Propagation Of Rayleigh Waves Research Articles

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.

Distributed acoustic sensing for seismic surface wave data acquisition in an intertidal environment

This paper assesses the use of Distributed Acoustic Sensing (DAS) for shallow marine seismic investigations, in particular the collection of seismic surface wave data, in an intertidal setting. The paper considers appropriate selection and directional sensitivity of fiber optic cables and validates the measured data with respect to conventional seismic data acquisition approaches ,using geophones and hydrophones, along with independent borehole and Seismic Cone Penetration Test (SCPT) data. In terms of cable selection, a reduction of amplitude and frequency response of an armored cable is observed, when compared to an unarmored cable. For seismic surface wave surveys in an offshore environment where the cable would need to withstand significant stresses, the use of the armored variant with limited loss in frequency response may be acceptable, from a practical perspective. The DAS approach has also shown good consistency with conventional means of surface wave data acquisition, and the inverted Vs is also very consistent with downhole SCPT data. Observed differences in phase velocity between high tide (Scholte wave propagation) and low tide (Rayleigh wave propagation) are not thought to be related to the particular type of interface wave due to shallow water depth. These differences are more likely to be related to the development of capillary forces in the partially saturated granular medium at low tide. Overall, this study demonstrates that the proposed novel approach of DAS using seabed fiber-optic cables in the intertidal environment is capable of rapidly providing near-surface shear wave velocity data across considerable spatial scales (multi-km) at high resolution, beneficial for the design of subsea cables routes and landfall locations. The associated reduction in deployment and survey duration, when compared to conventional approaches, is particularly important when working in the marine environment due to potentially short weather windows and expensive downtime.

Impact of memory-dependent heat transfer on Rayleigh waves propagation in nonlocal piezo-thermo-elastic medium with voids

PurposeThis paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.Design/methodology/approachThe analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.FindingsComputational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.Research limitations/implicationsThe results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.Practical implicationsThis investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.Originality/valueThis study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

The influence of an anticline structure on ambient noise spectral anomalies at an underground gas storage

SUMMARY The purpose of this study is to investigate the seismic ambient noise spectral anomalies that occur near gas reservoirs. These anomalies involve a significant spectral amplification of the vertical component for frequencies generally between 1.5 and 4 Hz and have been reported at various hydrocarbon sites worldwide. There are differing views on the mechanisms responsible for these anomalies. The guideline for this study is that many hydrocarbon reservoirs share a common geological feature: an anticline structure. It appears to cause site effects that influence the amplitude of the ambient noise wavefield. This research examines a dense real data set of ambient noise recorded at the Chémery underground gas storage site in France. The analysis identifies stable spectral anomalies between 1.2 and 2.4 Hz that are correlated to the position of the anticline structure, which also corresponds to the position of the gas bubble. We use a beamforming technique to study the composition and the origin of the ambient noise, and show that the variations of the spectral anomalies over time are correlated to changes in the source wavefield. Finally, we perform numerical simulations of Rayleigh wave propagation within a realistic 3-D velocity model of the Chémery site, while using source distributions directly extracted from real data analysis. The comparison of the simulated anomalies with real data yields a satisfactory qualitative fit. We conclude that the fundamental-mode Rayleigh wave site effect on the anticline is the main mechanism of the spectral anomaly.

Effect of thermal diffusivity on Rayleigh waves in human tissue

This work examines the nature of human tissue under the context of dual phase lag thermoelastic diffusion theory using the principle of propagation of Rayleigh wave along the stress free, thermally insulated/isothermal, and impermeable/isoconcentrated conditions. The governing equations for the tissue are formed by considering the third-order approximation of Taylor’s expansion for the modified Fourier’s law of heat conduction and modified Fick’s law of mass diffusion in terms of phase lag parameters. The irrational secular equations of Rayleigh waves are derived, which are then rationalized to extract their complex roots. The phase speeds and the attenuation coefficients are evaluated from these complex roots. The variation of these phase speeds and attenuation coefficients are plotted graphically against angular frequency for two significant modes. The behavioral patterns of displacement components, temperature, and concentration fields are computed and are expressed graphically. The paths of the particle motion are represented graphically. Some results of published articles are recovered from the present formulation to validate our results.

