Effects of the initial stress on the propagation and localization properties of Rayleigh waves in randomly disordered layered piezoelectric phononic crystals

In this paper, the effects of the initial stress on the propagation and localization properties of the Rayleigh surface waves in randomly disordered layered piezoelectric phononic crystals are studied. Due to different mechanical properties between the piezoelectric material and the polymer, different initial stresses in these two layers satisfying the equilibrium condition and interfacial compatibility are considered, which is more suitable for the practical cases. The transfer matrix between two consecutive piezoelectric unit cells is derived according to the continuity conditions. The expression of the localization factor is presented, and the wave localization properties are analyzed. Numerical calculations for the PVDF/PZT–2 periodic composites with the initial stress are performed. The band gap characteristics are studied taking the mechanical and electrical coupling into account. It is found that the localization degree can be influenced by the piezoelectric constants. With the increase in the piezoelectric constant, the stop band regions are enlarged for the ordered structures, and the localization properties of Rayleigh waves are strengthened for the disordered systems. The Rayleigh waves will be localized in mistuned periodic piezoelectric composites. The characteristics of band gaps and wave localization in ordered and disordered piezoelectric phononic crystals can be significantly changed by tuning the initial stress.     

Stress waves in a linear viscoelastic cylinder

Steady-state solutions of stress waves travelling in a linear viscoelastic cylinder of infinite length are obtained by a method almost similar to Pochhammer-Chree's.

Torsional, longitudinal, and flexural waves are considered. The results acquired are in the form in which complex elastic moduli and propagation constant appear in place of corresponding quantities in elastic solutions. Corrections of the Rayleigh type for phase velocity and attenuation constant are also derived.     

Propagation and localization of acoustic and elastic waves in heterogeneous materials: renormalization group analysis and numerical simulations

We describe and discuss the recent progress in the study of propagation and localization of acoustic and elastic waves in heterogeneous media. The heterogeneity is represented by a spatial distribution of the local elastic moduli. Both randomly distributed elastic moduli as well as those with long-range correlations with a nondecaying power-law correlation function, are considered. The motivation for the study is twofold. One is that recent analysis of experimental data for the spatial distribution of the elastic moduli of rock indicated that the distribution is characterized by the type of long-range correlations that we consider in this study. The second motivation for the problem is to understand whether localization of electrons (which, in quantum mechanics, are described by wave functions) has any analogy in the propagation of classical waves in disordered media. The problem is studied by two approaches. One of them is based on developing a dynamic renormalization group (RG) approach to analytical analysis of the governing equations for wave propagation. The RG analysis indicates that, depending on the type of the disorder (correlated vs. uncorrelated), one may have a transition between localized and extended regimes in any spatial dimension. The second approach utilizes numerical simulations of the governing equations in two- and three-dimensional media. The results obtained by the two approaches are in agreement with each other. Using numerical simulations, we also describe how the characteristics of a propagating wave may be used for probing the differences between heterogeneous media with short- and long-range correlations. To do so, we study the evolution of several distinct characteristics of the waves, such as the amplitude of the coherent wave front, its width, the spectral densities, the scalogram (wavelet transformation of the waves’ amplitudes at different scales and times), and the dispersion relation. It is demonstrated that such properties have completely different characteristics in uncorrelated and correlated media. Finally, it is shown how wave propagation may be used for establishing a link between the static and dynamical properties of heterogeneous media.     

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.     

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.     

Analysis of Acoustic Emission Propagation in Metal-to-Metal Adhesively Bonded Joints

Acoustic emission (AE) monitoring shows promise as one of the most effective methods for condition monitoring of adhesively-bonded joints. Previous research has demonstrated its ability to detect, locate and classify adhesive joint failure, though in these studies little attention appears to have been paid to the differences in AE wave propagation through the bonded and un-bonded sections of the specimens tested, or to the effects of the wave modes excited or the propagation distances. This paper details an experimental study conducted on large aluminium sheet specimens to identify the effects of the presence of an adhesive layer on AE wave propagation. Three specimens are considered; a single aluminium sheet, two aluminium sheets placed together without adhesive, and an adhesively-bonded specimen. A pencil lead break (PLB) is used as a simulated AE source, and is applied to the three specimens at varying propagation distances and orientations. The acquired signals are processed using wavelet-transforms to explore time-frequency features, and compared with modified group-velocity curves based on the Rayleigh–Lamb equations to allow identification of wave-modes and edge-reflections. The effects of propagation distance and source orientation are investigated while comparison is made between the three specimens. It is concluded that while the wave propagation modes can be approximated as being constant throughout all three specimens, there is a significant change in the received waveforms due to the attenuation of high-frequency components exhibited by the bonded specimen. These findings may be utilised to provide a deeper understanding of acquired AE data, improving the current abilities to identify, locate and characterise damage mechanisms occurring within adhesive joints, ultimately improving safety in the use of adhesive bonding for critical applications.     

