Interaction Of Rayleigh Waves Research Articles

Machine learning enhanced characterization of surface defects using ultrasonic Rayleigh waves

Rayleigh waves are successfully employed for the characterization of surface defects through the utilization of both time and frequency domain analysis. However, a significant challenge arises when attempting to cover a broad range of the defect depth to Rayleigh wavelength ratio with a single method. This paper presents an enhanced methodology that integrates optimized machine learning (ML) algorithms to expand the coverage of defect depth assessment. An experimentally validated numerical model is firstly established to simulate the interaction of Rayleigh waves with surface defects and utilized to generate a significant quantity of labeled Rayleigh wave signals. The features of received Rayleigh wave patterns are effectively extracted and serve as indicators of defect parameters. The ML framework encompasses the extraction and selection of optimal features, the construction of model architecture, and the tuning of hyperparameters. Three dimensionality optimization techniques—principal component analysis, correlation coefficient analysis, and expert knowledge integration—are compared. Additionally, six machine learning models (decision tree, support vector machine, k-nearest neighbors, random forest, gradient-boosting machine, and artificial neural network) are optimized using particle swarm optimization and subjected to comparison. The results reveal that: (1) principal component analysis yields the highest performance, suggesting the potential for feature dimensionality reduction without relying on expert knowledge; (2) among the models examined, the random forest model and artificial neural network with hyperparameter tuning demonstrate superior performance in predicting defect depth; and (3) the optimized machine learning methods consistently outperform empirical approaches in accurately predicting defect depths across a wide range. Furthermore, the proposed method shows promise for extension to determine additional parameters associated with surface defects, including their width and angle of inclination.

Frequency-dependent scattering of wideband laser-generated Rayleigh waves for vertical surface crack characterization

Wideband laser-generated Rayleigh waves have been extensively exploited for surface crack characterization, most of which, nonetheless, are of a nature of either numerical simulation or experimental observation. Earlier, an elastodynamic reciprocity theorem-based theoretical model was proposed by the authors Xu L et al 2022 Ultrasonics 118 106578, Xu L et al 2021 J. Sound Vib. 509 116226, aimed at scrutinizing the interaction of narrowband Rayleigh-Lamb waves with a surface or subsurface crack. In this study, the model is extended to a wideband scenario to analytically explore the interaction of a wideband laser-generated Rayleigh wave with a surface crack, as well as the resultant crack-scattered Rayleigh wavefield. First, under the narrowband scenario, a dimensionless parameter is formulated based on the closed-form solution to the magnitude of the narrowband scattered Rayleigh wavefield, revealing that the scattering effect of a surface crack on the Rayleigh wave is frequency-dependent and there exists a characteristic frequency, at which the crack-scattered Rayleigh wavefield manifests the strongest intensity. Similarly, under the wideband scenario, such dependence can be calibrated by a spectral damage indicator (SDI), which facilitates the evaluation of the severity of the surface crack using the wideband laser-generated Rayleigh wave. Proof-of-concept simulation is performed to verify the model. Quantitative agreement between the analytical and numerical results validates the accuracy of the proposed model and SDI. Experiment is also conducted to demonstrate the effectiveness of the frequency-dependent scattering of wideband laser-generated Rayleigh waves for vertical surface crack characterization.

Numerical study of Rayleigh wave interaction with wedge geometry

Numerical study of Rayleigh wave interaction with wedge geometry

On the effective medium model of the interaction of Rayleigh waves with mass–spring oscillators on the surface

The interaction of Rayleigh surface waves with a random arrangement of oscillators on the surface of an elastic half-space is analyzed with the help of the surface elastodynamic Green’s function formalism and the effective medium model valid in the long-wavelength limit is derived. It is shown that in order to apply the central assumption of the model, namely, that the local surface displacement at the contact point of an oscillator is equal to the average effective medium displacement, the spring constant of the oscillators must be corrected to include the stiffness of the contact calculated in the quasistatic approximation. The previous results pertaining to the interaction of Rayleigh and Lamb waves with microspheres are shown to be correct despite the apparent inconsistencies in the assumptions.