Anisotropic Reversible‐Jump McMC Shear‐Velocity Tomography of the Eastern Alpine Crust

AbstractThe eastern Alpine crust has been shaped by the continental collision of the European and Adriatic plates beginning at 35 Ma and was affected by a major reorganization after 20 Ma. To better understand how the eastern Alpine surface structures link with deep seated processes, we analyze the depth‐dependent seismic anisotropy based on Rayleigh wave propagation. Ambient noise recordings are evaluated to extract Rayleigh wave phase dispersion measurements. These are inverted in a two step approach for the azimuthally anisotropic shear velocity structure. Both steps are performed with a reversible jump Markov chain Monte Carlo (rj‐McMC) approach that estimates data errors and propagates the modeled uncertainties from the phase velocity maps into the depth inversion. A two layer structure of azimuthal anisotropy is imaged in the Alpine crust, with an orogen‐parallel upper crust and approximately orogen‐perpendicular layer in the lower crust and the uppermost mantle. In the upper layer, the anisotropy tends to follow major fault lines and may thus be an apparent, structurally driven anisotropy. The main foliation and fold axis orientations might contribute to the anisotropy. In the lower crust, the N‐S orientation of the fast axis is mostly confined to regions north of the Periadriatic Fault and may be related to European subduction. Outside the orogen, no clearly layered structure is identified. The anisotropy pattern in the northern Alpine foreland is found to be similar compared to SKS studies which is an indication of very homogeneous fast axis directions throughout the crust and the upper mantle.

Experimental investigation of Rayleigh wave propagation in a locally resonant metamaterial layer resting on an elastic half-space

In this experimental investigation, we explore the propagation characteristics of surface Rayleigh waves in a Locally Resonant Metamaterial (LRM) layer positioned on an elastic half-space. The study focuses on characterizing the dispersion and attenuation properties of these waves and validating analytical and numerical models of the LRM. For practical purposes, we utilize a thin-plate sample and construct the LRM layer, featuring multiple rows of sub-wavelength resonators, by machining the resonators at one edge of the plate. Employing a piezoelectric transducer coupled to the plate and a laser vibrometer, we actuate and receive the surface-like waves propagating at the plate edge. Two resonant layer configurations, comprising 3 and 5 rows of resonators, corresponding to heights of ∼0.6λh and λh, where λh represents the reference wavelength of Rayleigh waves, are examined. The experimental observations reveal the hybridization of the fundamental surface mode at the resonant frequency of the embedded resonators, leading to the creation of a low-frequency bandgap. This bandgap, attributed to the local resonance mechanism, exhibits a remarkable attenuation of surface wave amplitudes. To support our experimental findings, we conduct both analytical and numerical studies. These analyses demonstrate the confinement of the lowest-order surface mode within the frequency ranges proximate to the resonators’ resonance. The insights gained from this experimental study contribute to the advancement of strategies for mitigating surface waves through the application of resonant metamaterials and metastructures.

Rayleigh wave through half space semiconductor solid with temperature dependent properties

The article focuses on Rayleigh wave propagation in a homogeneous isotropic semi-conductor thermoelastic medium rotating with fixed angular frequency with temperature-dependent properties. The elastic constants depend upon the temperature function. The effects of temperature dependency parameter, time derivative, and fractional order are illustrated. By the theory of thermo-elasticity, waves result in the generation of thermal signals that propagate through the medium. A heat conduction model of three-phase lag (3PL) along with fractional order time derivative is used to analyze the thermal signals. The secular equations of Rayleigh waves are derived mathematically at the stress-free, carrier density and thermally insulated boundaries. Some specific properties like velocity, attenuation coefficient, specific heat loss and penetration depth for Rayleigh waves have been evaluated and presented graphically. The secular equations are computed numerically and depicted graphically using Matlab.

Wave propagation analysis in transversely isotropic piezoelastic medium based on nonlocal strain gradient theory

The purpose of this research is to study the propagation of surface waves in transversely isotropic piezoelastic medium based on nonlocal strain gradient theory. A characteristics equation for the existence of surface waves is discussed. This equation could be easily reduced to the ones of the gradient strain theory, nonlocal theory, and classical theory. It has also been concluded that there exist cut-off frequency for the wave propagating in size-dependent materials based on the nonlocal strain gradient theory. The dispersion equation which surface wave speed satisfies is derived from the free traction condition on the surface of half-space with consideration of electrically open circuit conditions. The effect of the nonlocal parameter, the strain gradient parameter on the existence of surface waves as well as the Rayleigh wave propagation is illustrated through some numerical examples.

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.

High-Accuracy Simulation of Rayleigh Waves Using Fractional Viscoelastic Wave Equation

