Wave Dispersion Research Articles

Mechanical metastructure with embedded phononic crystal for flexural wave attenuation

Destructive interference-based metamaterials have shown excellent characteristics in elastic wave manipulation and vibration attenuation. Nevertheless, challenges persist in the application due to limited space and lightweight design, as current metastructures require additional beam structure. To simplify the design of metamaterials for flexural wave manipulation, this paper presents a new class of embedded phononic crystal for manipulating flexural wave propagation in both one and two-dimensional space by taking advantage of destructive interference, which can effectively suppress the mechanical vibration of a beam structure with a broad band gap. The flexural wave dispersion characteristic in a non-uniform beam structure is derived based on the Euler–Bernoulli beam theory, and an embedded phononic structure with the mechanism of destructive interference is presented to demonstrate its effectiveness in mitigating mechanical vibration. Subsequently, four typical units of embedded phononic structures are designed for attenuating flexural wave propagation in a beam structure. Finally, both numerical simulations, including one and two-dimensional phononic crystals, and physical experiments are implemented to evaluate the performance of the presented metastructure for flexural wave manipulation, which indicates that the proposed embedded phononic structures can effectively mitigate structural vibration in the low-frequency domain. To the best of our knowledge, it is the first attempt to design the metabeam with embedded phononic structures by taking advantage of destructive interference.

Rest length controlled tunable band structure in periodic tensegrity metastructure – a numerical study using a novel consistent stiffness and mass formulation

Elastic wave propagation in various periodic metastructures and its application to wave filtering, vibration isolation, acoustic cloaking, etc., have gained significant attention among researchers in recent years. Despite the presence of band gaps, traditional lattice structures lack dynamic tunability. The solution lies in using tensegrity as unit cells. This article presents analysis of tunable wave propagation through a metastructure formed by tessellation of a 2D tensegrity unit cell in one dimension. Equations of motion of the unit cell are derived with consideration of flexibility and distributed mass of the bars, which is often neglected in the literature. The formulation is extended for wave dispersion analysis using the Floquet–Bloch theory. Next, the order of the formulation is reduced for decoupled analysis of symmetric and antisymmetric modes. The dispersion relations for different modes have been validated with nonlinear as well as linearized frequency response analysis under impulse load. Next, the effect of rest length of strings and alternating arrangement of bars on band gaps is studied in detail.

Rainbow trapping of out-of-plane mechanical waves in spatially variant beam lattices

We numerically and experimentally investigate the propagation of mechanical waves in two-dimensional periodic and spatially graded elastic beam lattices. Experiments on metallic lattices admit the characterization of the linear elastic wave dispersion over a wide range of frequencies, resulting in complete, experimentally-constructed dispersion surfaces in excellent agreement with predictions obtained from finite element-based Bloch wave analysis. While Timoshenko beam theory is shown to be sufficiently accurate for predicting the lowest modes, experiments prove that solid finite elements are required to capture the dispersion relations at higher frequencies as well as when mode coupling occurs. Based on an improved numerical procedure, group velocity maps further highlight the directionality of wave dispersion and allow for the simple identification of bandgaps. In addition to classically studied periodic trusses, we extend the framework to spatially graded structures and demonstrate acoustic rainbow trapping in beam lattices undergoing out-of-plane vibrations. Our experiments confirm broadband vibration attenuation of the typical meta-wedge type previously observed only in optics and few mechanical studies. Results further show convincing agreement between Bloch theory-based predictions, finite element simulations, and experimental measurements. Such spatially-variant architected lattices show great promise for steering the motion of elastic waves in applications from wave guiding and wave shielding to energy harvesting.

