Rayleigh wave propagation in centrosymmetric materials with micro-stiffness, flexoelectric and micro-inertia effects

A theoretical investigation of Rayleigh waves propagation in polarized media has been carried out using a reformulated flexoelectric theory for isotropic dielectrics with micro-inertia effect. Within this non-classical theory, the internal energy density is the functional of the strain tensor, dilatation gradient, deviatoric part of stretch gradient and rotation gradient tensors, polarization vector, and polarization gradient. The obtained system of governing equations additionally contains three material length-scale parameters to account the micro-stiffness effect, one material constant to capture the micro-inertia effect, two flexoelectric constants to describe the flexoelectric effect and three length scale parameters related to the polarization gradient. To solve the coupled governing equations, the method of Lamé-type potentials for mechanical displacement and electric polarization vectors is used. The influences of various factors such as micro-stiffness, flexoelectricity, electric quadrupoles and micro-inertia effects on the phase velocity of the Rayleigh waves in a homogeneous isotropic half-space are studied. It is found that above effects become significant with the increase of the wavenumber. This study can be important for the investigation of high frequency surface acoustic waves in dielectric materials.

Ultrasonic surface acoustic wave elastography: A review of basic theories, technical developments, and medical applications

Physiological and pathological changes in tissues often cause changes in tissue mechanical properties, making tissue elastography an effective modality in medical imaging. Among the existing elastography methods, ultrasound elastography is of great interest due to the inherent advantages of ultrasound imaging technology, such as low cost, portability, safety, and wide availability. However, most current ultrasound elastography methods are based on the bulk shear wave; they can image deep tissues but cannot image superficial tissues. To address this challenge, ultrasonic elastography methods based on surface acoustic waves have been proposed. In this paper, we present a comprehensive review of ultrasound-based surface acoustic wave elastography techniques, including their theoretical foundations, technical implementations, and existing medical applications. The goal is to provide a concise summary of the state-of-the-art of this field, hoping to offer a reliable reference for the further development of these techniques and foster the expansion of their medical applications.

A Dual-Mode Surface Acoustic Wave Delay Line for the Detection of Ice on 64°-Rotated Y-Cut Lithium Niobate

Ice accumulation on infrastructure poses severe safety risks and economic losses, necessitating effective detection and monitoring solutions. This study introduces a novel approach employing surface acoustic wave (SAW) sensors, known for their small size, wireless operation, energy self-sufficiency, and retrofit capability. Utilizing a SAW dual-mode delay line device on a 64°-rotated Y-cut lithium niobate substrate, we demonstrate a solution for combined ice detection and temperature measurement. In addition to the shear-horizontal polarized leaky SAW, our findings reveal an electrically excitable Rayleigh-type wave in the X+90° direction on the same cut. Experimental results in a temperature chamber confirm capability for reliable differentiation between liquid water and ice loading and simultaneous temperature measurements. This research presents a promising advancement in addressing safety concerns and economic losses associated with ice accretion.

Integrated Rayleigh wave streaming-enhanced sensitivity of shear horizontal surface acoustic wave biosensors

Shear horizontal surface acoustic wave (SH-SAW) sensors are regarded as a promising alternative for label-free, sensitive, real time and low-cost detection. Nevertheless, achieving high sensitivity with SH-SAW has approached its limit imposed by the mass transport and probe-target affinity. We present here an SH-SAW biosensor accompanied by a unique Rayleigh wave-based actuator. The platform assembled on an ST-quartz substrate consists of dual-channel SH-SAW delay lines fabricated along a 90°-rotated direction, whilst another interdigital electrode (IDT) is orthogonally placed to generate Rayleigh waves so as to induce favourable streaming in the bio-chamber, enhancing the binding efficiency of the bio-target. Theoretical foundation and simulation have shown that Rayleigh acoustic streaming generates a level of agitation that accelerates the mass transport of the biomolecules to the surface. A fourfold improvement in sensitivity is achieved compared with conventional SH-SAW biosensors by means of complementary DNA hybridization with the aid of the Rayleigh wave device, giving a sensitivity level up to 6.15 Hz/(ng/mL) and a limit of detection of 0.617 ng/mL. This suggests that the proposed scheme could improve the sensitivity of SAW biosensors in real-time detection.

A Numerical Study of the Dynamic Crack Behavior of Brittle Material Induced by Blast Waves

Blast stress waves profoundly impact engineering structures, exciting and affecting the rupture process in brittle construction materials. A novel numerical model was introduced to investigate the initiation and propagation of cracks subjected to blast stress waves within the borehole-crack configuration. Twelve models were established with different crack lengths to simulate sandstone samples. The influence of crack length on crack initiation and propagation was investigated using those models. The linear equation of state was used to express the relationship between the pressure and density of the material. The major principal stress failure criterion was used to evaluate the failure of elements. A triangular pressure curve was adopted to produce the blast stress wave. The results indicated that the pre-crack length critically influenced the crack initiation and propagation mechanism by analyzing the stress history at the crack tip, crack propagation velocity, and distance. The inducement of a P-wave and S-wave is paramount in models with a short pre-crack. For long pre-crack models, Rayleigh waves significantly contribute to crack propagation.