Finite element analysis of laser-generated Rayleigh wave for sizing subsurface crack in frequency domain

In order to realize the quantitative detection of subsurface cracks, finite element method (FEM) was used to study the interaction of laser-generated Rayleigh wave and subsurface crack with different buried depths and lengths in this paper. The transmitted and reflected Rayleigh waves of subsurface cracks were analyzed in frequency domain, it is found that the center frequency of transmission wave decreases with the increase of crack length when the buried depth of crack remains unchanged, and increases with the increase of crack depth when the crack length remains unchanged. The center frequency of reflected Rayleigh wave is independent of crack length, and has a quadratic function relation with the buried depth of subsurface crack. The relationships, between the ratio of buried depth to incident Rayleigh wavelength and the ratio of reflected Rayleigh wave frequency to incident Rayleigh wave frequency, and the ratio of crack length to incident Rayleigh wavelength and the ratio of transmitted Rayleigh wave frequency to incident Rayleigh wave frequency, were obtained respectively based on the frequency analysis. The relationships were verified by the simulation signals, it is found that the maximum relative error of the buried depth of the subsurface cracks determined by the proposed relationship is 5.939%, and the maximum relative error of the length of the subsurface cracks is 12.149%. The research results show that the proposed method is promising in quantitative characterization of the buried depth and length of subsurface cracks in metallic materials.

Nonlinear interaction of Rayleigh waves in isotropic materials: Numerical and experimental investigation

Surface treatment intensity monitoring is still an open and challenging nondestructive testing problem. For the estimation of residual stress with ultrasonic measurements, local linear and nonlinear elastic constants are needed as input. In this paper, nonlinear elastic-wave interactions (also called wave mixing or scattering) — namely, the generation of secondary ultrasonic waves in a nonlinear medium — are considered as a prospective means for near-surface nonlinear elastic parameter evaluation. The allowed interactions between bulk and surface waves, as well as the dependence of the scattering efficiency on the frequency and angle between source waves, were investigated through an analytical model, then compared with FEM simulations and experimental results. Finally, possible future steps for the development of the applied methods for the determination of near-surface higher-order elastic constants are discussed. In addition, several problem-relevant data processing procedures are presented.

Symmetry of the Magnetoelastic Interaction of Rayleigh and Shear Horizontal Magnetoacoustic Waves in Nickel Thin Films on LiTaO3

We study the interaction of Rayleigh and shear horizontal surface acoustic waves (SAWs) with spin waves in thin Ni films on a piezoelectric LiTaO$_3$ substrate, which supports both SAW modes simultaneously. Because Rayleigh and shear horizontal modes induce different strain components in the Ni thin films, the symmetries of the magnetoelastic driving fields, of the magnetoelastic response, and of the transmission nonreciprocity differ for both SAW modes. Our experimental findings are well explained by a theoretical model based on a modified Landau--Lifshitz--Gilbert approach. We show that the symmetries of the magnetoelastic response driven by Rayleigh- and shear horizontal SAWs complement each other, which makes it possible to excite spin waves for any relative orientation of magnetization and SAW propagation direction and, moreover, can be utilized to characterize surface strain components of unknown acoustic wave modes.

Contribution of the acoustic waves to near-field heat transfer

Calculations of the radiative and phonon heat transfer between metals in an extreme near field in presence of electrostatic potential difference are given. Potential difference leads to a coupling between the radiation field and acoustic waves in solid, as a result of which the heat flux between two gold plates associated with p -polarized electromagnetic waves increases by many orders of magnitude as the potential difference varies from 0 to 10 V. The radiative heat transfer is compared with the phonon heat transfer associated with the electrostatic and van der Waals interactions between the surface displacements. For large potential difference and small distances the radiative heat transfer is reduced to the electrostatic phonon heat transfer. A particular case of surface acoustic waves—Rayleigh waves is studied in details. Conditions are obtained for the existence of surface phonon polaritons associated with the interaction of Rayleigh waves with an electromagnetic field. The surface Rayleigh and bulk acoustic waves can give contributions of the same order. The obtained results can be used to control heat fluxes at the nanoscale using the potential difference and to create coherent radiation sources based on the properties of the Rayleigh waves