Improving signal-to-noise ratios of ambient noise cross-correlation functions using local attributes

SUMMARY For seismographic stations with short acquisition duration, the signal-to-noise ratios (SNRs) of ambient noise cross-correlation functions (CCFs) are typically low, preventing us from accurately measuring surface wave dispersion curves or waveform characteristics. In addition, with noisy CCFs, it is difficult to extract relatively weak signals such as body waves. In this study, we propose to use local attributes to improve the SNRs of ambient noise CCFs, which allows us to enhance the quality of CCFs for stations with limited acquisition duration. Two local attributes: local cross-correlation and local similarity, are used in this study. The local cross-correlation allows us to extend the dimensionality of daily CCFs with computational costs similar to global cross-correlation. Taking advantage of this extended dimensionality, the local similarity is then used to measure non-stationary similarity between the extended daily CCFs with a reference trace, which enables us to design better stacking weights to enhance coherent features and attenuate incoherent background noises. Ambient noise recorded by several broad-band stations from the USArray in North Texas and Oklahoma, the Superior Province Rifting EarthScope Experiment in Minnesota and Wisconsin and a high-frequency nodal array deployed in the northern Los Angeles basin are used to demonstrate the performance of the proposed approach for improving the SNR of CCFs.

Visualization of non-linear continuous wave dispersion effects on fiber grating with spreadsheets in online learning

Spreadsheet software is a practical and straightforward computing and graphics tool. The use of Spreadsheets can reduce the risk of practicum in class and can be used remotely. This research presents a simple way to build a physics simulation based on mathematical equations in spreadsheet software. The simulation aims to visualize the effect of non-linear continuous wave dispersion on fiber gratings. Simulations can visualize different modes. The mathematical equations in fiber optics for non-linear effects are quite complex. Visualization can assist students in interpreting mathematical equations and making connections between theoretical and experimental modeling.

Crustal structure beneath the Western Dharwar Craton segment of Western Ghats: Insights from ambient noise correlation technique

The Western Ghats (WG) comprise three major tectonic blocks: the Deccan Volcanic Province (DVP), Western Dharwar Craton (WDC) and Southern Granulite Terrain (SGT) from north to south. Among these, the WDC region encompasses the oldest basement rocks, including greenstone belts and calc-alkaline plutons dating back to ∼3.0 to 3.4 Ga. While the crustal structure of the DVP and SGT segments of the WG has been extensively studied, knowledge regarding the crustal structure beneath the WDC segment of the WG is limited due to the scarcity of seismic stations. To address this gap, we utilized continuous waveform data from a newly established network of seismic stations by the National Centre for Earth Science Studies (NCESS), in addition to other available stations and deciphered the shallow crustal shear-wave velocity structure along a profile beneath the WDC segment of the WG using ambient noise cross-correlation and surface wave dispersion. The results reveal a continuous upper layer characterized by a high shear wave velocity of ∼3.6 km/s with notable variation in thickness along the profile. Furthermore, a thick middle layer with velocities reaching up to ∼3.9 km/s and a lower layer with velocities of ≥4.2 km/s are observed. Intriguingly, variations in the thickness of the upper layer, ranging from 5 km to 20 km, are noted beneath the study region. The thickness of this layer exhibits changes in relation to topographical variations, with this dependency diminishing for deeper layers. Notably, high shear wave velocity perturbations (∼10 %) are observed in the upper layer beneath low-elevation regions, possibly indicating the presence of Tonalite–Trondhjemite–Granodiorite (TTG)-type gneiss − a significant rock type in the WDC region, alongside greenstone belts and late calc-alkaline to potassic plutons. These findings suggest that the uneven topography of the WG may result from long-term erosion, exposing deeper and higher-density rocks and leading to higher shear wave velocities at shallow depths. This study serves as a foundation for further exploration into the influence of the upper crustal layer and its correlation with the evolution of the WG.

