Elastic Surface Waves Research Articles

Localization of elastic surface waves based on defect modes in non-Bragg structures

Abstract The non-Bragg defect mode (NBDM) of elastic surface waves is experimentally investigated by inserting a defect in the middle of an antisymmetric periodic corrugated aluminum plate, which has been known as the non-Bragg structures since the observed band gaps are different from the traditional Bragg ones. Generally, the non-Bragg band gaps, existing away from the Bragg ones in a perfectly periodic waveguide, are created by the resonances of different transverse guided modes. The transmission spectra of elastic surface waves in antisymmetric structures with defects reveal the presence of defect modes within the non-Bragg gaps. Notably, the NBDM exhibits significant distribution characteristics in comparison to the traditional Bragg defect mode, including more complex elastic wave higher-order modes and localized wave energy near the defect. Consequently, the NBDM observed in the antisymmetric periodic waveguide with defects holds potential for utilization in other elastic wave functional devices, including filters and wave intensifiers.

Soil moisture estimation in the unsaturated zone using surface wave measurements and hybrid modeling framework

Abstract Soil moisture plays a critical role in influencing various facets of ecosystem dynamics. The preference for measuring soil moisture without physical intrusion has been desirable for precise assessments while minimizing disruptions to soil structural, hydraulic, and biological characteristics. In this study, we explored the potential of surface elastic waves as a proxy to estimate soil moisture profiles to a depth of 1.05 m at intervals of 0.1 m. We conducted a multichannel analysis of surface waves (MASW) survey and measured soil moisture at depths of 0.15 m and 0.35 m. To address the limited availability of soil moisture measurements, we developed a mechanistic soil moisture model as a substitute for measured soil moisture profiles. Our results showed that as soil moisture increased, the propagation of surface waves became more pronounced due to reduced frictional resistance. However, it was not straightforward to link measured surface wave responses and subsurface soil moisture profile. To address these challenges, we developed a convolutional neural network (CNN) with the inputs of the frequency-velocity and frequency-wavenumber images obtained from the measured surface waves. We found that the integration of MASW and CNN proved effective in estimating soil moisture profiles to a depth of 1.05 m at intervals of 0.1 m without causing disturbances to the soil (MAE = 0.0035 m3 m−3). This study suggested that the combined use of surface waves and CNN hold promise in measuring soil moisture profiles without physical disruptions. As such, the proposed approach could serve as a viable alternative to noninvasive soil moisture sensors.

Revealing regional variations in scleral shear modulus in a rabbit eye model using multi-directional ultrasound optical coherence elastography

The mechanical properties of the sclera play a critical role in supporting the ocular structure and maintaining its shape. However, non-invasive measurements to quantify scleral biomechanics remain challenging. Recently introduced multi-directional optical coherence elastography (OCE) combined with an air-coupled ultrasound transducer for excitation of elastic surface waves was used to estimate phase speed and shear modulus in ex vivo rabbit globes (n = 7). The scleral phase speed (12.1 ± 3.2 m/s) was directional-dependent and higher than for corneal tissue (5.9 ± 1.4 m/s). In the tested locations, the sclera proved to be more anisotropic than the cornea by a factor of 11 in the maximum of modified planar anisotropy coefficient. The scleral shear moduli, estimated using a modified Rayleigh-Lamb wave model, showed significantly higher values in the circumferential direction (65.4 ± 31.9 kPa) than in meridional (22.5 ± 7.2 kPa); and in the anterior zone (27.3 ± 9.3 kPa) than in the posterior zone (17.8 ± 7.4 kPa). The multi-directional scanning approach allowed both quantification and radial mapping of estimated parameters within a single measurement. The results indicate that multi-directional OCE provides a valuable non-invasive assessment of scleral tissue properties that may be useful in the development of improved ocular models, the evaluation of potential myopia treatment strategies, and disease characterization and monitoring.

Surface acoustic waves in porous soils with two-layered infiltration

Abstract Two stage mathematical and computer models based on the finite element solution of Richards’ equation for water infiltration in two-layered fluid-saturated soil and modal analysis using a semi-analytical approach for vertically stratified soils are presented and briefly described. Dispersion curves of surface waves in the layered poroelastic half-space are computed and studied. The features of porous water infiltration effect on the characteristics of surface elastic waves are discussed.