Seismic metasurface on an orthorhombic elastic half-space

The article is studying a seismic meta-surface in the case of an oscillatory system arranged on the surface of an orthorhombic elastic half-space. The approach is based on the asymptotic hyperbolic-elliptic formulation for the Rayleigh wave excited by prescribed surface loading. The latter results in hyperbolic equations for surface displacements, with the right-hand sides involving the loading components. The derived model allows a formulation for the meta-surface in the form of a periodic spring-mass system attached to the surface as a hyperbolic equation for the horizontal displacement, with smooth contact stresses emerging from averaging the effect of a regular array of oscillators. The associated dispersion relation is constructed and illustrated numerically for both cases of exponential and oscillatory decay.

Thermo-acoustoelastic effect of Rayleigh wave: Theory and experimental verification

Previous studies showed that the thermally-induced ultrasonic bulk wave velocity change could be used to measure acoustoelastic coefficients and third-order elastic constants of elastic materials. This method is naturally immune from the ambient temperature effect and has improved sensitivity and a simpler test setup than the conventional acoustoelastic test. However, Rayleigh wave is preferred for thick components or structures with only one accessible surface. In this work, the thermo-hyperelastic constitutive equation, along with acoustoelastic theory, is used to derive the expression of the thermo-acoustoelastic coefficient (TAEC) of Rayleigh wave. The numerical relationship between the TAEC of Rayleigh wave and Murnaghan constants (l, m and n) are given for common metals. The TAEC expressions for Rayleigh wave and shear wave are similar, and both are dominated by the constant m. The TAEC of Rayleigh wave was measured on an aluminum 6061 specimen using the thermal modulation experiment in a temperature range of 22 ∼35 °C. The measured TAEC shows good agreement with the theoretical calculation. Then the third-order elastic constants were calculated based on TAECs of bulk waves and Rayleigh wave.

In situ nonlinear Rayleigh wave technique to characterize the tensile plastic deformation of stainless steel 316L

The acoustic nonlinearity parameter β is sensitive to dislocation parameters, which continuously change during plastic deformation. Dislocation-based damage in structures/components is the source of the failure; thus, β has been studied as a metric for non-destructive evaluation. This work consists of two parts: the development of an in situ experimental setup for nonlinear Rayleigh wave measurements, and characterization of the dependence of β on applied stress at different levels of initial plastic strain. First, we introduce an experimental setup and methods for repeatable in situ nonlinear ultrasonic measurements. Details on design considerations and measurement schemes are provided. In the second part, β was measured in situ during an incremental monotonic tensile test. The measured β monotonically decreases with plastic strain, but it is relatively insensitive to the applied stress during elastic deformation. This result highlights three aspects of the evolution of β, which have not been sufficiently emphasized in prior work: the apparent insensitivity of β to the applied stress during elastic deformation, decreasing β with plastic deformation, and the saturation of β. We attribute the trend of decreasing β to a scaling of β with monopole loop length during plastic deformation, which depends on initial microstructure. The saturation of β at 1.8% coincides with a planar-to-wavy transition of dislocation structures. The in situ nonlinear ultrasonic experimental method presented in this work is significant as the in situ results can provide broader insights on β and dislocation-based damage evolution than ex situ measurements alone.

Acoustoelectric Effect of Rayleigh and Sezawa Waves in ZnO/Fused Silica Produced by an Inhomogeneous In-Depth Electrical Conductivity Profile

The acousto-electric (AE) effect associated with the propagation of Rayleigh and Sezawa surface acoustic waves (SAWs) in ZnO/fused silica was theoretically investigated under the hypothesis that the electrical conductivity of the piezoelectric layer has an exponentially decaying profile akin to the photoconductivity effect induced by ultra-violet illumination in wide-band-gap photoconducting ZnO. The calculated waves' velocity and attenuation shift vs. ZnO conductivity curves have the form of a double-relaxation response, as opposed to a single-relaxation response which characterizes the AE effect due to surface conductivity changes. Two configurations were studied which reproduced the effect of UV light illumination from the top or from the bottom side of the ZnO/fused silica substrate: 1. the ZnO conductivity inhomogeneity starts from the free surface of the layer and decreases exponentially in depth; 2. the conductivity inhomogeneity starts from the lower surface of the ZnO layer contacting the fused silica substrate. To the author's knowledge, this is the first time the double-relaxation AE effect has been theoretically studied in bi-layered structures.

