Propagation Of Rayleigh Waves Research Articles

Backscattering enhancements by partially exposed spheres due to reflected subsonic Rayleigh waves at air-water interfaces.

Air-water interfaces can enable distinct target scattering mechanisms different from the mechanism under free field conditions. In this study, backscattering experiments are performed by lowering an acrylic or polymethylmethacrylate sphere through the air-water interface into the water and insonifying the sphere from below at grazing incidence. Pronounced backscattering enhancements associated with the subsonic Rayleigh wave propagation mechanism are observed before the specular reflection point of the sphere reaches the water. The results indicate that, for a partially exposed sphere, subsonic Rayleigh waves can pass through the air-water interface and circumnavigate the sphere multiple times. The phase velocities of Rayleigh waves are different when propagating above and below the air-water interface. Moreover, subsonic Rayleigh waves are partially reflected when passing through the air-water interface, generating wavefronts that propagate in the reverse direction.

Enhanced generation and reception of ultrasonic Rayleigh waves through in-phase superposition of waves: theory and experiment

Ultrasonic Rayleigh waves have been widely used in nondestructive testing and evaluation as they are sensitive to surface anomalies and conditions of a solid body. The techniques for the generation and reception of Rayleigh waves are mainly based on empirical methods, but theoretical research on these processes can better benefit their practical applications. In this work, a specific theory using a numerical integration is proposed to model wave beam fields generated by the widely used transducers, and to explain the enhanced generation and reception of Rayleigh waves. The simulation results show that Rayleigh waves are enhanced and can be detected through in-phase superposition of waves which are generated by the real sound sources in the solid surface. The reception of Rayleigh waves is also considered, the properties of received waves are thoroughly studied and a reception method with a line source is proposed. Several experiments have been performed to verify the proposed theory, and some important properties or potential applications of corresponding or optimized transducers are discussed based on the theoretical and experimental results.

Using Passing Trains as Seismic Sources for Refraction Microtremor Site Characterisation Surveys: Rugeley, Staffordshire, UK

Microtremor seismic surveys are routinely used to provide shear wave velocities that are converted to soil stiffness site profiles. In this paper, we look to assess the feasibility of using trains as seismic sources to characterize near-surface geology, define the optimum survey parameters to collect train-induced vibrations (i.e., array location and orientation to the railway) and find how the geology affects train-induced vibration characteristics. Three-component train-induced shear wave vibrations were recorded on short (44 m) and long (115 m) linear seismic arrays, both parallel and orthogonal to the nearby railway embankment, using standard seismic refraction recording equipment. The collected data were divided into short/long array size/orientation and seismic components for each survey configuration. 1D shear wave velocity-depth profiles were also generated for all data sets. Results showed thst long linear arrays with vertical components, parallel to the railway embankment, was optimal with the greater depth ranges. The vertical component amplitude of train-induced vibrations was found to be affected by the site geology, increasing with the thickening of Quaternary deposits and having different magnitudes for trains traveling in different directions. Results showed that different apparent shear-wave velocities were obtained from different train groups and different seismic components. The passenger trains (i.e. Virgin Trains Pendolino and British Midland 319 series) generate Rayleigh waves at higher frequencies than the freight trains.

Elastographic measurements on soft biological tissues using holographic imaging by Rayleigh wave tracing

Tissue elasticity is one of the significant diagnostic parameters to study disease progression in biological tissues. Elastography measurements hold strong potential for determining the mechanical properties of malignant tissues in clinical practice. Optical methods for quantifying the elastic properties have received the attention of both research and medical community. In the current work, we calculate the elastic modulus of tissue-mimicking phantoms and ex-vivo biological tissue using holographic imaging by tracing Rayleigh wave propagation on the tissue surface. Rayleigh waves produced by the electromechanical actuator over a set of excitation frequencies are imaged by an ultrafast camera. The phase map reconstruction of the Rayleigh wave is carried out using a phase-shifting algorithm and the distance-time slope method is analyzed to compute Rayleigh wave velocities. The elastic modulus calculated by holographic imaging is validated against the gold standard mechanical compressional testing data. The quantitative results obtained from this current optical system combining holographic imaging and Rayleigh wave tracing are highly effective in ex-vivo and in-vivo tissue characterization and carry high potential as a promising tool in clinical translations and commercial adaptations.