Surface circular-arc defects interacted by laser-generated Rayleigh wave

In this work, the finite element method (FEM) is used to investigate the propagation of laser-generated Rayleigh wave along the material surface at the quarter-arc transition surface under the thermoelastic regime, and to establish the relationship between the circular-arc radius and the time domain characteristics of reflected and transmitted Rayleigh waves. The simulation shows that the amplitude of the reflected Rayleigh wave decreases whereas the amplitude of the transmitted Rayleigh wave increases as the radius increases, which is significantly different from the well-studied interaction of Rayleigh waves with the perpendicular transition surface. By introducing the circular-arc defects which are easily formed in some engineering components during the material surface quenching, we find that the depth gauging of the surface circular-arc defects is more accurate in comparison to the surface rectangular defects based on the arrival time of the transmitted Rayleigh wave. This is further verified by the corresponding experimental results. These foundings are of practical values for detecting the depth of the arc defect quantitatively by the laser ultrasonic technique.

Investigation of Rayleigh wave interaction with surface defects

The current article is concerned with the interaction of Rayleigh waves with surface defects of arbitrary shape in a homogeneous, isotropic, linearly elastic half-space. Using a linear superposition principle, the interaction generates a scattered field which is equivalent to the field radiated from a distribution of horizontal and vertical tractions on the surface of the defect. These tractions are equal in magnitude but opposite in sign to the corresponding tractions obtained from the incident wave. The scattered field is then computed as the superposition of the displacements radiated from the tractions at every point of the defect surface using the reciprocity theorem approach. The far-field vertical displacements are compared with calculations obtained by the boundary element method (BEM) for circular, rectangular, triangular and arbitrary-shaped defects. Comparisons between the theoretical and BEM results, which are graphically displayed, are in excellent agreement. It is also discussed the limitations of the proposed approximate theory.
 Keywords:
 half-space; Rayleigh wave; surface defect; reciprocity theorem; boundary element method (BEM).

A metasurface comprising spiral shaped local resonators for surface acoustic waves

The interaction of Rayleigh waves, propagating on lithium niobate, with a metasurface consisting of a square array of spiral-like vertical oscillators is investigated. We observe confinement of the acoustic energy throughout the height of the oscillators and note that this confinement also takes place at relatively low frequencies compared to circularly symmetric resonators of similar dimensions. A transmission study reveals that the bandgap attenuation is large (~25 dB) at both high and low frequencies, a characteristic that could be exploited in the design of new RF filters.

Numerical study on the mechanism of laser-generated Rayleigh waves’ interaction with a surface notch at high temperature

Quantitative characterization of surface notches in metallic materials has long been a hot research topic. In order to quantitatively characterize a surface notch, the finite element method is used to study the interaction of Rayleigh waves with different types of surface defects, and we then compare the difference between their displacement signals. The simulation results show that the oscillation signal following the Rayleigh pulse resulting from the mode-convened shear wave can quantitatively characterize the surface notch at different temperatures, where the notch width and depth can be characterized by the arrival time and the temporal cycles of the oscillation signal, respectively. Moreover, as the temperature increases, the arrival time of the oscillation signal will be delayed, but the temporal cycles will remain unchanged. This research provides a theoretical basis for the quantitative detection of surface defects at high temperature.