Velocimetry of GHz elastic surface waves in quartz and fused silica based on full-field imaging of pump–probe reflectometry

This study reports an imaging method for gigahertz surface acoustic waves in transparent layers using infrared subpicosecond laser pulses in the ablation regime and an optical pump–probe technique. The reflectivity modulations due to the photoelastic effect of generated multimodal surface acoustic waves were imaged by an sCMOS camera illuminated by the time-delayed, frequency-doubled probe pulses. Moving the delay time between 6.0nsto11.5ns, image stacks of wave field propagation were created.Two representative samples were investigated: wafers of isotropic fused silica and anisotropic x-cut quartz. Rayleigh (SAW) and longitudinal dominant high-velocity pseudo-surface acoustic wave (HVPSAW) modes could be observed and tracked along a circular grid around the excitation center, allowing the extraction of angular profiles of the propagation velocity. In quartz, the folding of a PSAW was observed. A finite element simulation was developed to predict the measurement results. The simulation and measurement were in good agreement with a relative error of 2% to 5%.These results show the potential for fast and full-field imaging of laser-generated ultrasonic surface wave modes, which can be utilized for the characterization of thin transparent samples such as semiconductor wafers or optical crystals in the gigahertz frequency range.

Elastic surface wave attenuation in layered soil by metastructures

AbstractSeismic metastructures are able to effectively attenuate or convert elastic surface waves, attracting increasing attention in different areas such as civil engineering. However, the effects of the source depth and layered characteristics of viscous soil on metastructures for elastic surface wave reduction with Bragg bandgap mechanism remain challenging, which are the key issues for practical applications. In this work, we calculate the dispersion and transmission of metastructures in layered soil and confirm that the metastructures can effectively attenuate the elastic surface waves within the bandgaps. Then, the influence of the embedded depth of the metastructures, the depth of the vibrating source, layered characteristics of viscous soil on the surface vibration reduction are further discussed. It is found that surface vibration attenuation is enhanced by increasing the embedded depth of the metastructures and the density of the first layer. The width of the bandgap increases with the introduction of soil viscosity. On the contrary, the surface vibration attenuation decreases if the vibrating source is placed at a certain depth which requires the bandgap of bulk waves of the metastructures. This study of the seismic metastructures in layered soil provides a guidance in surface vibration reduction in practice.

Mathematical Analysis on Dispersion Relation of Rayleigh Wave for an Initially Stressed Magneto-Poroelastic Material with Corrugated and Impedance Boundary

This study showcases the Mathematical modelling of elastic surface waves and the analysis of dispersion relations of Rayleigh-type of wave in an initially stressed homogeneous porous magneto-elastic material having corrugated and impedance boundary exhibitions. Adoption of the classical harmonic method of wave analysis, non-dimensionalization of the resulting equations of motion, and corrugated-impedance boundary conditions produced by the modeled problem are also captured. The dispersion equation was analytically and graphically presented. Effects of the contributing physical quantities, such as impedance and corrugated boundary parameters, on Rayleigh waves for the chosen material are analyzed. The magnetic field’s influences and the wavenumber associated with the corrugated boundary surfaces on the material increase the dispersion relations of the Rayleigh wave profile on the material. In addition, we noted that the dispersion relations of the wave increases for increasing phase velocity and some parameters of voids. Also, a void parameter triggered a decrease on the dispersion profile of the Rayleigh wave when increased while noting some uniform exhibitions from other voids coefficients. This work holds the potential to provide more insights into studies involving displacement distributions in earthquake sciences, stress-strain analysis in Structural Engineering materials, among others.

Определение диэлектрических свойств воды в тонком слое

A technique is proposed for determining the dielectric properties of water in a nanoscale layer at frequencies corresponding to orientation polarization. The method is based on the registration of the change in the velocity of elastic surface waves resulting from the interaction with a thin layer of a liquid. It was assumed that the dispersion of the dielectric permittivity of water in the thin layer is described by the Debye's equations of dielectric relaxation. In order to demonstrate the capabilities of the proposed method, the values of the real part of the dielectric permittivity of adsorbed water at various frequencies f (43.2; 64.8; 108; 129.6, 194.4, 302.4, 388.8 MHz) were experimentally determined at a fixed thickness of the adsorption layer h (2.2; 2.8; 3.7; 13 nm). The determination of the value of the imaginary part of the dielectric permittivity as well as the calculation of the time of dielectric relaxation, static, and high-frequency dielectric permittivities was enabled by the use of the experimental values and Debye's equations. A comparison was made between the dielectric properties of adsorbed water and those of water in the bulk liquid phase. The high-frequency dielectric permittivity of adsorbed water was found to be lower than that of water in the bulk liquid phase, while the static dielectric permittivity was significantly higher. The dielectric relaxation time of adsorbed water is dependent on the thickness of the adsorption layer and is significantly longer than that of water in the bulk liquid phase.