Non-destructive testing of slab-like structures including pavements using Lamb and Rayleigh waves-based dispersion analysis

ABSTRACT Lamb and Rayleigh waves-based dispersion analysis has been carried out for non-destructive surface wave testing of different slab-like structures involving a concrete roof slab, a concrete floor, a concrete pavement, and an asphaltic pavement. An impact was generated by gently striking the slab’s free surface with a hammer. A method has also been given to generate the governing (predominant) dispersion mode in the case of Rayleigh wave propagation considering the complex nature of the dispersion function | D ( c , κ ) | ; c and κ refer to phase velocity and wavenumber, respectively. The theoretical dispersion plots generated from the inversion analysis by varying the values of different input parameters were subsequently closely matched with the corresponding obtained field dispersion images for different cases in order to back compute the elastic profile of the slab/pavement. For developing the dispersion images, the Park’s wavefield transformation method was employed. For checking the thicknesses of the different layers, cylindrical cores were also extracted. The study is expected to be useful for evaluating different slab-like structures, including pavements, by using surface wave-based non-destructive tests.

Research and application of Rayleigh wave extraction method based on microtremors signal analysis

This study investigates the method and application of single-channel, three-component microtremor signal co-directional Rayleigh surface-wave extraction. The research focuses on filtering linear polarization waves using polarizability wave and phase-difference filtering, which were analyzed based on both simulated data and real microtremor signals. Additionally, the study examines the use of time-frequency analysis to analyze microtremor signals and identify Rayleigh wave propagation direction. The combination of these methods leads to a set of procedures for extracting high-SNR co-directional Rayleigh surface waves from microtremor signals, which was applied to the elliptical polarizability imaging method. Results indicate that the proposed data processing process effectively filters linear polarization waves and accurately determines the propagation direction of the Rayleigh wave, leading to significant improvement in the accuracy of elliptical polarizability exploration results. This provides a reference for obtaining high signal-to-noise ratio data in microtremor Rayleigh wave seismic exploration.

Nonlinear Rayleigh wave propagation in a layered half-space in dual-phase-lag

We investigate nonlinear Rayleigh wave propagation in a layered thermoelastic medium composed of a slab rigidly bonded to the surface of a half-space under prescribed external thermal boundary conditions within the dual-phase-lag theory. The heat conduction coefficient for both the slab and the matrix have a linear dependence on temperature. Our aim is to assess the effect of temperature dependence of the heat conductivity, as well as the thermal relaxation times, on the process of wave propagation in the layered medium. Poincaré expansion of the solution in a small parameter and the generation of higher harmonics allow to evaluate the coefficient of this nonlinear coupling in the slab through heat wave propagation measurement. For the used numerical values, the results show that some characteristics of the problem, e.g. the temperature, heat flux and one stress component suffer jumps at the interface, while the other stress components are continuous there. The jump in the heat flux is noticeable only in the first order of nonlinearity. The existence of jumps at the interface may be of interest for measurements. Comparison with the case of the half-space showed that the presence of the slab contributes to faster damping of the solution with depth in the half-space.

Microstructure realization of a lattice-based polar solid for arbitrary elastic waveguiding

The ability to precisely directing and controlling longitudinal (P) and transverse (S) waves in 2D solids along an arbitrary trajectory has attracted significant research interest and is crucial for practical applications such as imaging, cloaking, and wave focusing. Here, we report, design and examine an inhomogeneous lattice-based polar medium for ideal elastic waveguide, whose microstructures are inversely determined by the discrete transformation elasticity (DTE). Microstructures of the suggested medium, which are realized through global linear transformation and local affine transformation, enables arbitrary waveguides to transport elastic waves with minimal energy loss. Numerical simulation is then conducted to demonstrate that the lattice-based polar waveguide can efficiently steer both in-plane P and S wave modes over a broad frequency band. We also leverage the medium for Rayleigh wave control on curved surfaces. The constructed polar surface can break the conventional limit of the Rayleigh wave propagation on both concave and convex surfaces with extreme curvatures. This study is not only a concrete manifestation of the polar material, discrete transform elasticity, and their advantages but also provides a great potential in engineering applications such as signal detection, vibration control, and earthquake protection.

