Wave Dispersion Research Articles

Nonlinear thermoelastic wave propagation in general FGM sandwich rectangular plates

The present work is dedicated to investigating the thermoelastic wave propagation behavior of sandwich rectangular plates (SRP) made of functionally graded material (FGM). The main contribution lies in the partial modification of basic theoretical expressions and solution methods to improve the accuracy of practical system models. An analytical model with three types of general configurations is established. The porosity distribution in FGM layers depends on the degree of mixture of the constituent materials, with the FGM layers without porosity taken as a reference model. The effect of porosity within FGMs is addressed through a refined analytical formulation of material properties, and the temperature-dependent material properties of FGM sandwich structures (FGMSS) maintain continuity through the thickness. This improved framework introduces a porosity function encompassing three distinct structural and geometrical functions: the core-to-thickness ratio (CTR), porosity volume fraction (PVF), and porosity distribution function (PDF). It is worth mentioning that the theoretical expressions maintain good continuity and reliability under the influence of thermal conditions and system parameters of the proposed structures. Furthermore, considering the generation of thermal strain energy (TSE) caused by thermal expansion of the structure in the normal direction, an improved analytical approach for determining TSE in rectangular plate structures is then investigated by introducing the Green's nonlinear strain (GNS). Hamilton's principle is applied to derive the wave motion equations and analytical solutions for the wave dispersion relations are derived. Furthermore, accurate numerical simulation is performed and the solution is verified with data available in published resources. In addition, we present a systematic parametric analysis to examine the effects of porosity, configuration, power-law exponent (PLE), PVF, CTR, temperature, and wave number on the thermoelastic wave propagation behavior of FGMSRP.

Unusually Low-frequency Whistler-mode Waves and Their Association with High-energy Protons Observed Upstream of Martian Bow Shock

Whistler-mode waves upstream of planetary bow shock are often referred to as “1-Hz waves” due to the center of their observed frequency range being at ∼1 Hz. A series of whistler-mode waves were observed upstream of the Martian bow shock by MAVEN on 2015 August 14, with unusually low frequencies centered at ∼0.4 Hz. These waves were accompanied (though not synchronized) by the significant flux enhancement of high-energy protons up to ∼10 keV. By analyzing the wave dispersion property and the wave–particle interaction condition, we find that the observed whistler-mode waves have the potential of resonating with protons of ∼1 keV with large pitch angles up to nearly perpendicular to the background magnetic field, thereby providing a feasible means of accounting for proton acceleration. Our results indicate the possible origin of energized protons in the Martian environment through the interaction with whistler-mode waves, and their potential relationship with the unique upstream conditions.

Single-step self-compression of ultrashort pulses below 20 fs by all-fiber supercontinuum generation

We present an ultrashort-pulsed laser source with time-widths as short as 20 fs at around 1.5 µm. For this purpose, the pulses have been spectrally broadened and temporarily compressed by means of supercontinuum generation in a highly nonlinear optical fiber. Inspired by numerical simulations, we have experimentally confirmed that the emission of a resonant dispersive wave is a key indicator for the optimum configuration to achieve maximum temporal compression. No dispersion control stage is needed, which results in the simplicity of the system. An extensive analysis has been made concerning the quality of the pulses obtained, particularly in terms of time-width (at half height and at 1/e height of the maximum) as well as their time-bandwidth product. The complex retrieval of the pulses shows that the smallest temporal width obtained experimentally is 17 fs. A comparison with values found in the literature also shows that our pulses are among the best that can be found with this technology.

