quasi-Rayleigh Waves Research Articles

Surface acoustic waves in laterally periodic superlattices

The existence of surface acoustic waves (SAWs) is studied in laterally periodic superlattices, modelled as an anisotropic elastic half-space with an arbitrary periodic variation of its material properties along the stratification direction (call it X) parallel to the surface. Unlike a homogeneous half-space, such a structure allows for more than one (dispersive) SAW. Specifically, it is shown that any superlattice with a generic shape of periodicity profile admits at most three SAW dispersion branches ω(Kx), i.e., at most three different SAW frequencies at any fixed Bloch wavenumber Kx. Moreover, the total number of SAWs at fixed Kx in a pair of superlattices with periodicity profiles obtained from one another by the inversion of the axis X cannot exceed three either. At least one SAW branch must exist in one of these two superlattices unless the bulk-wave threshold is the so-called exceptional (i.e., admits surface skimming wave). The SAW branch is unique in the particular case of a superlattice invariant to the inversion X→−X. The above general results are illustrated by the perturbation theory derivations for the weakly modulated superlattices. Explicit leading-order formulas are obtained for the quasi-Rayleigh wave branch evolving from the Rayleigh wave in each of the mutually ”inverse” superlattices and for the quasibulk wave branch evolving from the exceptional bulk-wave threshold in one of the superlattices.

Soil-structure interaction assessment combining deconvolution of building and field recordings with polarization analysis: application to the Matera (Italy) experiment

AbstractIn this study, the wavefield radiated from a building to its surroundings is identified and extracted from M4.6 earthquake recordings collected by sensors installed in a building and on the nearby athletic field in Matera (Italy) using a new approach for soil-structure interaction assessment. The proposed approach for earthquake data analysis combines in an innovative way two methods already used in seismology and engineering seismology: deconvolution and polarization analysis. The approach enables the identification, reconstruction, and characterization of the wavefield radiated from a vibrating building into its surroundings, and the estimation of the amount of energy associated with it. The approach consists of four steps: (1) estimation of the resonant frequencies of the building, (2) deconvolution of the earthquake recordings from a building and its surroundings, (3) identification of the seismic phases, reconstruction of the signal transmitted from the building to its surroundings, and estimation of its energy, and (4) polarization analysis. Analysis of recordings of the M4.6 event highlighted that the motion related to the wavefield radiated from the building to the ground was mostly linearly polarized in the radial and transverse planes, while a clear ellipticity was observed only in the horizontal plane. The wavefield radiated from the building might be dominated by unconventionally polarized surface waves, i.e., quasi-Rayleigh waves or a combination of quasi-Rayleigh and quasi-Love waves. The results indicated that the energy transmitted from the analyzed vibrating building to its surroundings was significant and decreased the ground motion shaking due to the out-of-phase motion.

Single-point dispersion measurement of surface waves combining translation, rotation and strain in weakly anisotropic media: theory

SUMMARY A new approach is proposed for measuring the dispersion relation of surface waves in weakly anisotropic media using a single station, which consists of translational displacement and rotation or strain. The azimuth-dependent surface wave dispersion curve can be directly obtained by using the amplitude ratio of translational displacement to rotation or strain. Using observations from earthquakes from a variety of azimuths allows us to characterize the anisotropy of subsurface media. The amplitude ratio gives the localized azimuth-dependent dispersion relations of the formation beneath a receiver without requiring knowledge of the source or structure along the path. The theory shows that in anisotropic media the coupled quasi-Rayleigh wave and quasi-Love wave will result in elliptically polarized rotational motions. In addition, rotational motion information allows the determination of backazimuth even in general anisotropic media. We carry out numerical experiments, investigate the effects of noise and degree of anisotropy and demonstrate the potential for field studies.

Engineering the beat phenomenon of quasi-Rayleigh waves for regions with minimal Surface Acoustic Wave (SAW) amplitude

Surface Acoustic Waves (SAW) are prevalent in a variety of scientific fields. Typically, the ability to manipulate these surface waves has a significant impact on the efficacy of any SAW-based device. In this paper, we present a simple method for designing localized regions that have minimal SAW amplitude. These localized regions have valley-like drops in SAW amplitude and are achieved by using the spatial beat phenomenon of quasi-Rayleigh waves. Controlling the beat phenomenon allows us to manipulate where and how these localized regions appear in the waveguide. In particular, the localized regions can be designed to have variable widths and can be positioned consecutively due to minimal wave scattering. The design methodology and physics are described in detail, and several supplementary simulations are provided to demonstrate the efficacy of the proposed method. Lastly, we briefly discuss how the proposed approach could potentially be exploited to implement a localized high-pass filter and enables SAW wave propagation that avoids surface obstacles.