Acoustoelectric Effect for Rayleigh Wave in ZnO Produced by an Inhomogeneous In-Depth Electrical Conductivity Profile

The acousto-electric (AE) effect associated with the propagation of the Rayleigh wave in ZnO half-space was theoretically investigated by studying the changes in wave velocity and propagation loss induced by in-depth inhomogeneous changes in the ZnO electrical conductivity. An exponentially decaying profile for the electrical conductivity was attributed to the ZnO half-space, for some values of the exponential decay constant (from 100 to 500 nm), in order to simulate the photoconductivity effect induced by ultra-violet illumination. The calculated Rayleigh wave velocity and attenuation vs. ZnO conductivity curves have the form of a double-relaxation response as opposed to the single-relaxation response which characterizes the well-known AE effect due to surface conductivity changes onto piezoelectric media. As to the author's knowledge, this is the first time the double-relaxation AE effect has been theoretically predicted.

A Novel and Non-Invasive Approach to Evaluating Soil Moisture without Soil Disturbances: Contactless Ultrasonic System

Soil moisture has been considered a key variable in governing the terrestrial ecosystem. However, it is challenging to preserve indigenous soil characteristics using conventional soil moisture monitoring methods that require maximum soil contacts. To overcome this issue, we developed a non-destructive method of evaluating soil moisture using a contactless ultrasonic system. This system was designed to measure leaky Rayleigh waves at the air-soil joint-half space. The influences of soil moisture on leaky Rayleigh waves were explored under sand, silt, and clay in a controlled experimental design. Our results showed that there were strong relationships between the energy and amplitude of leaky Rayleigh waves and soil moisture for all three soil cases. These results can be explained by reduced soil strengths during evaporation processes for coarse soil particles as opposed to fine soil particles. To evaluate soil moisture based on the dynamic parameters and wave properties obtained from the observed leaky Rayleigh waves, we used the random forest model. The accuracy of predicted soil moisture was exceptional for test data sets under all soil types (R2 ≥ 0.98, RMSE ≤ 0.0089 m3 m-3). That is, our study demonstrated that the leaky Rayleigh waves had great potential to continuously assess soil moisture variations without soil disturbances.

A Sensitive Frequency Range Method Based on Laser Ultrasounds for Micro-Crack Depth Determination

The laser ultrasonic method using the characteristics of transmitted Rayleigh waves in the frequency domain to determine micro-crack depth is proposed. A low-pass filter model based on the interaction between Rayleigh waves and surface cracks is built and shows that the stop band, called the sensitive frequency range, is sensitive to the depth of surface cracks. The sum of transmission coefficients in the sensitive frequency range is defined as an evaluated parameter to determine crack depth. Moreover, the effects of the sensitive frequency range and measured distance on the evaluated results are analyzed by the finite-element method to validate the robustness of this depth-evaluating method. The estimated results of surface cracks with depths ranging from 0.08 mm to ~0.5 mm on the FEM models and aluminum-alloy samples demonstrate that the laser ultrasounds using the characteristics of Rayleigh waves in the frequency domain do work for quantitative crack depth.

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.

Design and experiment of array Rayleigh wave-EMAT for plane stress measurement

The Rayleigh wave excited by the electromagnetic acoustic transducer (EMAT) is an effective selection for surface plane stress measurement. However, the propagation velocity of Rayleigh wave on the metal surface is easily affected by the original rolling process. Besides, the direction of the plane stress state is usually unknown, which means that the propagation velocity cannot be expressed linearly by the stress. As a result, the traditional measurement model of one transmitter and one receiver can only realize the decouple of plane stress components by rotating method, which not only brings position error but also low measurement efficiency. Therefore, this paper focuses on a novel Rayleigh wave-EMAT for plane stress ultrasonic measurement. Firstly, the Rayleigh wave measurement model is established based on the acoustoelastic equation and displacement expression. Furthermore, an array Rayleigh wave-EMATintegrating three transmitters and three receivers is designed. Finally, the typical plane stress state of 5052 aluminum alloy plate after friction stir welding (FSW) is measured. The experimental results show good agreement compared with the hole-drilling method, which verifies the effectiveness of proposed method and designed EMAT.