The Correlation Between P Wave Dispersion and Left Ventricle Mass Index (LVMI) in Heart Failure Patients in H. Adam Malik Central General Hospital Medan

The Correlation Between P Wave Dispersion and Left Ventricle Mass Index (LVMI) in Heart Failure Patients in H. Adam Malik Central General Hospital Medan

Dispersion of waves propagating in the ice-covered Arctic Ocean

The Arctic Ocean was modeled as an ice–seawater–sediment system, where the ice cover and seawater were assumed to be inhomogeneous solid and liquid, respectively, while the sediment was assumed to be homogeneous liquid. Transfer matrixes relating the displacements and stresses at the lower surface and those at the upper surface for a thin solid layer, and a thin liquid layer were derived. Furthermore, a dispersion equation for waves propagating in the ice-covered Arctic Ocean was derived using the transfer matrix technique. The phase- and group-velocity dispersion curves were obtained by solving the dispersion equation numerically. The results show that the dispersion curves for the Arctic Ocean with ice cover are much more complex than those without ice cover. Except for the new mode, the phase-velocity curve for the n-th (n > 2) mode exhibited a slight distortion, which caused a sharp peak in the group-velocity curve. These peak values, which depend on the order of the mode, may be significantly higher than the speed of sound in seawater. The variation of the ice cover thickness had significant influence on the dispersion curves of the first and second modes. Moreover, the influence of the seawater depth on the dispersion curves were investigated.

Strain-induced multi-band spin-wave logic gate based on alligator-type magnonic crystal/PZT structure

Here, we report the results of strain-controlled spin-wave propagation regimes in a double-period multiferroic structure. It consists of an alligator-type magnonic crystal with a period of 250 μm and a piezoelectric layer, featuring a periodic counter-pin-type electrode system with a period of 125 μm. Employing microwave measurements, we acquired the transmission and dispersion of spin waves under various external electric field configurations applied to the piezoelectric layer. The formation of bandgaps in the magnon spectrum and the variation of the spin-wave transmission when altering the configurations of the external electric field are demonstrated. A finite element method reveals that the combination of the non-uniformity in the initial internal magnetic field of the magnonic crystal, which is caused by the presence of periodic alligator-type regions, together with elastic deformations, heightens the amplitude of the modulation of the internal magnetic field. Micromagnetic modeling has demonstrated that this modulation enhancement results in the variation of the spin-wave transmission at the frequency of the magnonic bandgap center of the magnonic crystal. The proposed design of the reconfigurable magnonic crystal creates a condition for the nucleation of the spin-wave bandgap, with further enhancement of the spin-wave reflection from the periodic grating induced by strain. We demonstrate the potential use of the proposed device as a multi-band NAND/NXOR spin-wave based logic gate.

The Effect of Glycemic Status on P Wave Dispersion.

Background and aim The growing number of people with diabetes mellitus (DM) across the world is a public health concern. The diabetes epidemic involves enormous health costs to the patients, their careers, and society at large. Cardiovascular diseases such as atrial fibrillation (AF) often develop in the diabetic population. An increase in the P wave dispersion (PWD) has been established as an independent risk factor for the occurrence of AF, hence the present study was conducted to establish a possible relationship between PWD and the glycemic status of the individualto predict the occurrence of AF ahead of clinical symptomology. Methodology A comparative cross-sectional study was conducted at a tertiary care hospital after obtaining approval from the institutional ethics committee and written consent of each study subject. The main steps included the selection and categorization of the study population based on their glycemic status, collection of demographic data, performing ECGs calculating PWD using digital calipers, and recording the data systematically for evaluation. Results In this study, 234 patients with a mean age of 53.3 ± 13.1 years were studied, of which 121 (51.7%) were maleand 113 (48.29%) were female. The 234 patients were divided into four groups based on their glycemic status - 74 uncontrolled DM patients (31.62%), 51 type 2 DM (T2DM) patients (21.78%), 56 prediabetespatients (23.93%), and 53 patients in thecontrol group (22.64%; not a known case of diabetes with normal HbA1c and fasting blood sugar (FBS) levels).Minimal correlation was observed between FBS with PWD (r value0.175)and age with PWD (r value0.161), butstatisticalsignificance was observed only between age and PWD (p-value 0.014).The difference in means between the four different study groupswas found to be not statistically significant (p-value- 0.104); hence, no intergroup variation was noted. Conclusion Advancing age and higher fasting blood sugars have shown minimal correlation with widening P-wave dispersion. With further studies involving larger populations, this can be a promising aid in identifying PWD as a probable early predictor of atrial arrhythmias among diabetic patients.