The propagation of Rayleigh waves is usually accompanied by dispersion, which becomes more complex with inherent attenuation. The accurate simulation of Rayleigh waves in attenuation media is crucial for understanding wave mechanisms, layer thickness identification, and parameter inversion. Although the vacuum formalism or stress image method (SIM) combined with the generalized standard linear solid (GSLS) is widely used to implement the numerical simulation of Rayleigh waves in attenuation media, this type of method still has its limitations. First, the GSLS model cannot split the velocity dispersion and amplitude attenuation term, thus limiting its application in the Q-compensated reverse time migration/full waveform inversion. In addition, GSLS-model-based wave equation is usually numerically solved using staggered-grid finite-difference (SGFD) method, which may result in the numerical dispersion due to the harsh stability condition and poses complexity and computational burden. To overcome these issues, we propose a high-accuracy Rayleigh-waves simulation scheme that involves the integration of the fractional viscoelastic wave equation and vacuum formalism. The proposed scheme not only decouples the amplitude attenuation and velocity dispersion but also significantly suppresses the numerical dispersion of Rayleigh waves under the same grid sizes. We first use a homogeneous elastic model to demonstrate the accuracy in comparison with the analytical solutions, and the correctness for a viscoelastic half-space model is verified by comparing the phase velocities with the dispersive images generated by the phase shift transformation. We then simulate several two-dimensional synthetic models to analyze the effectiveness and applicability of the proposed method. The results show that the proposed method uses twice as many spatial step sizes and takes 0.6 times that of the GSLS method (solved by the SGFD method) when achieved at 95% accuracy.

Generation of ultrashort Rayleigh wave pulses using the combination of temporal and spatial pulse compression technique

Rayleigh waves generated by electromagnetic acoustic transducers (EMATs) have been widely used in nondestructive testing and evaluations. To improve the signal to noise ratio (SNR) and spatial resolution of Rayleigh waves simultaneously, the combination of temporal and spatial pulse compression (TSPC) technique is proposed. By analyzing the topology diagram of the typical pulse compression technique, a frequency modulated signal acts as the stretcher and a wavelength modulated meander line coil acts as the compressor. Experimental results indicate that the ultrasound fields of Rayleigh waves using the proposed TSPC technique show a spike shape in the spatial domain. Compared with the typical meander-line coil EMATs, the TSPC technique shows significant improvement of the generated Rayleigh waves. The SNR has increased by 12 dB while the main lobe width has decreased by about 98%.

Mathematical perspective on XFEM implementation for models involving contribution on interfaces

Models involving interfaces with discontinuities or even singularities of some fields across them are very frequent in real life problems modelling. In the last decades, the use of the eXtended Finite Element Method (XFEM) instead of the traditional FEM has become more and more popular, mainly because of two advantages: the mesh of the domain can be independent of the interface position, therefore avoiding remeshing, and it allows to enrich an area with specific shape functions fitted to the particular properties (singularities, discontinuities) of the expected solution, obtaining more accurate results with less computational efforts. Nevertheless, a critical point of XFEM is its implementation since it varies from one problem to another, due to the different kind (and number) of degrees of freedom on each node. A diligent organization of nodes, degrees of freedom and enrichment functions is fundamental to achieve an efficient implementation. Our aim in this paper is to provide a common reference framework for the implementation of XFEM from a mathematical point of view, providing the readers with a set of tools that will allow them to apply it to any kind of problem. To this aim, we present a detailed description of XFEM implementation, with special emphasis on the terms that involve integration over interfaces. The proposed tools are presented in a general context, and as an example, we will apply them to a problem of solids mechanics. In particular, we will contextualize the procedure on a Rayleigh waves propagation problem in a cracked structure considering a Signorini contact condition on the crack sides.

Rayleigh Wave Propagation With Rotation, Two Temperature With Diffusion in Context to Dual Phase Lag Thermoelasticity

Rayleigh Wave Propagation With Rotation, Two Temperature With Diffusion in Context to Dual Phase Lag Thermoelasticity

A nonlocal strain gradient theory for wave propagation analysis in transversely isotropic elastic medium

This paper has the objective of studying the propagation of surface waves in a transversely isotropic medium based on nonlocal strain gradient theory (NSGT). A characteristics equation for the existence of surface waves is discussed. This equation could be easily reduced to the ones of the gradient strain theory, nonlocal theory and classical theory. It has also been concluded that there exist escape frequency and cut-off frequency for the wave propagating in size-dependent materials based on the NSGT. Dispersion equation for the propagation of Rayleigh-type waves at the free surface has been derived. The effect of the nonlocal parameter, the strain gradient parameter on the Rayleigh wave propagation is considered through some numerical examples.

Low-frequency and wide bandgap seismic metamaterials for Rayleigh wave attenuation

This study introducesa seismic metamaterial (SM) for mitigating low-frequency seismic Rayleigh waves when embedded in the ground.. Dispersion curves and vibration modes of a unit cell incorporatingthe SM were calculated using the Bloch theorem and sound cone method in a numerical model. The lowest frequency of the bandgaps (BGs) is 1.6 Hz, with the maximum absolute bandwidth reaching 18 Hz, matching the seismic wave considered in this study. Furthermore, a comprehensive analysis of vibrational modes revealed the mechanism responsible for BG formation. Numerical simulations in both the time and frequency domains confirmed the attenuation of Rayleigh waves by finite models containing SMs, along with theconversion of Rayleigh waves into body waves. Additionally, the effects of material and geometric parameters on BG frequency range is discussed. Complex SM structures were devised by combining two distinct SMs with varying geometric parameters, achieving a complete broadband attenuation range. Finally, realistic seismic Rayleigh wave propagation through complex SMs was simulated, conclusively validating their effectiveness in providing broadband attenuation.