Formation Model for Acoustic Characteristics of Solid Media with Ordered Fracturing

Introduction. The development of new structural materials and improvement of existing technologies for the production of new products on their basis lead to the emergence of new types of medium discontinuities. Therefore, the development of new models of discontinuities that take the previously ignored parameters into account seems to be relevant for the purposes of nondestructive testing and structural measurements. This concerns, e.g., the roughness of adjacent surfaces of microcrack ordered sets.Aim. Theoretical substantiation for the processes of elastic waves propagation through an elastic medium containing an ordered lattice of microcracks with boundary conditions in the linear slip approximation, modified by taking into account the parameters of micro-convexities of microcrack rough boundaries. Database formation for experimental studies aimed at determining the physical and mechanical characteristics of structural materials.Materials and methods. The acoustic characteristics of materials were determined based on the derivation and solutions of dispersion equations describing the formation and propagation of effective longitudinal, transverse, and Rayleigh surface elastic waves in elastic media with ordered cracking. Their values were also used to determine the effective speed of Rayleigh surface waves.Results. The conducted simulation of elastic wave formation processes showed that an increase in the concentration of microcracks leads to a decrease in the phase velocities of effective longitudinal, transverse, and surface waves, as well as to an increase in the attenuation coefficients at given ultrasound frequencies and material parameters.Conclusion. The radius of the microsphere that replaces the surface micro-convexity and the roughness parameter Rz have a significant impact on the formation of physical and mechanical characteristics of materials, which are determined by the results of ultrasonic measurements. The developed model can be recommended as a basis for interpreting the results of ultrasonic measurements.

New Shear Horizontal (SH) Surface-Plasmon-Polariton-like Elastic Surface Waves for Sensing Applications.

The advent of elastic metamaterials at the beginning of the 21st century opened new venues and possibilities for the existence of new types of elastic (ultrasonic) surface waves, which were deemed previously impossible. In fact, it is not difficult to prove that shear horizontal (SH) elastic surface waves cannot exist on the elastic half-space or at the interface between two conventional elastic half-spaces. However, in this paper we will show that SH elastic surface waves can propagate at the interface between two elastic half-spaces, providing that one of them is a metamaterial with a negative elastic compliance s44(ω). If in addition, s44(ω) changes with frequency ω as the dielectric function ε(ω) in Drude's model of metals, then the proposed SH elastic surface waves can be considered as an elastic analogue of surface plasmon polariton (SPP) electromagnetic waves, propagating at a metal-dielectric interface. Due to inherent similarities between the proposed SH elastic surface waves and SPP electromagnetic waves, the new results developed in this paper can be readily transferred into the SPP domain and vice versa. The proposed new SH elastic surface waves are characterized by a strong subwavelength confinement of energy in the vicinity of the guiding interface; therefore, they can potentially be used in subwavelength ultrasonic imaging, superlensing, and/or acoustic (ultrasonic) sensors with extremely high mass sensitivity.

A Note on Counting the Multiplicities of Elastic Surface Waves Using Weyl’s Law

A Note on Counting the Multiplicities of Elastic Surface Waves Using Weyl’s Law

Attenuation of Rayleigh and pseudo surface waves in saturated soil by seismic metamaterials

Seismic metamaterials have received extensive research interest due to their bandgap properties, simplicity in design principles, and stability in response. They have been developed to protect buildings or architectures susceptible to damage from surface elastic waves. In practice, the ground soil is generally a multiphase medium, and the influence of its permeability and viscosity on seismic metamaterials is not yet clear. In this work, we developed a formulation that combines Biot’s theory and Bloch-Floquet theorem to investigate the complex band structures and transmission properties of Rayleigh and pseudo surface waves (PSWs) for pillared and inclusion-embedded seismic metamaterials in saturated soil. It is shown that the ratio of fluid viscosity and permeability η/κ have an impact on the surface wave attenuation and the performances of seismic metamaterials, where the smaller ratio benefits the surface wave broadband attenuation and metamaterials attenuating effects. The complex band structures reveal that inclusion-embedded metamaterials can support the propagation of PSWs having a phase velocity higher than that of the transverse bulk waves. The PSWs are significantly affected by the rubber viscosity due to the mode displacements concentrated in the rubber coatings. The higher viscosity of metamaterials also allows for broadband attenuation of Rayleigh surface waves. The results of this study will present an appropriate way to design viscoelastic seismic metamaterials in saturated soil for low-frequency surface wave attenuation.