Analysis of the Circumferential Wave Dispersion of an Acoustic Signal Backscattered by a Porous Tube: Cortical Bone

Analysis of the Circumferential Wave Dispersion of an Acoustic Signal Backscattered by a Porous Tube: Cortical Bone

On the Origin of the Hawaiian Swell: Lithosphere and Asthenosphere Seismic Structure From Rayleigh Wave Dispersion

AbstractIn this study, we revisit the shear‐wave velocity structure of the lithosphere and asthenosphere surrounding the Hawaiian hotspot and Hawaiian swell using Rayleigh wave data spanning periods of 20–125 s from the PLUME project. A primary goal of this investigation is to probe the origin of the Hawaiian swell and the mechanism that elevates the topography, providing insights into mantle dynamics beneath hotspot swells. In the shear velocity model, the 30–70 km depth range is largely featureless with weak and local anomalies, indicating that the elevation of the Hawaiian swell cannot be attributed to upper lithospheric reheating or replacement. In contrast, at 80–150 km depth, a pronounced region of anomalously low velocities is well‐resolved, with the lowest velocities found beneath the Hawaii‐Maui‐Molokai part of the island chain. Minimum shear velocities are approximately 4.0 km/s at 100–120 km depth, which is an ∼8%‐10% velocity decrease relative to the surrounding velocities away from the swell. This pattern suggests that hot, buoyant mantle from deeper plume sources laterally spread out near the top of the normal oceanic asthenosphere. We find that the low‐velocity pattern in the asthenosphere exhibits a strong correlation with the overall shape of the Hawaiian swell topography. Assuming that density anomalies are proportional to shear velocity anomalies, we demonstrate that the anomalous elevation of the swell can be explained by the uplift of a 30‐km‐thick elastic plate loaded from below by this buoyant, low‐seismic‐velocity layer in the asthenosphere.

Azimuth correction for passive surface wave dispersion based on polarization analysis

SUMMARY Passive surface wave methods have found extensive application in near-surface investigation due to their benefits of low costs, non-invasiveness and high accuracy. Linear arrays are usually adopted in urban environments for their convenience and efficiency. However, the distribution of noise sources in densely populated urban areas varies rapidly in time and space, making it challenging to estimate accurate dispersion spectra using a linear array. To solve this problem, we propose a polarization analysis-based azimuthal correction method. We first obtain the azimuth of each segment by calculating the correlation coefficient of three-component ambient noise data. The normalized correlation coefficient is then applied for quality control to select reliable segments. For selected segments, the overestimated velocity caused by directional sources are corrected to obtain accurate dispersion spectra. A synthetic test is conducted to demonstrate the feasibility of our method. Compared with the dispersion spectra obtained without any correction, the dispersion spectra obtained following the suggested scheme are more consistent with the theoretical dispersion curves. Two real-world examples at crossroads show the superiority of the proposed technique in obtaining higher resolution dispersion energy and more accurate phase velocities. In addition, our approach can attenuate the artefacts and improve the dispersion measurements.

Peregrine solitons and resonant radiation in cubic and quadratic media.

We present the fascinating phenomena of resonant radiation emitted by transient rogue waves in cubic and quadratic nonlinear media, particularly those shed from Peregrine solitons, one of the main wavepackets used today to model real-world rogue waves. In cubic media, it turns out that the emission of radiation from a Peregrine soliton can be attributed to the presence of higher-order dispersion, but is affected by the intrinsic local longitudinal variation of the soliton wavenumber. In quadratic media, we reveal that a two-color Peregrine rogue wave can resonantly radiate dispersive waves even in the absence of higher-order dispersion, subjected to a phase-matching mechanism that involves the second-harmonic wave, and to a concomitant difference-frequency generation process. In both cubic and quadratic media, we provide simple analytic criteria for calculating the radiated frequencies in terms of material parameters, showing excellent agreement with numerical simulations.