Broadband Rayleigh wave attenuation utilizing an inertant seismic metamaterial

In this work, a concept of constructing inertant seismic metamaterials for Rayleigh wave attenuation using inerter-based vibration absorbers (IDVAs) is proposed. The dynamic behaviors of the vibration absorbers are controlled by an inertant mechanical network, while three typical oscillator configurations are considered in the design of the proposed inertant seismic metamaterial. An expanded effective medium method is developed to obtain the dispersion of Rayleigh waves, which is separated into three branches by two broad Rayleigh wave band gaps at low frequencies. The influences of the inertance-to-mass ratio as well as the stiffness ratio on the Rayleigh wave propagation are thoroughly discussed. The results show that the multiple-resonance IDVAs can efficiently open low frequency band gaps of the inertant seismic metamaterial without having to increase the mass of the resonators. Band gaps of the low-frequency Rayleigh waves can be further merged to form an extra wide one by adding dissipative mechanisms, which further enhance the attenuation of the Rayleigh waves. Specifically, by analyzing the corresponding displacement fields, it is observed that the seismic energy propagating as Rayleigh surface waves is converted to that propagating as bulk waves not concentrated to the surface, which offers a protected area behind the inertant seismic metamaterials for the facilities located at the surface of the half space. This work provides a new approach for seismic vibration isolations utilizing inertant seismic metamaterials that can be applied in protecting large infrastructures or civil engineering architectures.

A numerical study on effect of underground cavities on seismic ground response due to Rayleigh wave propagation

Recent studies found that some structural damage can be attributed to the effect of surface waves. A shallow underground structure may be heavily influenced by surface waves, which makes to lose energy over distance more slowly than body waves. This study deals with evaluating the effect of Rayleigh waves (R-waves) interaction with underground cavities on the seismic ground response and amplification pattern using the Finite Element Method (FEM). First, the FEM model was verified to ensure its accuracy. Then, the influences of the effective parameters, such as cavity burial depth, distance from the cavity axis, and dimensionless incident frequency were investigated. Parametric studies revealed that the amplitude of ground motion is greater in the presence of a cavity with respect to that in the free-field condition. It was indicated that shallow cavities cause more amplification than cases with a larger depth ratio. By moving away from the wave source, the response of receiver points has a declining trend. Due to the complex interaction of R-waves with a cavity, the right side of the cavity has less amplitude than the left side. Finally, by increasing the dimensionless incident frequency, the distribution of the surface displacements and wave diffraction patterns gradually becomes more complicated while the peak displacement components decrease. Consequently, in light of the importance of the R-wave interaction with subsurface spaces, the findings of this study can help improve seismic design procedures and seismic microzonation guidelines.

Correlation of the mechanical and structural properties of trabecular bone assessed by wave propagation and imaging methods

This study aimed to assess the correlation of the location- and direction-dependent mechanical and structural properties of trabecular bone using the wave propagation and imaging methods and to propose a non-invasive approach for the assessment of the quality of trabecular bone. Two bovine femur trabecular bone specimens were prepared and tested using the Rayleigh wave propagation tests and CT-scan imaging. The elastic modulus of the specimens was estimated in different regions of interest (ROIs) and wave propagation directions by the solution of the presented Rayleigh wave propagation model. The structural parameters of the specimens were also obtained via the processing of CT-scan images for all of the tested ROIs and directions. The estimated elastic modulus was in the range between 321and 1322 MPa for different ROIs and directions, showing significant heterogeneity and anisotropy of the bone specimens. The Pearson correlation and linear regression analyses were carried out between the obtained mechanical and structural properties, which revealed that the elastic modulus decreased with the trabecular separation and increased with the trabecular thickness and bone volume fraction. A semi-empirical relation was developed to obtain the elastic modulus of trabecular bone using the structural parameters obtained from imaging or vice versa.