Stoneley waves in isotropic crustal rocks under the theory of generalized thermoelastic diffusion

This paper investigates the propagation of Stoneley waves through bonded and unbonded interfaces between two dissimilar homogeneous transversely isotropic generalized thermo-elastic diffusion rocks. The governing equations for the current problem are obtained and are solved to determine the characteristic polynomial equations for both mediums in terms of penetration depth. These equations are solved using Ferrari’s approach, and the variation in penetration depths with angular frequency and wavenumber is shown. The secular equations of the Stoneley waves are developed using proper boundary conditions and these equations have been solved numerically to determine the phase velocity and attenuation coefficients. We have discovered three modes of the Stoneley waves in thermo-diffusive crustal rocks. We have confirmed that the paths of particle motion for Stoneley waves are elliptic in nature. Some known results [Kumar et al. [2017] “Mathematical modeling of Stoneley wave in a transversely isotropic thermoelastic media”, Applications and Applied Mathematics 12(1), 319–336; Kumar and Kansal [2008b] “Propagation of Rayleigh waves on free surface of transversely isotropic generalized thermoelastic diffusion”, Applied Mathematics and Mechanics29(11), 1451–1462] are recovered from this analysis to validate our investigation.

Effect of homogeneous coated layer on periodic barrier for Rayleigh wave isolation

Ambient vibrations induced by vehicles and construction activities can caused a significant adverse impact on building safety and human health. Periodic barriers based on phononic crystals (PC) have a broad application perspective to attenuate the propagation of Rayleigh waves caused by ground vibrations. However, due to the limited size of the units, it is difficult to create an efficient bandgap for attenuating low-frequency ground vibrations. Therefore, the present work aims to develop an innovative design that can significantly increase the efficiency of periodic barriers. To achieve this goal, we proposed a one-dimensional PC consisting of Eps geofoam and soil. The surface of the PC coated with a homogeneous layer composed of soil or concrete. The band structures of the proposed periodic barriers are calculated using the plane wave expansion method. The results are verified by 2D finite element simulation. The numerical results show that the height and density of the cover layer play an important role in the formation of the bandgap. Further, influence of initial stress and Young's modulus on the bandgap is analyzed. Finally, the transmission spectrum of Rayleigh waves is calculated and the vibration reduction property is discussed. The numerical results demonstrate that the phononic crystal coated with concrete layer can improve the vibration mitigation efficiency. This work could provide an interesting solution for periodic barriers made up of smaller numbers of elements.

Effects of surface topography and subsurface structural irregularities of river embankments on Rayleigh wave propagation

A numerical investigation of surface wave propagation in the surface wave exploration of river embankments is implemented using 3D shallow soil models with different subsurface shapes and S-wave velocities. The focus is on the effects of surface and subsurface irregularities on the propagation and dispersion characteristics of Rayleigh waves generated by a surface source and observed at points along the crest of the embankment. Rayleigh wave dispersion curves observed along the embankment crest are found to be contaminated by reflected waves, with the amount of contamination affected more by the position of the velocity boundary at the bottom edge of the embankment than the surface topography. When the velocity boundary is close to the ground surface, especially at the toe of the slope, the effect of reflected waves is sufficiently large to generate biases in the phase velocity estimates.Graphical

Effect of SiO2 protective layer on LiNbO3 structured SAW resonators and temperature characteristics study

In this paper, using LiNbO3 as the piezoelectric substrate, Pt as the electrode and SiO2 as the protective layer, a multi-physics field coupled finite element model was used to investigate the effect of the protective layer thickness on the Rayleigh wave propagation characteristics, and the relationship between the protective layer thickness and the frequency–temperature coefficient TCF and electromechanical coupling coefficient K 2 is established. The frequency characteristics of the device and the microscopic changes of the electrode and substrate structures under high temperature were analyzed experimentally. The results show that no acoustic mode shift occurs when the normalized thickness is less than 31.25%. As the thickness of the protective layer increases, the vibration displacement in the direction of L wave, SH wave and SV wave decreases, and the thickness of the protective layer can be increased appropriately to reduce the interference of SH wave to Rayleigh wave; |TCF| decreases with increasing thickness of the protective layer. Changes in the thickness of the protective layer at different temperatures lead to fluctuations in K 2; the protective layer structure leads to a slight decrease in Q value. As the temperature increases, the fluctuation of the resonant frequency of the SAW resonator increases. The SiO2 protective layer can effectively protect LiNbO3 materials while improving the high-temperature working stability of Pt electrodes.