Rayleigh wave amplitude distortions above a reservoir: new insights from elastic modelling

Surface waves usually dominate the ambient noise above the microseism frequency (∼0.1 Hz). Their dispersion curves are routinely inverted for shear velocity profiles, while their amplitude is often neglected. Amplitude, however, can also carry useful information. We address the problem of predicting Rayleigh wave amplitude anomalies due to the interaction of incident Rayleigh waves with an embedded elastic inclusion (gas reservoir) between 0.5 and 5 Hz. The proposed method is designed for ambient noise applications, so we use multiple time-windows containing signals from randomly excited sources. Using the spectral-element method in the radial-vertical 2-D plane, we show that frequency-dependent spectral anomalies arise at the surface in the vicinity of the inclusion. The anomalies generated by a deep inclusion are enhanced for the overtones because of their deeper penetration. Depending on the wavefield modal content and the complexity of the background model, the anomalies can reach about 20 per cent of the initial power spectral density. For comparison, the anomalies generated by a structural anticline in a realistic sedimentary basin are one order of magnitude higher in our simulations. The Born-based finite-frequency amplitude sensitivity kernels are useful for the interpretation of the results. The anomalies are most sensitive to Vs inside the inclusion, followed by ρ, as expected for surface waves. The sensitivity is concentrated in slow shallow layers when they are present in the model.

Debonding detection in CFRP-retrofitted reinforced concrete structures using nonlinear Rayleigh wave

Abstract This paper proposes the use of nonlinear Rayleigh wave to inspect debonding in carbon fibre reinforced polymer (CFRP) retrofitted reinforced concrete structures. The proposed method requires a network of transducers that are used to scan the CFRP-retrofitted reinforced concrete structures by sequentially actuating and receiving Rayleigh wave. The nonlinear feature used for the debonding detection is second harmonic generation due to the interaction of Rayleigh wave at the debonding between the CFRP and concrete interfaces. A damage image reconstruction algorithm is proposed to provide a graphical representation for detecting and locating the debonding in the CFRP-retrofitted reinforced concrete structures. In this study, experimental case studies are used to demonstrate the performance of the proposed debonding detection technique. A transducer network with four piezoelectric transducers is used to actuate Rayleigh wave and measure the second harmonic in the experiments. The results show that the proposed debonding detection technique is reliable in detecting and locating the debonding in the CFRP-retrofitted reinforced concrete structures.

Numerical simulation of the interaction of laser-generated Rayleigh waves with subsurface cracks

In this article, the interaction of a laser-generated Rayleigh wave with a subsurface crack has been simulated in detail. The finite element method (FEM) was used to model a subsurface hollow with a rectangular shape, which was used to represent the subsurface crack. By studying the contributions of all of the reflected and mode-converted signals from the subsurface crack, the arrival time of those signals and the mechanism underlying their occurrence could be fully explained. The first negative peak of the reflected waves originated from the top corner of the subsurface crack. The arrival time of this peak first decreased and then increased as the depth of the subsurface crack increased, which was due to the mode conversion when the diffracted bulk mode interacted with the free surface. However, when the depth of the crack remained the same and the height of the subsurface crack increased, the arrival time of the first negative peak of the reflected waves remained the same but the arrival time of the following reflected peaks maintained a linear relationship with the height of the crack. Furthermore, the sources and mechanism of the reflected waves were studied. It was found that the interval time of the peaks was dependent on the height of the crack, and a method for measuring the height of subsurface cracks has been proposed in this paper. The results of the simulation enable the quantitative measurement of the size of subsurface cracks and the height measuring method has the potential to measure the height of subsurface defects and structures.

Role of Shape and Numbers of Ridges and Valleys in the Insulating Effects of Topography on the Rayleigh Wave Characteristics