Remote characterization of surface slots by enhanced laser-generated ultrasonic Rayleigh waves

Characterization of surface features is essential in many industrial applications, especially for features with large depths, high aspect ratios or under extreme conditions. This work presents a non-contact method to characterize surface slots with large lengths using ultrasonic Rayleigh waves generated by a pulsed laser. A delay-and-sum superposition technique is applied to enhance the signal to noise ratio of transmitted Rayleigh waves. The length of the slot can be calculated from the time-of-flight information of Rayleigh waves without any prior knowledge of its orientation, width or aspect ratio. Both numerical simulations and experiments are conducted to demonstrate the proposed method, showing excellent performance. Furthermore, mode conversion has been studied to understand its impact on the reconstruction accuracy. Given the non-contact feature of the laser ultrasonic technique, the proposed method provides a simple and feasible avenue for the rapid characterisation of normal and angled surface features with high aspect ratio in extreme environments.

Rayleigh-Wave Dispersion Analysis and Inversion Based on the Rotation

Rotational observation is essential for a comprehensive description of the ground motion, and can provide additional wave-field information. With respect to the three typical layered models in shallow engineering geology, under the assumption of linear small deformation, we simulate the 2-dimensional radial, vertical, and rotational components of the wave fields and analyze the different characteristics of Rayleigh wave dispersion recorded for the rotational and translational components. Then, we compare the results of single-component inversion with the results of multi-component joint inversion. It is found that the rotational component has wider spectral bands and more higher modes than the translational components, especially at high frequencies; the rotational component has better anti-interference performance in the noisy data test, and it can improve the inversion accuracy of the shallow shear-wave velocity. The field examples also show the significant advantages of the joint utility of the translational and rotational components, especially when a low-velocity layer exists. Rotational observation shall be beneficial for shallow surface-wave exploration.

Surface Acoustic Wave (SAW) Sensors: Physics, Materials, and Applications

Surface acoustic waves (SAWs) are the guided waves that propagate along the top surface of a material with wave vectors orthogonal to the normal direction to the surface. Based on these waves, SAW sensors are conceptualized by employing piezoelectric crystals where the guided elastodynamic waves are generated through an electromechanical coupling. Electromechanical coupling in both active and passive modes is achieved by integrating interdigitated electrode transducers (IDT) with the piezoelectric crystals. Innovative meta-designs of the periodic IDTs define the functionality and application of SAW sensors. This review article presents the physics of guided surface acoustic waves and the piezoelectric materials used for designing SAW sensors. Then, how the piezoelectric materials and cuts could alter the functionality of the sensors is explained. The article summarizes a few key configurations of the electrodes and respective guidelines for generating different guided wave patterns such that new applications can be foreseen. Finally, the article explores the applications of SAW sensors and their progress in the fields of biomedical, microfluidics, chemical, and mechano-biological applications along with their crucial roles and potential plans for improvements in the long-term future in the field of science and technology.

On the Utility of Horizontal-to-Vertical Spectral Ratios of Ambient Noise in Joint Inversion with Rayleigh Wave Dispersion Curves for the Large-N Maupasacq Experiment

Horizontal-to-Vertical Spectral Ratios (HVSR) and Rayleigh group velocity dispersion curves (DC) can be used to estimate the shallow S-wave velocity (VS) structure. Knowing the VS structure is important for geophysical data interpretation either in order to better constrain data inversions for P-wave velocity (VP) structures such as travel time tomography or full waveform inversions or to directly study the VS structure for geo-engineering purposes (e.g., ground motion prediction). The joint inversion of HVSR and dispersion data for 1D VS structure allows characterising the uppermost crust and near surface, where the HVSR data (0.03 to 10s) are most sensitive while the dispersion data (1 to 30s) constrain the deeper model which would, otherwise, add complexity to the HVSR data inversion and adversely affect its convergence. During a large-scale experiment, 197 three-component short-period stations, 41 broad band instruments and 190 geophones were continuously operated for 6 months (April to October 2017) covering an area of approximately 1500km2 with a site spacing of approximately 1 to 3km. Joint inversion of HVSR and DC allowed estimating VS and, to some extent density, down to depths of around 1000m. Broadband and short period instruments performed statistically better than geophone nodes due to the latter’s gap in sensitivity between HVSR and DC. It may be possible to use HVSR data in a joint inversion with DC, increasing resolution for the shallower layers and/or alleviating the absence of short period DC data, which may be harder to obtain. By including HVSR to DC inversions, confidence improvements of two to three times for layers above 300m were achieved. Furthermore, HVSR/DC joint inversion may be useful to generate initial models for 3D tomographic inversions in large scale deployments. Lastly, the joint inversion of HVSR and DC data can be sensitive to density but this sensitivity is situational and depends strongly on the other inversion parameters, namely VS and VP. Density estimates from a HVSR/DC joint inversion should be treated with care, while some subsurface structures may be sensitive, others are clearly not. Inclusion of gravity inversion to HVSR/DC joint inversion may be possible and prove useful.