Dispersion of Rayleigh wave in a functionally graded piezoelectric layer over elastic substrate

The Rayleigh wave propagation in a functionally graded piezoelectric layer over elastic substrate have been considered. The material gradient is taken as exponentially varying in the layer. The dispersion relation is obtained for electrically open and short cases in the form of determinant. The novelty of the current work is that the solution is obtained analytically with variable separable method approach to convert partial differential equations to ordinary differential equations and following orthodox method to get the final solution which is not considered in the existing literature. The numerical analysis of the results has been aided by the deployment of a particular model. In general, the wave number decreases as the inhomogeneity parameter rises, while the layer thickness and velocity have systemic impacts. The results have been discussed through graphs which are plotted with help of Mathematica 7. The impacts of inhomogeneity and layer thickness are taken into account. Similar characteristics can be seen in the phase shift for these parameters. The results attained can be used to enhance piezoelectric devices.

Propagation of Rayleigh Wave in Sandy Media with Imperfect Interface

In the present study, the propagation of Rayleigh wave in a sandy layer overlying a sandy semi-infinite media is investigated, with the interface considered imperfect. Expressions for displacement components are obtained. The dispersion frequency equation is derived using suitable boundary conditions. In particular cases, when interface is perfect and elastic media replace sandy media are also discussed. The effects of imperfectness and sandy parameter on the Rayleigh waves’ phase velocity are investigated using MATLAB software. The theoretical results obtained may find useful applications in geophysics, civil engineering and soil mechanics

Variation on propagation of Rayleigh waves in thermo-poroelastic solids

We analyse the dispersion and attenuation of Rayleigh-wave propagation along on isothermal free surface of a thermo-poroelastic medium. The thermo-poroelastic theory, including the Lord-Shulman (LS) and Green-Lindsay (GL) theories, predicts three compressional waves and one shear wave, which induce two Rayleigh-type surface waves, R1 and R2 modes along the interface by evanescent potential functions specified by vertical imaginary wavenumbers. The GL model can give a stronger P1 and P2 wave thermal attenuation and consequently a stronger velocity dispersion than the LS model. We investigate the influence of frequency and surface boundary condition. The additional thermal diffusion exhibits the inverse dispersion in R1 waves, and makes the pseudo surface-wave transition under the closed (CP) and partial permeable (PP) surface toward high frequencies. Another T wave affects the energy inference along the surface and induce the other R2 waves under the open surface (OP). The thermal dispersion occurs at characteristic frequencies around the thermal relaxation peaks, which induces the high-velocity T wave toward low frequencies when the Maxwell–Vernotte–Cattaneo relaxation time increases. Until the T wave propagates faster than the P2 wave, the Rayleigh equations lose the R2 poles making the prohibition of R2-wave propagation.

Effect of initial stresses on the surface wave propagation in highly anisotropic piezoelectric composite media

The present work analyses the propagation phenomenon of the Rayleigh wave in a piezoelectric-orthotropic substrate beneath a piezoelectric-orthotropic layer under the influence of initial stresses. The dispersion equations of Rayleigh wave propagation on the considered composite structure are obtained by employing suitable non-traditional boundary conditions for electrically open circuits and electrically short circuits. The data of two different PVDF materials have been considered to investigate the latent characteristics of Rayleigh wave propagation in the considered structure. Numerical calculations have been carried out to study the impact of initial stresses on the phase velocity of Rayleigh wave against wave number in all the considered directions of wave propagation for both electrical cases. A comparative study has also been carried out to unfold the impact of initial stresses in all the directions of Rayleigh wave propagation in electrical open- and short-circuit cases and manifested graphically. The obtained result is well-matched with the classical case of the Rayleigh wave for validation and is discussed as one of the problem's special cases. This study may help to improve the design of electrically generating and detecting acoustic devices.

Rayleigh and love surface waves with regard to seismic stress state of earth bed

This article presents the results of studies on the propagation of surface seismic waves, which directly affect the stability and strength of a high embankment of the subgrade. The subgrade is the foundation of the railway track. In an elastic half-space with a layer in which surface waves propagate, the conditions for the existence and propagation of a harmonic Rayleigh wave are considered. The equations of motion of a medium in a layer and half-space and their solutions in the form of plane waves propagating in phase along the contact boundary, some general laws of Rayleigh wave propagation are given. The accepted theories and calculation methods' main provisions are proposed for designing a durable and reliable subgrade and considering its seismic stress state.