Hybrid Spin and Anomalous Spin-Momentum Locking in Surface Elastic Waves.

Transverse spin of surface waves is a universal phenomenon which has recently attracted significant attention in optics and acoustics. It appears in gravity water waves, surface plasmon polaritons, surface acoustic waves, and exhibits remarkable intrinsic spin-momentum locking, which has found useful applications for efficient spin-direction couplers. Here we demonstrate, both theoretically and experimentally, that the transverse spin of surface elastic (Rayleigh) waves has an anomalous sign near the surface, opposite to that in the case of electromagnetic, sound, or water surface waves. This anomalous sign appears due to the hybrid (neither transverse nor longitudinal) nature of elastic surface waves. Furthermore, we show that this sign anomaly can be employed for the selective spin-controlled excitation of symmetric and antisymmetric Lamb modes propagating in opposite directions in an elastic plate. Our results pave the way for spin-controlled manipulation of elastic waves and can be important for a variety of areas, from phononic spin-based devices to seismic waves.

Smart patterning for topological pumping of elastic surface waves.

Topological pumping allows waves to navigate a sample undisturbed by disorders and defects. We demonstrate this phenomenon with elastic surface waves by strategically patterning an elastic surface to create a synthetic dimension. The surface is decorated with arrays of resonating pillars that are connected by spatially slow-varying coupling bridges and support eigenmodes located below the sound cone. We establish a connection between the collective dynamics of the pillars and that of electrons in a magnetic field by developing a tight-binding model and a WKB (Wentzel-Kramers-Brillouin) analysis. This enables us to predict the topological pumping pattern, which we validate through numerical and experimental steering of waves from one edge to the other. Furthermore, we observe the immune nature of the topologically pumped surface waves to disorder and defects. The combination of surface patterning and WKB analysis provides a versatile platform for controlling surface waves and exploring topological matter in higher dimensions.

Backscattering enhancements by partially exposed cylindrical shells due to reflected flexural waves at air–water interfaces

For smooth curved objects in contact with a flat interface, the propagation paths of supported surface elastic waves can be altered by the interface, thereby enhancing the characteristics of the backscattered echo returns. In this study, backscattering experiments are conducted on an empty stainless steel cylindrical shell that breaks through an air–water interface and is insonified from below at grazing incidence. The shell has a thickness-to-radius ratio of 5%. The frequencies of interest fall within the vicinity of and below the coincidence frequency, which corresponds to a ka range of 13.8–20.1. The experimental results demonstrate that, for the partially exposed cylindrical shell, the flexural waves can traverse the interface and circumnavigate the shell multiple times. The flexural waves experience mode transitions upon passing through the interface, existing as a0− waves below the interface and a0 waves above the interface. Simultaneously, the flexural waves undergo partial reflection each time they pass through the interface, guiding them to follow a reverse path and generating a periodic series of echo returns, which leads to the enhancement of backscattering. The shift in resonance frequency in relation to the changing exposure is analyzed and predicted using the phase matching theory.

Dispersion of surface elastic waves on Z-LiNbO3 films on Z-sapphire

Epitaxial thin films of lithium niobate with a thickness of 160 nm, oriented along the crystallographic c axis, were grown by direct liquid injection chemical vapor deposition on c-sapphire substrates. Different families of very high-frequency surface acoustic waves with general polarization exist in such piezoelectric films on high-velocity substrates. Surface Brillouin light scattering measurements, complemented with fast finite element analysis of wave dispersion, demonstrate Rayleigh, leaky shear, and leaky longitudinal surface waves, excited at frequencies between 10 and 30 GHz. The Brillouin technique reveals dispersion and anisotropy of propagation without the implementation of high-frequency surface acoustic wave transducers.

The lens capsule significantly affects the viscoelastic properties of the lens as quantified by optical coherence elastography.