Validation of Rayleigh Wave Theoretical Formulation with Single-Station Rotational Records of Mine Tremors in Lower Silesian Copper Basin

The classical Rayleigh surface rotational wave in terms of its theoretical notation and, resulting from this, properties associated with the induced seismic phenomena in mines are presented. This kind of seismic wave was analysed in-depth from the point of view of the parameters governing the form of its mathematical notation based on the similarity to the records obtained during the induced seismicity in near-field 6-DoF monitoring. Furthermore, conducted field measurements made it possible to relate the amount of the emitted seismic energy to the expected highest amplitude of rotational vibrations in the entire field of their impact on the rock mass. As a result, this made it possible to impose the completely defined R wave to the numerical models of given objects; the safety level, when subjected to the dynamic load induced by the rotational wave, would be an objective of the performed analyses. The conducted preliminary analyses were prepared for a plane strain state, for which the values of seismic rotations were evaluated concerning the energy and the distance of the seismic event’s source. As a result of the performed simulations, it was found that the results of the calculations matched with a satisfying degree with the field seismic measurements of the rotational ground motion induced by propagating the seismic wave. Such a verified analytical description of the theoretical formulas can be the basis for the implementation of R-wave characteristics into seismic codes and numerical analyses of object stability in the Lower Silesian Copper Basin region.

Inversion of surface damage and residual stress in ground silicon wafers by laser surface acoustic wave technology

The paper presents a study of surface acoustic waves propagation in a damage layer with finite thickness and residual stress on an orthotropic semi-infinite medium to reveal the application of laser ultrasound in the surface inspection of ground silicon wafers. Biot's theory of small deformations influenced by initial stress forms the basis for this study. Considering the case that the displacement and boundary forces are continuous at the interface and the forces vanish on the free surface, the required dispersion relation is obtained. We consider a sample of (100) silicon wafer by grinding with fine abrasive grains, which has a machined face with a micrometer-level thickness of surface damage and residual stress. In order to discuss the impact of propagation directions, degree of surface damage, residual compressive stress on the velocity characteristics of surface waves, the numerical computation of the dispersion equations is performed. It has been found that surface damage has a significant effect on the dispersion curve, while the residual compressive stress can only cause a small decrease Δc in the surface wave velocity. The velocity decrease Δc becomes obvious at high frequencies. For a fixed residual compressive stress and frequency, Δc hardly changes with the degree of surface damage and propagation directions. Based on the above characteristics, we study the inverse problem on detecting both surface damage and residual stress simultaneously by SAW velocities and give a corresponding iterative algorithm. This study may provide theoretical guidance for non-destructive testing of residual stress.

RAYLEIGH WAVE AND WELL HEAD RESPONSE TO CALCULATE POROSITY IN THE EDWARDS AQUIFER OF SOUTH-CENTRAL TEXAS, USA

We use the magnitude and centroid period of Rayleigh wave along with the amplitude of fluctuations of water level in a well to calculate effective porosity of a karst aquifer at the site scale. The radial and vertical displacements of Rayleigh wave are first related to the confining pressure of rock, which is then related to fluid pressure via the Gassmann equation. Three seismograms recorded at station 633A of the USARRAY and the induced responses of Well J-17 in the Edwards Aquifer (Texas) allow the calculation of an effective porosity between 17.0 and 24.4 percent, the average of which is close to the total porosity of core samples determined by geophysical well logs. This paper provides an innovative method to measure effective porosity in aquifers. Because of the long wavelengths of Rayleigh wave, the interdisciplinary approach is advantageous in that the resulting effective porosity is at the site scale which includes large conduits or voids.

Enhanced Performance of ZnO/SiO2/Al2O3 Surface Acoustic Wave Devices with Embedded Electrodes

With the advent of the 5G era, surface acoustic wave (SAW) devices with a larger bandwidth and better temperature stability are strongly required, meanwhile the dimensions of devices are continuously scaling down. In this work, a new layout of ZnO/SiO₂/Al₂O₃ SAW devices with embedded electrodes was developed, and with the help of the finite element method (FEM), the propagation characteristics were simulated. Through adopting embedded electrodes, a large electromechanical coupling coefficient (K²) of 6.6% for the Rayleigh mode can be achieved (5 times larger than that of the conventional ZnO/Al₂O₃ structure), feasible for wideband SAW devices, and a low acoustic velocity (V_p) of 2960 m/s is exhibited simultaneously, which benefits the miniaturization of SAW devices. The dramatic enhancement of K² is mainly attributed to the more efficient excitation of SAW in piezoelectric films. Furthermore, a SiO₂ overlay is added on the top of the structure to gain an excellent zero temperature coefficient of frequency (TCF). Experimentally, we successfully fabricated SAW one-port resonators based on the proposed structure and good characteristics of high K², low V_p, and small TCF as simulated were confirmed. Our results show that the proposed structure provides a viable route to design SAW devices with a large bandwidth, small size, and robust temperature compensation for practical use.