On Backus average in modelling guided waves

We study the Backus (1962) average of a stack of layers overlying a halfspace to examine its applicability for the quasi-Rayleigh and Love wave dispersion curves. We choose these waves since both propagate in the same model. We compare these curves to values obtained for the stack of layers using the propagator matrix. In contrast to the propagator matrix, the Backus (1962) average is applicable only for thin layers or low frequencies. This is true for both a weakly inhomogeneous stack of layers resulting in a weakly anisotropic medium and a strongly inhomogeneous stack of alternating layers resulting in a strongly anisotropic medium. We also compare the strongly anisotropic and weakly anisotropic media, given by the Backus (1962) averages, to results obtained by the isotropic Voigt (1910) averages of these media. As expected, we find only a small difference between these results for weak anisotropy and a large difference for strong anisotropy. We perform the Backus (1962) average for a stack of alternating transversely isotropic layers that is strongly inhomogeneous to evaluate the dispersion relations for the resulting medium. We compare the resulting dispersion curves to values obtained using a propagator matrix for that stack of layers. Again, there is a good match only for thin layers or low frequencies. Finally, we perform the Backus (1962) average for a stack of nonalternating transversely isotropic layers that is strongly inhomogeneous, and evaluate the quasi-Rayleigh wave dispersion relations for the resulting transversely isotropic medium. We compare the resulting curves to values obtained using the propagator matrix for the stack of layers. In this case, the Backus (1962) average performs less well, but—for the fundamental mode—remains adequate for low frequencies or thin layers.

Comparison of quasi-Rayleigh waves and Rayleigh waves, and clarifying the cut-off frequency of quasi-Rayleigh waves

The Partial Wave Method is unique in that it establishes a foundation on which various elastodynamic guided waves can be compared. In this paper, the method is used to compare quasi-Rayleigh waves and Rayleigh waves, and investigate the eccentricities of the Partial Wave Method at phase velocities equal to the Rayleigh wave speed. The comparison results in the definition of two types of quasi-Rayleigh waves and an explanation for quasi-Rayleigh wave behavior reported in the literature at frequencies that do not satisfy Viktorov’s quasi-Rayleigh wave condition. These conclusions are also verified by the superposition of A0 and S0 mode wave-structures calculated using the semi-analytical finite element method.

Observation of Guided Acoustic Waves in a Human Skull

Human skull poses a significant barrier for the propagation of ultrasound waves. Development of methods enabling more efficient ultrasound transmission into and from the brain is therefore critical for the advancement of ultrasound-mediated transcranial imaging or actuation techniques. We report on the first observation of guided acoustic waves in the near field of an ex vivo human skull specimen in the frequency range between 0.2 and 1.5MHz. In contrast to what was previously observed for guided wave propagation in thin rodent skulls, the guided wave observed in a higher-frequency regime corresponds to a quasi-Rayleigh wave, confined mostly to the cortical bone layer. The newly discovered near-field properties of the human skull are expected to facilitate the development of more efficient diagnostic and therapeutic techniques based on transcranial ultrasound.

Ultrasonic Quasi-Rayleigh Waves - Propagation Properties and Detection of Mechanical Damage

This article examines the propagation of quasi-Rayleigh waves and their trial application to detect defects in plate structures. With their specific propagation properties, quasi-Rayleigh waves have the potential to extend the scope of conventional ultrasound defect detection methods. This would enable detection across longer distances and with higher sensitivity, with earlier identification of surface defects in plate structures as a result. The article contains a basic description of quasi-Rayleigh waves, together with their propagation properties, with respect to a particular isotropic material (steel). The propagation of quasi-Rayleigh waves is then demonstrated using a smooth plate and a plate featuring a unilateral obstacle. The behaviours of propagating waves are determined using three approaches: analytical, numeric and experimental. The last part of the article provides a diagram and a description of the experimental measurement assembly and a case of detecting a surface defect in a plate structural part.