On the Applicability of Kramers–Kronig Dispersion Relations to Guided and Surface Waves

In unbounded media, the acoustic attenuation as function of frequency is related to the frequency-dependent sound velocity (dispersion) via Kramers–Kronig dispersion relations. These relations are fundamentally important for better understanding of the nature of attenuation and dispersion and as a tool in physical acoustics measurements, where they can be used for control purposes. However, physical acoustic measurements are frequently carried out not in unbounded media but in acoustic waveguides, e.g., inside liquid-filled pipes. Surface acoustic waves are also often used for physical acoustics measurements. In the present work, the applicability of Kramers–Kronig relations to guided and surface waves is investigated using the approach based on the theory of functions of complex variables. It is demonstrated that Kramers–Kronig relations have limited applicability to guided and surface waves. In particular, they are not applicable to waves propagating in waveguides characterised by the possibility of wave energy leakage from the waveguides into the surrounding medium. For waveguides without leakages, e.g., those formed by rigid walls, Kramers–Kronig relations remain valid for both ideal and viscous liquids. Examples of numerical calculations of wave dispersion and attenuation using Kramers–Kronig relations, where applicable, are presented for unbounded media and for waveguides formed by two rigid walls.

Study of P wave dispersion in patients with paroxysmal atrial fibrillation and its role in prediction of atrial fibrillation recurrence

BackgroundIt has been known that increased P wave duration and P wave dispersion reflect prolongation of intra-atrial and interatrial conduction time and the inhomogeneous propagation of sinus impulses, which are well-known electrophysiologic characteristics in patients with atrial arrhythmias and especially paroxysmal atrial fibrillation. The objective of this study was assessment of P wave dispersion value in cases with paroxysmal atrial fibrillation and its role in predicting recurrence.ResultsForty-eight patients with documented paroxysmal AF were subjected to clinical evaluation, electrocardiogram and routine Doppler echocardiogram. We found that a statistically significant association was detected between P wave dispersion and older age, diabetic and hypertensive cases with positive correlation also detected with left atrial dimension (LAD), left ventricle size and diastolic dysfunction grade. Mean corrected P wave dispersion and corrected QT interval were higher among cases using sotalol, ca channel blockers, among cases using nitrates and among cases with Morris index > 0.04. Higher mean value of corrected QT was associated with biphasic P v1 shape. Old age, female sex, P wave dispersion and QT wave dispersion are statistically significant predictors of PAF recurrence.ConclusionP wave dispersion in patients with paroxysmal atrial fibrillation was strongly correlated to older age, diabetic and hypertensive patients and also with left atrial dimension (LAD), left ventricle size and diastolic dysfunction grade. Also, mean corrected P wave dispersion can predict atrial fibrillation recurrence in patients with Morris index > 0.04, old age, female sex, and QT wave dispersion.

Effect of nonlocality on the dispersion relations of mechanical metamaterials

The advent of mechanical metamaterials, with their unconventional and programmable properties, has revolutionised the field of engineering across length scales. Their design remains an area of interest to researchers requiring careful analysis of unit cells so as to achieve desired mechanical and wave dispersion behaviour. While metamaterials are known to extract their unique properties from the internal geometry of the unit cells, the contributions of the constituent materials are typically accounted for via their local material properties in the form of Young’s modulus and Poisson’s ratio. In this article, we demonstrate that material nonlocality of the constituents can also play a crucial role in modulating the nontrivial properties of metamaterials. Such nonlocality can arise from various sources, such as finer scale inhomogeneity like defects, inclusions etc. Towards this, we propose a nonlocal continuum model by upscaling a discrete potential through a stochastic gradient estimator (SGE) interpreted herein as a generalised Cauchy–Born rule. The nonlocal parameters can also be estimated from experimental data by solving an inverse problem, similar to the estimation of constitutive parameters in classical continuum mechanics. The proposed model accurately captures the dispersion behaviour at the continuum level as compared to its discrete counterpart. We further incorporate the model within the transfer matrix method to derive the dispersion relations of a metabar as a function of the constituent material nonlocality. We envisage that the present study introduces a new handle in the form of constituent material nonlocality for designing architected metamaterials with unprecedented mechanical functionalities.