Multiple Rayleigh waves guided by the planar surface of a continuously twisted structurally chiral material

The Stroh formalism was adapted for Rayleigh-wave propagation guided by the planar traction-free surface of a continuously twisted structurally chiral material (CTSCM), which is an anisotropic solid that is periodically non-homogeneous in the direction normal to the planar surface. Numerical studies reveal that this surface can support either one or two Rayleigh waves at a fixed frequency, depending on the structural period and orientation of the CTSCM. In the case of two Rayleigh waves, each wave possesses a different wavenumber. The Rayleigh wave with the larger wavenumber is more localized to the surface and has a phase speed that changes less as the angular frequency varies in comparison with the Rayleigh wave with the smaller wavenumber.

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.

Experimental and Theoretical Study of Multifrequency Surface Acoustic Wave Devices in a Single Si/SiO2/ZnO Piezoelectric Structure

The propagation of surface acoustic waves (SAWs) along a ZnO/SiO₂/Si piezoelectric structure is experimentally and theoretically studied. Six surface acoustic modes were experimentally detected in the 134 to 570 MHz frequency range, for acoustic wavelength λ = 30 μm, and for SiO₂ and ZnO layers with a thickness of 1 and 2.4 μm. The numerical and three-dimensional (3D) finite element method analysis revealed that the multilayered substrate supports the propagation of Rayleigh and Sezawa modes (R_m and S_m), their third and fifth harmonics at λ/3 and λ/5. The velocity of all the modes was found in good agreement with the theoretically predicted values. Eigenfrequency, frequency domain, and time domain studies were performed to calculate the velocity, the electroacoustic coupling coefficient, the shape of the modes, the propagation loss, and the scattering parameter S₂₁ of the SAW delay lines based on the propagation of these modes. The sensitivity to five different gases (dichloromethane, trichloromethane, carbontetrachloride, tetrachloroethylene, and trichloroethylene) was calculated under the hypothesis that the ZnO surface is covered by a polyisobutylene (PIB) layer 0.8 µm thick. The results show that the modes resonating at different frequencies exhibit different sensitivities toward the same gas. The multi-frequency ZnO/SiO₂/Si single device structure is a promising solution for the development of a multiparameters sensing platform; multiple excitation frequencies with different sensing properties can allow the parallel analysis of the same gas with improved accuracy.

The effect of EMAT coil geometry on the Rayleigh wave frequency behaviour

Understanding of optimal signal generation and frequency content for electromagnetic acoustic transducers (EMATs) is key to improving their design and signal to noise ratio. Linear and meander coil designs are fairly well understood, but other designs such as racetrack or focused coils have recently been proposed. Multiple transmission racetrack coil EMATs, with focused and unfocused designs, were constructed. The optimum driving frequency for maximum detected signal was found to range between 1.1 and 1.4 MHz on aluminium for a 1.5 mm width coil. A simple analytical model based on the instantaneous velocity of a wave predicts a maximum signal at 1.44 MHz. Modelling the detection coil as a spatial square wave agrees with this, and predicts a general relation of f_P=0.761v/L between the optimum frequency f_P, the wave velocity v, and the coil width L. A time domain model of the detection coil predicts a 1.4-1.5 MHz peak for continuous wave excitation, with a frequency that decreases as the length of the wavepacket is decreased, consistent with the experimental data. Linear coil modelling using the same technique is shown to be consistent with previous work, with improving detection at lower wave frequencies, and signal minima at every integer multiple of the wavelength. Finite Element Analysis (FEA) is used to model the effects of the spatial width of the racetrack generation coil and focused geometry, and no significant difference is found between the focused and the unfocused EMAT response. This highlights the importance of designing the EMAT coil for the correct lift-off and desired frequency of operation.

Rayleigh-type waves on a coated elastic half-space with a clamped surface

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localized waves that do not exist on a clamped homogeneous half-space. Non-traditional effective boundary conditions along the substrate surface incorporating the effect of the coating are derived using a long-wave high-frequency procedure. The derived conditions are implemented within the framework of the earlier developed specialized formulation for surface waves, resulting in a perturbation of the shortened equation of surface motion in the form of an integral or pseudo-differential operator. Non-uniform asymptotic formula for the speeds of the sought for Rayleigh-type waves, failing near zero frequency and the thickness resonances of a layer with both clamped faces, follow from the aforementioned perturbed equation. Asymptotic results are compared with the numerical solutions of the full dispersion relation for a clamped coated half-space. A similarity with Love-type waves proves to be useful for interpreting numerical data. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.