Influence of mirror image forces on dispersion and phonon acoustic mode width of quasi-Rayleigh wave interacting with adsorbed atoms

Influence of mirror image forces on dispersion and phonon acoustic mode width of quasi-Rayleigh wave interacting with adsorbed atoms

Ultrasonic Defect Detection of Structural Plates Using Quasi-Rayleigh Waves

Abstract This article discusses the application of so-called ultrasonic quasi-Rayleigh waves to detect surface defects of mechanical constructions, namely plate structures. The application of quasi-Rayleigh waves allows the extension of the scope of detection using conventional ultrasonic methods that are based on bulk waves. This extension means larger distances as well as higher sensitivity of the detection of surface defects such as fatigue or corrosion cracks. An advantage of this method is the transfer of wave energy from one side of a plate to another, which helps to overcome one-sided obstacles (such as cross-pieces, reinforcement elements). The article describes characteristic properties of quasi-Rayleigh waves that are important for the proper (in terms of frequency in particular) design of the excitation of waves towards the structure. FEM simulation results then provide information regarding the sensitivity of the wave response to the presence and sizes of surface defects (perpendicular slots) in an isotropic material with the properties of steel. The theoretical knowledge is set against experimental measurements obtained with the use of a steel plate with cross-pieces welded to it.

Деформаційний потенціал акустичної квазірелеєвської хвилі, взаємодіючої з адсорбованими атомами

Деформаційний потенціал акустичної квазірелеєвської хвилі, взаємодіючої з адсорбованими атомами

OUP accepted manuscript

We examine the sensitivity of the Love and the quasi-Rayleigh waves to model parameters. Both waves are guided waves that propagate in the same model of an elastic layer above an elastic halfspace. We study their dispersion curves without any simplifying assumptions, beyond the standard approach of elasticity theory in isotropic media. We examine the sensitivity of both waves to elasticity parameters, frequency and layer thickness, for varying frequency and different modes. In the case of Love waves, we derive and plot the absolute value of a dimensionless sensitivity coefficient in terms of partial derivatives, and perform an analysis to find the optimum frequency for determining the layer thickness. For a coherency of the background information, we briefly review the Love-wave dispersion relation and provide details of the less common derivation of the quasi-Rayleigh relation in an appendix. We compare that derivation to past results in the literature, finding certain discrepancies among them.

SAW Temperature Sensor on Quartz.

For biomedical applications, narrow temperature range and high sensor accuracy requirements define the need for high temperature sensitivity. Wireless SAW sensors connected to antennas need a reference element to account for changes in electromagnetic coupling between the transmitter and receiver antennas. A pair of sensors with different temperature sensitivities may serve as a self-referenced sensor assembly. This justifies the need for materials with useful SAW resonator properties and with the largest difference between temperature coefficients of frequency (TCF) for a resonator pair on a single substrate. We have identified several cuts of quartz having useful properties with a TCF difference up to 140 ppm/°C for a pair of resonators on a single substrate. As a rule, placing such resonators on a single substrate requires their rotation by up to 90° relative to each other. The limited range of cuts presents a unique opportunity to place both resonators along the X+90° direction with one resonator using Bleustein-Gulyaev-Shimizu (BGS) waves (with electrodes placed along the x-axis) and the other one (with electrodes inclined by about ±10° to the x-axis) using quasi-Rayleigh waves. These cuts are close to the 70°Y cut where a high TCF difference is reached together with acceptable characteristics of the resonators. Resonators were designed for all useful cuts (including the 70°Y cut) and tested. The use of different periods in reflectors and interdigital transducer (IDT) together with individual choice of gaps between reflectors and IDT meant achieving low spurious content in resonator responses. The quality factors reached values up to 3500 at central frequencies around 915 MHz for both BGS and quasi-Rayleigh types of waves. The measured difference of the TCF is about 138 ppm/°C on 70°Y cut that is close to the calculated value.

Features of the Amplitude-Frequency Characteristics of Electromagnetic Emission during Uniaxial Compression of Dielectric Composites

We have studied the electromagnetic emission from samples of epoxy resin filled with sand subjected to uniaxial compression. Capacitive sensor measures the electrical component of the response when excited electromagnetic emission of ultrasonic pulse using a differential amplifier. It was shown the influence of the load on the spectral signal characteristics: with increasing pressure, the formation of bands at frequencies corresponding to possibly quasi-Rayleigh waves generation. It is concluded that the use of the experimental geometry studies the main contribution to the response of electromagnetic emissions create born normal vibrations, which are damped standing waves.