A numerical investigation of longitudinal wave for thermo-acoustoelastic effects on fluid-embedded in two viscoelastic layer plates at higher temperatures

Ultrasound has become indispensable for inspecting complex structures due to its efficient propagation in both liquids and solid materials. Extensive research has been conducted across various domains, encompassing wave behavior, structural interactions, material dispersion due to heterogeneity, propagation characteristics near boundaries, defect detection, and signal processing. In this context, longitudinal waves are particularly favored for examining thick components exhibiting surface defects or thermal gradients across their depth. In our current work, we employed a numerical approach based on the Transfer Matrix Method (TMM) to model ultrasound signals backscattered under normal incidence by a multilayer structure immersed in water. This method involves representing each layer using a quadrupole formalism that combines stresses and velocities. Simultaneously, we harnessed the thermodynamic equation for aqueous solutions and Fourier’s law to derive the expression for the thermo-acoustic coefficient of longitudinal waves within a fluid embedded between two parallel immersed plates, enabling precise control of the fluid temperature over a range from 0 °C to 700 °C. In the time domain, we evaluated the ultrasonic parameters of a fluid exposed to a temperature range from 0 to 700 °C. This evaluation was supported by a variety of multilayer structures designed to ensure the accurate processing of backscattered signals. These structures were excited by longitudinal waves, with a central frequency fixed at 5 MHz. The results obtained emphasize the sensitivity of longitudinal waves to temperature variations and reveal the presence of wave dispersion induced by temperature fluctuations. In order to investigate this dispersion, we conducted an extensive study of ultrasonic longitudinal wave propagation across a range of excitation frequencies from 2 to 12 MHz. This study encompassed the calculation of phase and group velocities, as well as the corresponding attenuation. The results confirm the relevance of our research to various applications and highlight the complex interaction between longitudinal wave dispersion and temperature variations.

Investigation of phonons and magnons in [Ni80Fe20/Au/Co/Au] N multilayers

The interaction between phonons and magnons is a rapidly developing area of research, particularly in the field of acoustic spintronics. To discuss this interaction, it is necessary to observe two different waves (acoustic and spin waves) with the same frequency and wavelength. In the Ni80Fe20/Au/Co/Au system deposited on a silicon substrate, we observe the interaction between spin waves and surface acoustic waves using Brillouin light scattering spectroscopy. As a result, we can selectively control (activate or deactivate) the magnetoelastic interaction between the fundamental spin wave mode and surface acoustic waves. This is achieved by adjusting the magnetostrictive layer thickness in the multilayer. We demonstrate that by adjusting the number of layers in a multilayer structure, it is possible to precisely control the dispersion of surface acoustic waves while having minimal impact on the fundamental spin wave mode.

Two Effective Degrees of Freedom Can Represent the Dominant Features of Global Rayleigh Wave Dispersion Maps

AbstractObjectively exploring global variations in crust and upper mantle structure helps constrain fundamental aspects of Earth's plate tectonic and convective processes. Here we adopted a Variational Auto‐Encoder to explore the degrees of freedom of global Rayleigh wave dispersion maps at 4–40 mHz. We found that two latent variables sufficiently represent the global variations, suggesting inherent coupling between crustal and mantle seismic properties. We propose that the two extracted latent variables mostly correspond with crustal thickness and upper mantle thermal structure. The first variable shows low values for continental mountain belts and ocean spreading ridges, contrasted by high values for abyssal plains. The second variable shows low values for most oceanic lithosphere and Phanerozoic continental areas, contrasted by high values for Archean cratons. Latent space correlations indicate that continental lithosphere has more strongly coupled depth features than beneath the oceans, which might be a consequence of its longevity.