The crystalline lens is a transparent, biconvex structure that has its curvature and refractive power modulated to focus light onto the retina. This intrinsic morphological adjustment of the lens to fulfill changing visual demands is achieved by the coordinated interaction between the lens and its suspension system, which includes the lens capsule. Thus, characterizing the influence of the lens capsule on the whole lens's biomechanical properties is important for understanding the physiological process of accommodation and early diagnosis and treatment of lenticular diseases. In this study, we assessed the viscoelastic properties of the lens using phase-sensitive optical coherence elastography (PhS-OCE) coupled with acoustic radiation force (ARF) excitation. The elastic wave propagation induced by ARF excitation, which was focused on the surface of the lens, was tracked with phase-sensitive optical coherence tomography. Experiments were conducted on eight freshly excised porcine lenses before and after the capsular bag was dissected away. Results showed that the group velocity of the surface elastic wave, , in the lens with the capsule intact ( ) was significantly higher (p < 0.001) than after the capsule was removed ( ). Similarly, the viscoelastic assessment using a model that utilizes the dispersion of a surface wave showed that both Young's modulus, E, and shear viscosity coefficient, η, of the encapsulated lens ( ) were significantly higher than that of the decapsulated lens ( ). These findings, together with the geometrical change upon removal of the capsule, indicate that the capsule plays a critical role in determining the viscoelastic properties of the crystalline lens.

The dual mechanism underlying laser excitation of bulk and surface elastic waves in ablative regime

It is usually considered that plasma pressure impulse is the only mechanism corresponding to the laser excitation of bulk and elastic surface waves in an ablative regime. We report the first observation of a dual mechanism where the laser-induced shockwave impacts the target and generates secondary bulk and surface elastic waves some dozens of nanoseconds after the primary ones are generated by the plasma pressure impulse. We propose that the superimposing of the two wave groups can cause additional frequency components that should be considered in research and applications employing elastic waves generated by strong laser ablation.

Ultrasonic diagnostics in the study of coatings applied by gas-flame spraying

The quality control of coatings when selecting a powder material for the restoration of worn surfaces by gas-flame spraying is hampered by the lack of an operational method of non-destructive diagnostics. We present the results of studying coatings applied by gas-flame spraying using ultrasonic diagnostics. The powder coatings obtained using different technologies of gas-flame spraying were studied. Features of the structural state of coatings were evaluated using a model based on the effect of the structural inhomogeneities of the coating on the velocity and attenuation of ultrasonic waves. It is shown that the amplitude-time characteristics of the pulse of surface elastic waves when they pass along the coating are consistent with the data obtained from friction and hardness tests, the characteristics of the pulse being dependent on the quality of the coating material. The obtained results can be used to improve the quality control of coatings formed by gas-flame spraying.

Joint estimation ofS-wave velocity and damping ratio of the near-surface from active Rayleigh wave surveys processed with a wavefield decomposition approach

SUMMARYThe use of surface wave measurements to derive an S-wave velocity profile of the subsurface has become a widely applied procedure; however, their potential use to reconstruct the S-wave material damping properties of the subsoil is generally overlooked, due to the difficulties in obtaining consistent surface wave amplitude information from field data and translating them into robust estimates of the dissipative properties of the near-surface. In this work, we adapt a wavefield decomposition technique for the processing of elastic surface wave data to the extraction of the complete set of properties of Rayleigh waves generated by a controlled source and propagating in dissipative geomaterials. Retrieved information includes multimodal phase velocity and ellipticity as well as the frequency-dependent attenuation coefficient. We exploit the key advantages of wavefield decomposition processing (joint interpretation of multicomponent recordings, coupled estimation of wave propagation parameters, modelling of multiple superimposing modes) to maximize the robustness of the retrieval of Rayleigh wave properties, especially of the dissipative ones. For the subsequent interpretation of Rayleigh wave dispersion, ellipticity and attenuation data we implement a joint Monte Carlo inversion yielding a coupled estimate of S-wave velocity and damping ratio profile for the subsurface; we incorporate a series of geophysical constraints to narrow down the searched parameter space to realistic soil models. We apply this processing and inversion scheme to a bespoke synthetic data set and to a field survey for the characterization of a strong motion station; in both cases, we succeed in retrieving Rayleigh wave multimodal dispersion, ellipticity and attenuation curves. From the inversion of data from the simulated seismogram we are able to reconstruct the properties of the synthetic model. As for the real case, we determine an S-wave velocity and damping ratio model for the soil column below the station, through which we are able to model the inelastic earthquake local response observed at the site. Basing on the results obtained for the real case, we argue that one of the advantages brought by our processing method—the possibility to process active Rayleigh wave data acquired by a 2-D array illuminated by different source positions—may play a key role in allowing to retrieve dissipative properties of the near-surface closer to the material damping of the soil materials, and less influenced by scattering determined by possible discontinuities in the subsurface.