves with sinusoidal terms, and a hyperbolic cosine term. By numerical computations, the vibration modes and frequency response of displacement are shown, as are various transducer performances. Mechanical losses of the layer materials were taken as complex Young's moduli with Q values assumed to be constant with frequency. Numerical calculations for 28-/spl mu/m PVDF with 25-/spl mu/m polyester enforcement have shown that (1) the resonance frequency is not necessarily proportional to the inverse of curvature radius as classical theory describes, and, furthermore, resonance diminishes for a certain range of radii, forming a stop band; (2) a back air cavity thinner than 150 /spl mu/m significantly increases the resonance frequency; (3) Type II generates much higher output pressure than Type I; (4) receiver sensitivities for Type I and Type II are not much different; and (5) the effect of radiation impedance is small leading to /spl sim/7% output reduction.     

Direct sequence spread spectrum differential phase shift keying SAW correlator on GaAs

This paper presents the design, fabrication, and experimental results for a differential phase shift keying (DPSK) single SAW-based correlator on GaAs for direct sequence spread spectrum applications. The DPSK modulation format allows for noncoherent data demodulation; the SAW device correlator acts as the despreader. Unlike the conventional technique of using two parallel correlators and a one data bit delay element, this new system uses two inline correlators. When implemented on SAW devices, this in-line structure has the advantage of an inherent one data bit delay, lower insertion loss, and less signal distortion than the parallel structure. The DPSK correlator is fabricated on a {100} cut GaAs substrate with SAW propagation in the 110 direction, Using this cut, which is widely used in electronics, Rayleigh waves are generated with a piezoelectric coupling coefficient of the same order as ST-cut quartz. The piezoelectric semiconductor GaAs is of great interest because it is the only substrate that can be used to integrate SAW devices directly with electronics on the same chip, resulting in smaller packaging, reduction of packaging parasitics, lower cost, and greater system integration. This paper presents experimental results for SAW in-line correlator structures on GaAs along with their despreading system performances. Experimental measurements in both the time and frequency domains were performed and were found to be in good agreement with theoretical predictions.     

Elastic wave propagation in cylindrical bars after brittle failures: Application to spalling tests

The effect of brittle failures on the elastic wave propagation along cylindrical bars is analysed. From experimental observations provided by spalling tests of ceramic materials, a theoretical analysis is carried out based on a finite elements simulation of the experiments and a mathematical analysis of the pulses by means of Fourier Transform techniques. Differences between the propagating waves before and after the material failure are revealed. After failure, the pulse is influenced by dispersion effects and its shape changes during propagation. To correct this effect, a procedure based on Bancroft's curves is suggested. Finally, some clues about the way to get consistent results from spalling tests are given.     

High velocity SAW using aluminum nitride film on unpolished nucleation side of free-standing CVD diamond

High performances surface acoustic wave (SAW) filters based on aluminium nitride (AlN)/diamond layered structure have been fabricated. The C-axis oriented aluminum nitride films with various thicknesses were sputtered on unpolished nucleation side of free-standing polycrystalline chemical vapor deposition (CVD) diamond obtained by silicon substrate etching. Experimental results show that high order modes as well as Rayleigh waves are excited. Experimental results are in good agreement with the theoretical dispersion curves determined by software simulation with Green's function formalism. We demonstrate that high phase velocity first mode wave (so-called Sezawa wave) with high electromechanical coupling coefficient are obtained on AlN/diamond structure. This structure also has a low temperature coefficient of frequency (TCF), and preliminary results suggest that a zero TCF could be expected.     

Propagation of boundary acoustic waves along a ZnO layer between two materials

Theoretical and experimental results on boundary acoustic waves propagated along a ZnO layer sandwiched between two materials are presented. It is shown that boundary acoustic waves can exist only when the material constants of the three materials satisfy the particular conditions obtained here. Experiments on SiO(2)/ZnO/SiO(2 ) were performed to verify the theoretical prediction of the existence of boundary waves. Boundary waves were excited and received by interdigital transducers and propagated along the ZnO layer. Propagation loss was practically the same as for Rayleigh waves, indicating a proper mode of the system. The results suggest that future SAW (surface acoustic wave) devices can be made without any package.     

Analytical calculation of blast-induced strains to buried pipelines

The aim of this paper is to introduce a robust methodology for the analytical calculation of strains in flexible buried pipelines due to surface point-source blasts. Following a brief bibliographic overview regarding the characteristics of ground waves produced by surface explosions, a method used to model wave propagation with radial attenuation and spherical front is presented. Strains due to P- and Rayleigh waves, which dominate the waveform generated by an explosion, are accordingly calculated by modeling the pipeline as a three-dimensional (3-D) cylindrical thin shell and ignoring soil–structure interaction. To simplify the design procedure, a set of easy-to-use relations for the calculation of maximum strains and their position along the pipeline axis is supplied. The derived expressions are evaluated through comparison against 3-D dynamic numerical analyses, field strain measurements in flexible pipelines due to a series of full scale blasts, and state-of-practice design methods. Comparisons show that the proposed methodology provides improved accuracy at no major expense of simplicity, as well as the advantage of properly accounting for the effect of local soil conditions.