Emission of five OAM dispersive waves in dispersion-engineered double-ring core fiber

Beams carrying orbital angular momentum (OAM) have exhibited significant potential across various fields, such as metrology, image coding, and optical communications. High-performance broadband coherent OAM sources are critical to the operation of optical systems. The emission of dispersive waves facilitates the efficient transfer of energy to distant spectral domains while preserving the coherence among the generated frequency components. Light sources that maintain consistency over a wide range can increase the efficiency of optical communication systems and improve the measurement accuracy in imaging and metrology. In this work, we propose a germanium-doped double ring-core fiber for five OAM dispersive waves (DWs) generation. The OAM1,1 mode supported in the fiber exhibits three zero-dispersion wavelengths (ZDWs) located at 1275, 1720 and 2325 nm. When pumped under normal dispersion, the output spectrum undergoes broadening and exhibits five DWs, situated around 955, 1120, 1450, 2795 and 2965 nm, respectively. Concomitant with blue-shifted and red-shifted dispersive waves, the spectrum spans from 895 to 3050 nm with high coherence. The effect of the fiber and input pulse parameters on DWs generation, as well as the underlying dynamics of the dispersive wave generation process, are discussed. As expected, the number and location of DWs generated in the output spectrum have agreement with the prediction of the phase-matching condition. Overall, this multiple DWs generation method in the proposed fiber paves the way for developing efficient and coherent OAM light sources in fiber-based optical systems.

Solutions of Surface-Wave Dispersion and Attenuation in Stratified Viscoelastic Media Using a Spectral-Element Approach

ABSTRACT Efficient and accurate calculation for the dispersion and attenuation of the surface waves in viscoelastic media is numerically challenging because the eigen wavenumbers are located in the complex domain. In this study, we propose a semianalytical spectral-element method (SASEM), which can determine the complex eigen wavenumbers by solving linear eigenvalue problems. By simplifying the structure of the eigenvalue problem, we significantly improve the calculation efficiency. The implementation of the frequency-dependent automatic discretization, semi-infinite element, and mode filter guarantees the correctness and accuracy of the modal solutions. Because no root-searching schemes are required, the root-skipping problem is naturally avoided. The numerical tests show that the SASEM can provide sufficiently accurate solutions with much less computation cost than traditional Muller’s method. Meanwhile, SASEM exhibits high flexibility when applied to media the parameters for which vary continuously with depth. To demonstrate the effectiveness of SASEM for complicated dispersion features, the dispersion curves and eigen wavefields of the viscoelastic media with a low-velocity layer are also analyzed. The results of numerical tests indicate the versatility, efficiency, and accuracy of our method. With further study, the proposed SASEM has the potential to become a promising tool for the investigation and retrieval of viscoelastic subsurface structures.

Improved modeling of anisotropic effects on seismic waves in layered transversely isotropic half-spaces: Implications for velocity profile inversion challenges

In this paper, we first derive the dynamic solution in a transversely isotropic (TI) elastic and layered half-space, induced by a time-harmonic vertical load on its surface. The solution is obtained via the efficient and unconditionally stable dual variable and position (DVP) matrix method along with the fast Fourier-Bessel series (FBS) expansion approach. In order to study the effect of material anisotropy, the degree of anisotropy, namely the ratio of the horizontal Young's modulus over vertical Young's modulus, is introduced as the key parameter, with a very reasonable assumption on other involved elastic constants in the layered TI half-space. This enables us to investigate the effect of material anisotropy on the wave Green's functions, dispersion curves, ellipticity, and polarity. By comparing with the effect of Poisson's ratio in the corresponding layered isotropic (ISO) half-space, we observe that nearly all the wave features with varying degrees of anisotropy in the TI layered half-space are similar to those with varying Poisson's ratio in the corresponding ISO half-space. This indicates the challenge or non-uniqueness in the inversion of TI velocity profiles using vertical surface loading only.

Dispersive wave generation in single higher-order modes of a large-core silica step-index fiber with pulse energies up to 12 nJ.