Thermoviscoelastic Excitation and Propagation of Rayleigh Waves in Viscoelastic Plates by a Pulsed Laser

According to thermoviscoelastic theory, the relations of laser-generated Rayleigh waves in viscoelastic plates with thermophysical and viscoelastic properties are investigated quantitatively. The displacement spectra are calculated in the frequency domain using the finite element method, and the temporal displacement waveforms are obtained by applying inverse fast Fourier transforms. And then, the effects of the laser parameters, including the laser spot radius, pulse rise time, and optical penetration depth, on the propagation of laser-generated Rayleigh waves are studied. In addition, the influence of the increase of each elastic modulus and viscous modulus of the viscoelastic plates on laser-generated Rayleigh waves is investigated in detail.     

CR/PU共混粘合剂红外透明性对涂层发射率的影响

用氯丁橡胶(CR)共混聚氨酯(PU)制备了不同红外透明性的粘合剂,并分别添加不同含量的铜粉等填料,制得不同发射率的红外隐身涂层。对粘合剂的红外光谱、发射率及涂层的发射率、微观形貌等进行了分析。结果表明,随粘合剂中聚氨酯含量的增大,粘合剂的透明性变差、发射率增大,涂层的发射率也增大;当铜粉添加量较大时,涂层发射率较小,粘合剂的红外透明性对涂层发射率的影响也相对小一些;并着重对其原因进行了分析。     

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 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     

Laser-induced surface acoustic waves for evaluation of elastic stiffness of plasma sprayed materials

The elastic properties of plasma sprayed deposits have been evaluated using a laser-excited surface acoustic wave (SAW) technique and an inversion processing analysis. The SAWs including Lamb and Rayleigh waves were generated in plasma sprayed NiCoCrAlY and ZrO₂, respectively, and their group velocity dispersions were used to determine the elastic properties (i.e.Young's modulus, Poison's ratio and density) of the deposits. Estimated elastic moduli from the velocity dispersions of A₀-mode Lamb waves are in the range of 40–140 GPa for the deposits, which are much lower than the values 220–240 GPa of the comparable dense materials. The dramatic reductions in modulus and density of ZrO₂ deposit have been attributed to the presence of high porosity and particularly microcracks. Moreover, this study has emphasized on exploiting the applicability of each kind of the SAWs for the elastic property evaluation of different sprayed materials. Both Lamb and Rayleigh wave dispersions are useful for the estimation of APS and VPS-deposited NiCrAlY, but S₀-Lamb and Rayleigh waves are exceptional for that of sprayed ZrO₂, because of its characterization of high acoustic attenuation and inconsequent displacement across the weak bonded interface of ZrO₂ and substrate.     

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.     

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.     

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocities and attenuation of ultrasonic waves in two-component media are determined. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results for effective moduli, velocity and/or attenuation as functions of concentration of spherical inclusion material, or porosity, are graphically displayed.     

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.     

Simulation of characteristics of a LiNbO3/diamond surface acoustic wave

High-frequency surface acoustic wave (SAW) devices based on diamond that have been produced to date utilize the SiO2/ZnO/diamond structure, which shows excellent characteristics of a phase velocity of over 10,000 m/s with a zero temperature coefficient; this structure has been successfully applied to high-frequency narrowband filters and resonators. To expand material systems to wideband applications, c-axis-oriented LiNbO3 on diamond was studied and a coupling coefficient up to 9.0% was estimated to be obtained. In this paper, the characteristics of LiNbO3/diamond with the assumption that the LiNbO3 film is a single crystal have been studied by theoretical calculations to find higher coupling coefficient conditions. Calculations are made for the phase velocity, the coupling coefficient, and the temperature coefficient of the Rayleigh wave and its higher mode Sezawa waves. As a result, LiNbO3/diamond is found to offer a very high electromechanical coupling coefficient of up to 16% in conjunction with a high phase velocity of 12,600 m/s and a small temperature coefficient of 25 ppm/deg. This characteristic is suitable for wide bandwidth applications in high-frequency SAW devices.     

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.     

Properties of interdigital transducers in relation to the substratecrystal symmetry

Exclusively from the crystal symmetry, we obtain results concerning properties of interdigital transducers radiating Rayleigh waves along high-symmetrical crystal directions. Three cases of high-symmetrical directions are considered: the propagation direction is parallel to a rotation axis, perpendicular to a mirror plane, or parallel to a rotoinversion axis of the substrate crystal. In respect to the symmetry properties of the piezoelectric tensor related to a mirror operation on a plane perpendicular to the propagation direction, the three original cases can be concentrated in three symmetry cases. The crystal symmetry determines the properties of the piezoelectric tensor, and consequently the wave excitation by transducers. These considerations enable one to ascertain the positions of the transduction centers and the influence of internal reflections to the amplitude characteristics. Furthermore, we are able to discuss natural single-phase unidirectional transducer (NSPUDT) effects in layer structures, the old question “crossed-field or in-line model”, and the existence of cross-coupling of waves, similar to multistrip couplers, in interdigital transducers (IDTs). The theoretical predictions are compared with our own and other authors' experimental results     

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