Rayleigh waves in an electroelastic medium with prestressed inhomogeneous coating

An approach to studying the influence of initial mechanical stresses and an electrostatic field on the structure and behavior of Rayleigh waves in piezoelectric media with non-homogeneous coatings is proposed. The paper considers two-component coatings made of functionally graded piezoelectric material with high-speed or low-speed inclusions. The initially deformed state of the coating is induced by the separate or combined action of initial mechanical stresses and an external electrostatic field. The influence of the type of non-homogeneity and the nature of initial mechanical stresses in the presence or absence of an initial electrostatic field on the features of Rayleigh wave propagation for problems with an electrically open or shorted surface is studied. It is established that the presence of a low-intensity initial electrostatic field only slightly affects the action of initial mechanical stresses depending on its direction. The presence of a high-intensity electrostatic field leads to additional deformation of the material, significant changes in the speeds of PAV modes, and substantial changes in the structure of the surface wave field. The obtained results are presented in dimensionless parameters and may be of practical interest in the development, design, and optimization of new materials for micro- and nanoscale devices and devices on Rayleigh surface acoustic waves with high performance characteristics.

Rayleigh wave manipulation based on phase shift between two periodic surface corrugations

The propagation of Rayleigh waves along solid surfaces has attracted great attention due to its ubiquity in seismic waves, non-destructive evaluation, acoustic surface wave devices, and so on. Moreover, Rayleigh waves in periodic structures and their related band gaps caused by Bragg resonances have also been investigated. In this paper, we theoretically and experimentally demonstrate the propagation mechanism of Rayleigh waves along the side wall of a periodically corrugated aluminum plate. As expected, the band gap structures are observed in the spectrum of Rayleigh waves. However, not all the band gaps are caused by the Bragg resonances. The additional band gaps created by the interference of different transverse modes are observed. Different from the well-known Bragg resonance, the different mode interference, producing stronger energy attenuation and wider band gap, is called non-Bragg resonances. The two resonances can be manipulated by varying the phase shift of two sidewall corrugations, achieving an effective prohibition of Rayleigh wave propagation. These findings on Rayleigh wave propagation in periodic structures provide a comprehensive understanding of wave-structure interactions, which can be used to regulate elastic waves in various applications, such as multifunctional elastic wave separators, filters, and modulators.

Nonlinear Rayleigh wave propagation in thermoelastic media in dual-phase-lag.

A model of generalized thermoelasticity within dual-phase-lag is used to investigate nonlinear Rayleigh wave propagation in a half-space of a transversely isotropic elastic material. It is assumed that the coefficient of heat conduction is temperature-dependent, a fact that plays an important role in the coupling behaviour analysis of thermoelastic and piezo-thermoelastic solids. Taking such a dependence into account becomes a necessity at higher temperatures and in nano-structures, when the material properties can no longer be considered as constants. Normal mode analysis is applied to find a particular solution to the problem under consideration. A concrete case is solved under prescribed boundary conditions and tentative values of the different material coefficients. The results are discussed to reveal the effect of temperature dependence of the heat conduction coefficient, as well as the thermal relaxation times, on nonlinear Rayleigh wave propagation. All quantities of practical interest are illustrated in two-and three-dimensional plots. The presented results may be useful in the detection of the second harmonic amplitudes through measurements related to the propagating heat wave.

Laser Generated Broadband Rayleigh Waveform Evolution for Metal Additive Manufacturing Process Monitoring

This work proposes that laser pulses can generate finite amplitude Rayleigh waves for process monitoring during additive manufacturing. The noncontact process monitoring uses a pulsed laser to generate Rayleigh waves, and an adaptive laser interferometer to receive them. Experiments and models in the literature show that finite amplitude waveforms evolve with propagation distance and that shocks can even form in the in-plane particle velocity waveform. The nonlinear waveform evolution is indicative of the material nonlinearity, which is sensitive to the material microstructure, which in turn affects strength and fracture properties. The measurements are made inside a directed energy deposition additive manufacturing chamber on planar Ti-6Al-4V and IN-718 depositions. By detecting the out-of-plane particle displacement waveform, the in-plane displacement and velocity waveforms are also available. The waveform evolution can be characterized (i) for one source amplitude by reception at different points or (ii) by reception at one point by applying different source amplitudes. Sample results are provided for intentionally adjusted key process parameters: laser power, scan speed, and hatch spacing.