Satellite-Based Wireless Sensor Development and Deployment Studies for Surface Wave Testing

Although cable-based seismic sensing systems have provided reliable data in the past several decades, they become a bottleneck for large-area monitoring and critical environmental (volcanic eruptions) sensing because of their cost, difficulty in deploying and expanding, and lack of accurate three-dimensional geographic information. In this paper, a new wireless sensing system is designed consisting of a portable satellite device, a self-sustaining power source, a low-cost computational core, and a high-precision sensor. The emphasis of this paper is to implement in low-cost hardware without requirements of highly specialized and expensive data acquisition instruments. Meanwhile, a computational-core-embedded algorithm based on compressive sensing (CS) is also developed to compress data size for transmission and encrypt the measured data preventing information loss. Seismic data captured by the accelerometer sensor are coded into compressive data packages and then transferred via satellite communication to a cloud-based server for storage. Acceleration and GPS information is decrypted by the ℓ₁-norm minimization optimization algorithm for further processing. In this research, the feasibility of the proposed sensing system for the acquisition of seismic testing is investigated in an outdoor field surface wave testing. Results indicate the proposed low-cost wireless sensing system has the capability of collecting ground motions, transferring data, and sharing GPS information via satellite communication for large area monitoring. In addition, it has a great potential of recovering measurements even with significant data package loss.

On the validity of several previously published perturbation formulas for the acoustoelastic effect on Rayleigh waves

This article revisits the evaluation by a perturbation theory of the modification of the Rayleigh wave velocity under a static loading varying with depth. Two derivations, that have been exposed in the past and presented as comparable, are questioned. A new derivation of the perturbation formula is given by adapting Auld's approach. Validation with exact calculations is provided. The examples cover depth-varying static stress as well as depth-varying third order elastic properties.

Measurement of Rayleigh Wave Beams Using Angle Beam Wedge Transducers as the Transmitter and Receiver with Consideration of Beam Spreading

A theoretical model, along with experimental verification, is developed to describe the generation, propagation and reception of a Rayleigh wave using angle beam wedge transducers. The Rayleigh wave generation process using an angle beam wedge transducer is analyzed, and the actual Rayleigh wave sound source distributions are evaluated numerically. Based on the reciprocity theorem and considering the actual sound source, the Rayleigh wave beams are modeled using an area integral method. The leaky Rayleigh wave theory is introduced to investigate the reception of the Rayleigh wave using the angle beam wedge transducers, and the effects of the wave spreading in the wedge and transducer size are considered in the reception process. The effects of attenuations of the Rayleigh wave and leaky Rayleigh wave are discussed, and the received wave results with different sizes of receivers are compared. The experiments are conducted using two angle beam wedge transducers to measure the Rayleigh wave, and the measurement results are compared with the predictions using different theoretical models. It is shown that the proposed model which considers the wave spreading in both the sample and wedges can be used to interpret the measurements reasonably.

Finite element analysis of the Rayleigh wave scattering in isotropic bi-material wedge structures

The numerical study is performed of the harmonic Rayleigh wave scattering in a composite structure constructed from two elastically isotropic 90°-wedges. These wedges are in contact along one pair of their faces. It is assumed that either the perfectly sliding contact or the perfectly rigid one is realized. The other pair of faces forms a plane border between the resulting bi-material wedge and the exterior half-infinite space occupied by vacuum. The finite element method is used. The perfectly matched layer spatially confines the computational domain. The dependences of the reflection and transmission coefficients of the Rayleigh wave on the angle of incidence, the Poisson ratio and the type of contact are obtained and analyzed for different combinations of materials. The behavior of the coefficient of the Rayleigh wave conversion into the interfacial wave which may exist on the internal boundary of the structure is also investigated. A number of relations between the coefficients of conversion are derived from symmetry considerations for structures with sliding contact and composed of identical isotropic materials.

A Theoretical Study of Love Wave Sensors Based on ZnO-Glass Layered Structures for Application to Liquid Environments

The propagation of surface acoustic Love modes along ZnO/glass-based structures was modeled and analysed with the goal of designing a sensor able to detect changes in the environmental parameters, such as liquid viscosity changes and minute amounts of mass supported in the viscous liquid medium. Love mode propagation was modeled by numerically solving the system of coupled electro-mechanical field equations and Navier–Stokes equations. The phase and group velocities and the attenuation of the acoustic wave propagating along the 30° tilted c-axis ZnO/glass structure contacting a viscous non-conductive liquid were calculated for different ZnO guiding layer thicknesses, added mass thicknesses, and liquid viscosity and density. The three sensor responses, i.e., the wave phase and group velocity, and attenuation changes are calculated for different environmental parameters and related to the sensor velocity and attenuation sensitivities. The resulted sensitivities to liquid viscosity and added mass were optimized by adjusting the ZnO guiding layer thickness corresponding to a sensitivity peak. The present analysis is valuable for the manufacture and application of the ZnO-glass structure Love wave sensors for the detection of liquid properties, such as viscosity, density and mass anchored to the sensor surface.