This research work is inspired by the recently accepted concept that high frequency Rayleigh waves are generated in the epicentral zone of shallow earthquakes. Such high frequency Rayleigh waves with large amplitude may develop much of spatial variability in ground motion which in turn may cause unexpected damage to long-span structures like bridges, underground pipelines, dams, etc., in the hilly regions. Further, it has been reported that topography acts as an insulator for the Rayleigh waves (Ma et al. BSSA 97:2066–2079, 2007). The above mentioned scientific developments stimulated to quantify the role of shape and number of ridges and valleys falling in the path of Rayleigh wave in the insulating effect of topography on the Rayleigh waves. The simulated results reveals very large amplification of the horizontal component of Rayleigh wave near the top of a triangular ridge which may cause intensive landslides under favorable condition. The computed snapshots of the wave-field of Rayleigh wave reveals that the interaction of Rayleigh wave with the topography causes reflection, splitting, and diffraction of Rayleigh wave in the form of body waves which in turn provides the insulating capacity to the topography. Insulating effects of single valley is more than that of single ridge. Further this effect was more in case of elliptical ridge/valley than triangular ridge/valley. The insulating effect of topography was proportional to the frequency of Rayleigh wave and the number of ridges and valleys in the string. The obtained level of insulation effects of topography on the Rayleigh wave (energy of Rayleigh wave reduced to less than 4% after crossing a topography of span 4.5 km) calls for the consideration of role of hills and valleys in seismic hazard prediction, particularly in case of shallow earthquakes.

Large scale metasurfaces for seismic waves control

Elastic metamaterials are artificial composites with subwavelength resonant particles hosted in a medium able to manipulate the propagation of elastic waves. When the resonant particles are placed at the free surface of the medium to form a resonant “metasurface,” the localization mechanism and the direction of surface waves can be fully controlled. In this talk, we discuss the use of resonant metasurfaces to control the propagation of vertically and horizontally polarized surface waves and their possible application for seismic waves mitigation. By combining analytical, numerical, and experimental studies, we describe the interaction of Rayleigh waves with a metasurface of vertical resonators and design large-scale resonant barriers to deviate damaging seismic Rayleigh waves into the medium bulk. Additionally, we investigate the effect of material stratification on the metasurface dynamics by analyzing the propagation of surface waves in unconsolidated granular media with depth-dependent stiffness profile. Finally, we describe the interaction of Love waves guided by a stratified medium with a metasurface of horizontal resonators and design large-scale resonant metalenses to redirect their propagation.

Interaction of Rayleigh waves with 2D dipolar exciton gas: impact of Bose–Einstein condensation

The theory of the interaction of a two-dimensional gas of indirect dipolar excitons with Rayleigh surface elastic waves has been developed. The absorption and renormalization of the phase velocity of a surface wave, as well as the drag of excitons by the surface acoustic wave and the generation of bulk acoustic waves by a two dimensional gas of dipolar excitons irradiated by external electromagnetic radiation, have been considered. These effects have been studied both in a normal phase at high temperatures and in a condensed phase of the exciton gas. The calculations have been performed in the ballistic and diffusion limits for both phases.

Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction

We consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space. In both cases the flexural plate, or Rayleigh surface, waves in the substrate interact with the resonators to create interesting effects such as effective band-gaps for surface waves or filters that transform surface waves into bulk waves; these effects have parallels in the field of optics where such sub-wavelength resonators create metamaterials in the bulk and metasurfaces at the free surfaces.Here we carefully analyse this canonical problem by extracting the dispersion relations analytically thereby examining the influence of both the flexural and compressional resonances on the propagating wave. For an array of resonators atop an elastic half-space we augment the analysis with numerical simulations. Amongst other effects, we demonstrate the striking effect of a dispersion curve which corresponds to a mode that transitions from Rayleigh wave-like to shear wave-like behaviour and the resultant change in the fields from surface to bulk waves.

The use of reflected Rayleigh waves to study rough contact interfaces

Ultrasonic reflectometry is commonly used in the field of tribology. Bulk waves that travel through a component are reflected from an interface and can be used to measure parameters such as contact stress and lubricant film thickness. This paper presents the development of a novel ultrasonic technique using Rayleigh waves that propagate along the surface of a component. An analytical model is first proposed to explain the interaction of Rayleigh waves with a contact interface. When contact parameters change, so does the amplitude of the reflected Rayleigh wave. From the reflected waves, it is possible to simultaneously predict both normal and tangential interface stiffness. Experiments have been conducted to show how the reflected waves change as cyclic loading is applied and the roughness of the contact interface varied. Results have shown there is good agreement between experimental data and analytical predictions. Potential application of this study includes the remote monitoring of sealing components such as o-rings or radial lip seals.