A generalized peridynamic material correspondence formulation using non-spherical influence functions

Peridynamics theory is a nonlocal continuum mechanics theory. The peridynamic material correspondence formulation provides passage for direct incorporation of any material constitutive models from the classical local continuum mechanics theory. The performance of the material correspondence formulation heavily relies on the influence function whose currently used form is spherical and depends only on the bond length. Together with the way how the nonlocal deformation gradient is constructed based on the material point horizon, this results in the well-known issue of material instability in the conventional peridynamic material correspondence formulation. In this paper, a generalized peridynamic material correspondence formulation that enables use both spherical and non-spherical influence functions is developed. A recently proposed class of parameterized non-spherical influence functions that depend on both the bond length and bond direction is used in the generalized formulation. Numerical examples including wave dispersion, small and finite deformation and linear elastic fracture analyses are studied to check the material stability, convergence characteristic, prediction accuracy and applicability to fracture problems without singularity issue of the proposed formulation. It is found that the proposed formulation is inherently stable, possesses linear convergence rate, yields highly accurate predictions for both small and finite deformation problems, and small horizon can be used to improve computational efficiency.

Forward modeling of quake’s infrasound recorded in the stratosphere on board balloon platforms

Acoustic waves generated by seismic waves contain information on the internal structure of planets, and can be sensed by pressure sensors onboard high-altitude balloons. To identify the various contributions (infrasound signal, noise, balloon response, etc.) in such pressure records, a full waveform modeling is implemented and completed by infrasound ray tracing and additional data analysis. Here, we analyze the Stratéole-2 pressure data associated with two earthquakes (Garcia et al. Geophys. Res. Lett. 49(15):e98844, 2022) and compared these to full waveform simulations by SPECFEM2D-DG-LNS software. Even if our simulations do not precisely reproduce the waveform observed in the frequency range [0.05, 0.3] Hz, we show that the waveform presents more sensitivity to quake and internal structure parameters than to atmospheric structure, and that seismic surface wave dispersion is observed in balloon pressure records. The long-duration pressure oscillations observed after the main infrasonic signal cannot be fully reproduced by our one-dimensional input model even when source time function complexity and aftershocks are considered. These features are ascribed mainly to the complex vertical ground movements below the balloon and partly to late secondary infrasound arrivals excited by the interactions of seismic waves with the topography. These results enhance the advantages and limitations of quake-related infrasound observations on board terrestrial and planetary balloon platforms.Graphical

The single-phase solution and Whitham modulation equations of the defocusing self-induced transparency system

Under investigation in this paper is the defocusing self-induced transparency system which can describe propagation characters of short pulses in Erbium doped fibers with a two-level medium. The single-phase periodic solution and Whitham modulation equations will be derived via finite-gap integration method and Whitham modulation theory. In addition, the oscillatory structure of dispersive shock waves will be constructed and analyzed.

Controllable multi-soliton spectral tunneling by airy pulses in photonic crystal fiber

A straightforward method to induce tunable multi-soliton spectral tunneling (SST) using a finite energy Airy pulse in a photonic crystal fiber (PCF) featuring three zero-dispersion wavelengths is proposed numerically in the paper. The study reveals that the distinctive multi-envelope structure of the Airy pulse enables the control of tunneling distances, properties, and soliton numbers through modulation of its attenuation factor and peak intensity. Notably, the SST process involving the Airy pulse generates multiple blue-shifted and red-shifted dispersion waves, along with associated trapping waves, contributing to the formation of an ultra-flat and ultra-wide supercontinuum. Furthermore, the velocity and efficiency of multi-SST can be manipulated to enhance the overall tunability of the phenomenon. The findings underscore the potential application of Airy pulse-driven SST in secure multi-frequency signal transmission and controlled supercontinuum generation, with the tunability of these processes being governed by the specific attenuation factor and peak power settings of the input Airy pulse. This work advances the understanding of multi-SST dynamics in PCFs and provides a theoretical framework for exploiting these dynamics in practical information security and optical spectrum management contexts.