The Kuramoto-Sivashinsky equation for adatoms interacting through quasi-Rayleigh waves and formation of ordered adatom structures

It is shown that the defect-deformational (DD) cooperative nucleation of ordered ensembles of nanoparticles on isotropic surfaces of solids with the participation of quasi-Rayleigh waves can be described by a closed two-dimensional nonlinear DD equation of the Kuramoto-Sivashinsry (KS) type. A solution to the linearized DDKS equation describes the threshold appearance of the periodic surface strain modulation accompanied by the simultaneous formation of adatom (surface defect) piles at extrema of the surface strain. Numerical solutions to the DDKS equation in linear and nonlinear regimes describe the formation of three types of surface structures of adatom piles (clusters): lamellar-like structures, cellular disordered and hexagonal ordered ones. In the well-developed nonlinear regime, generated ensembles of nanoparticles become trimodal regarding their size distribution due to the generation of the second harmonics, degenerate parametric decay and summation of wavevectors of DD gratings taking part in the DD selforganization. The selforganizing periodic cellular DD surface structure can serve as a selforganized template for the subsequent growth of nanoparticles in the processes of atoms deposition.

Transient elastic wave propagation and scattering in plates: comparison between pulsed TV-holography measurements and finite element method predictions

Pulsed TV-holography (PTVH) can be used for obtaining two-dimensional maps of instantaneous out-of-plane displacements in plates. In particular, our group has demonstrated that scattering patterns generated by the interaction of elastic waves with defects can be measured with PTVH and employed for the characterization of damage in nondestructive inspection of plate structures. Recently, we have succeeded in obtaining a quantitative description of experimental scattering patterns of quasi-Rayleigh (qR) waves produced by holes in harmonic regime using a finite element method (FEM) combined with a two-dimensional scalar wave equation, avoiding the standard and more complex vector approaches based on the rigorous linear elasticity theory. This scheme has been extended here for characterizing equivalent scattering phenomena in transient regime. Simulated scattering patterns, obtained with the scalar FEM, and the corresponding experimental patterns associated to the interaction of qR waves with holes, measured with our specifically developed PTVH system, have been compared. Results have shown that, except for the evaluation of the backscattering coefficient, a reasonable agreement between theory and experiment is obtained in both amplitude and phase, which confirms the feasibility and potential of the proposed scalar approximation for the characterization of experimental transient scattering patterns measured with our PTVH technique.

The effect of a surface impedance load on the behavior of quasi-Rayleigh waves near a cylindrical cavity

The effect of a surface impedance load on the properties of axisymmetric quasi-Rayleigh waves propagating along the boundaries of a cylindrical cavity is investigated. By solving the problem by means of the impedance method, a dispersion equation for these waves is obtained. It is shown that the equation can be represented as the condition that the determinant of the sum of impedance matrices of the load and the medium is zero. Analysis of this equation allows one to investigate the effect of the surface load on the behavior of quasi-Rayleigh waves and on their critical frequencies. The conditions that should be met by the impedance load for quasi-Rayleigh waves to be absent near the cavity or for one or two such waves to exist are determined. The choice of the load is specified for the propagating quasi-Rayleigh wave to possess preset dispersion properties. The conclusions drawn on the basis of this study are illustrated by several examples of load models that can be implemented in practice.

Specific features of quasi-Rayleigh waves caused by a two-component impedance load

Specific features of quasi-Rayleigh waves caused by a two-component impedance load

The effect of a surface impedance load on the properties of quasi-Rayleigh waves

The propagation of quasi-Rayleigh waves along an impedance-loaded plane boundary of an isotropic elastic half-space is studied theoretically. The dispersion equation of these waves is derived with allowance for the fact that an impedance load has both normal and tangential components. The conditions for the existence of such waves are analyzed depending on the magnitude and nature of each of these components. Specific examples of calculating the quasi-Rayleigh wave velocities are considered: for the models of surface and bulk cracked media, for a fluid layer in an elastic medium, and for a resonant load.

Cooperative defect-deformational nucleation of ordered adatom nanostructures with the participation of surface quasi-Rayleigh waves

Defect-deformational mean-field theory of cooperative nucleation of ordered ensembles of nanoparticles on the isotropic surface of solids with the participation of quasistatic Rayleigh waves is developed. The system of nonlinear kinetic equations for the Fourier-amplitudes of the concentration of surface defects (adatoms or dimers) is derived and nonlinear multimode dynamics of self-organization of hexagonal ensembles of nanoparticles is described within a mean-field approximation. The mechanism of the control of the ensemble symmetry with the help of external stress is considered. The theoretical results correspond to the experimental ones obtained in studies of formation of quasihexagonal ensembles of nanoparticles under laser-controlled deposition of Ga atoms on the tip of a silica fiber.