Simulation of SAW Humidity Sensors Based on ( 11 2 ¯ 0 ) ZnO/R-Sapphire Structures

The characteristics of two types of surface acoustic waves SAWs (Rayleigh waves and Love waves) propagating in bilayered structures of (112¯0)ZnO/R-sapphire are simulated by a finite element method (FEM) model, in which both SAWs have crossed propagation directions. Furthermore, based on the bilayered structures, the frequency responses of Rayleigh wave and Love wave humidity sensors are also simulated. Meanwhile, the frequency shifts, insertion loss changes and then the sensitivities of both humidity sensors induced by the adsorbed water layer perturbations, including the mechanical and electrical factors, are calculated numerically. Generally, the characteristics and performances of both sensors are strongly dependent on the thickness of the ZnO films. By appropriate selecting the ratio of the film thickness to SAW wavelength for each kind of the sensors, the performances of both sensors can be optimized.

The Simple Lamb Wave Analysis to Characterize Concrete Wide Beams by the Practical MASW Test

In recent years, the Lamb wave analysis by the multi-channel analysis of surface waves (MASW) for concrete structures has been an effective nondestructive evaluation, such as the condition assessment and dimension identification by the elastic wave velocities and their reflections from boundaries. This study proposes an effective Lamb wave analysis by the practical application of MASW to concrete wide beams in an easy and simple manner in order to identify the dimension and elastic wave velocity (R-wave) for the condition assessment (e.g., the estimation of elastic properties). This is done by identifying the zero-order antisymmetric (A0) and first-order symmetric (S1) modes among multimodal Lamb waves. The MASW data were collected on eight concrete wide beams and compared to the actual depth and to the pressure (P-) wave velocities collected for the same specimen. Information is extracted from multimodal Lamb wave dispersion curves to obtain the elastic stiffness parameters and the thickness of the concrete structures. Due to the simple and cost-effective procedure associated with the MASW processing technique, the characteristics of several fundamental modes in the experimental Lamb wave dispersion curves could be measured. Available reference data are in good agreement with the parameters that were determined by our analysis scheme.

A class of reduced-order models in the theory of waves and stability

This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through points on this grid. Thus, the method is interpolatory in nature, but the interpolation takes place in (frequency, wavenumber) space, rather than in physical space. Full details are presented for a non-trivial example, that of antisymmetric elastic waves in a layer. The method is related to partial fraction expansions and barycentric representations of functions. An asymptotic analysis is presented, involving Stirling's approximation to the psi function, and a logarithmic correction to the polynomial dispersion relation.

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is shown to coincide formally with the 'local' problem for a half-space with a vertical inhomogeneity localized near the surface. Subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface. The order of the correction is greater than the order of the better-known correction to the governing differential equations. The refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface. As an illustration, the effect of non-local elastic phenomena on the Rayleigh wave speed is investigated.

Finite element simulation of core inspection in helicopter rotor blades using guided waves

This paper extends the work presented earlier on inspection of helicopter rotor blades using guided Lamb modes by focusing on inspecting the spar-core bond. In particular, this research focuses on structures which employ high stiffness, high density core materials. Wave propagation in such structures deviate from the generic Lamb wave propagation in sandwich panels. To understand the various mode conversions, finite element models of a generalized helicopter rotor blade were created and subjected to transient analysis using a commercial finite element code; ANSYS. Numerical simulations showed that a Lamb wave excited in the spar section of the blade gets converted into Rayleigh wave which travels across the spar-core section and mode converts back into Lamb wave. Dispersion of Rayleigh waves in multi-layered half-space was also explored. Damage was modeled in the form of a notch in the core section to simulate a cracked core, and delamination was modeled between the spar and core material to simulate spar-core disbond. Mode conversions under these damaged conditions were examined numerically. The numerical models help in assessing the difficulty of using nondestructive evaluation for complex structures and also highlight the physics behind the mode conversions which occur at various discontinuities.

The analysis of the effect of homogeneous mechanical stress on the acoustic wave propagation in the "La3Ga5SiO14/fused silica" piezoelectric layered structure

The results of computer simulation taking into account the linear and nonlinear material constants have been presented. Study of the influence of external uniaxial mechanical stress on the dispersive characteristics of elastic waves in piezoelectric structures as "La3Ga5SiO14/fused silica" has been executed. The comparison of elastic wave velocity changes under the influence of an uniaxial stress while a full set of nonlinear material constants of crystalline layer+geometric nonlinearity, or only geometric nonlinearity of the layer induced by the static deformation of a substrate, has been fulfilled.