The generation of light in a laser system is constrained by the gain medium, limiting the available wavelengths. We demonstrate in-fiber generation of ultrafast pulses between ∼550 and 800 nm via dispersive wave generation (DWG), in higher-order modes (HOMs). Using higher-order modes enables power scaling, due to their large effective area compared to the fundamental modes of single-mode fibers and dispersion engineering, even in simple step-index fibers. The process occurs in a single higher-order mode, which we excite using passive glass components (an axicon and two telescopes). The output pulses have energies up to 12 nJ at the biologically relevant wavelength of 705 nm.

A new approach for solving fractional Kundu-Eckhaus equation and fractional massive Thirring model using controlled Picard’s technique with [formula omitted]-Laplace transform

This paper introduces a novel approach called the Controlled Picard technique along with ρ-Laplace transform for simulating the solutions of the fractional Kundu–Eckhaus equation (FKEE) and time-fractional massive Thirring model (FMTM). Significant applications of these equations can be found in nonlinear optics, weakly dynamic dispersive waves of water, and the study of quantum fields. Our proposed approach merges the Controlled Picard technique with the ρ-Laplace transform, resulting in an elegant framework that effectively solves nonlinear fractional equations without the need for Lagrange multipliers or Adomian polynomials. The inclusion of a small parameter h enhances convergence and is particularly advantageous for nonlinear differential equations. We demonstrate the accuracy and convergence of our method by comparing it with other analytical approaches. In addition, we offer graphical depictions of the numerical results to demonstrate the effectiveness as well as reliability of our suggested methodology. Overall, our approach is highly efficient, accurate, and straightforward to implement.

The effects of pore structure on wave dispersion and attenuation due to squirt flow: A dynamic stress-strain simulation on a simple digital pore-crack model

Squirt flow, a phenomenon typically observed in porous cracked rocks, occurs due to the contrasting compressibility between the pores and cracks, leading to the pore pressure diffusion and dissipation of wave energy. Understanding the influence of pore structure on wave dispersion and attenuation signatures due to squirt flow is essential for interpreting seismic and sonic logging data in various fields of earth and energy sciences, such as hydrocarbon exploration, geothermal energy exploitation, and CO2 sequestration. In this study, we construct a simple digital pore-crack model with varying pore structures and use a dynamic stress-strain simulation approach to characterize wave dispersion and attenuation signatures due to squirt flow. Numerical simulation suggests that, in addition to the commonly considered parameters such as porosity, crack density, and crack aspect ratio, additional pore structure parameters, such as pore size, pore aspect ratio, crack orientation, crack length, and crack width, significantly affect the wave dispersion and attenuation signatures. Increasing the pore size leads to the pronounced enhancement of attenuation magnitude and a decrease in characteristic frequency. We demonstrate that variations in crack length have a pronounced impact on attenuation magnitude, whereas crack width is decisive in controlling the characteristic frequency. Furthermore, it is found that the saturation paths (the gas filling the pore first or gas filling the crack first) considerably affect the velocity-saturation and attenuation-saturation relationship, suggesting that the coupling effects of pore structure and fluid distribution complicate the fluid pressure diffusion and wave attenuation behaviors. The presented results offer insights for deciphering pore structure parameters using attenuation- or dissipation-related seismic attributes.

Numerical study of the Amick–Schonbek system

AbstractThe aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one‐dimensional case, this system can be viewed as a dispersive perturbation of the hyperbolic Saint‐Venant (shallow water) system. The asymptotic stability of the solitary waves is numerically established. Blow‐up of solutions for initial data not satisfying the noncavitation condition as well as the appearance of dispersive shock waves are studied.

An inerter-based concept of locally resonant fluid-conveying pipe

Preventing damage or failure caused by vibrations in periodic fluid-conveying pipes needs appropriate mitigation strategies. This paper proposes a novel concept of locally resonant fluid-conveying pipe resting on periodically spaced inerter-based resonant supports, each including an inerter and linear springs. On adopting a Timoshenko beam model for the pipe, two types of inerter-based resonant supports are investigated, differing by the arrangement of the internal components, i.e., inerter and springs. For both types, elastic wave dispersion analyses of the infinite pipe demonstrate the existence of two low-frequency band gaps in the frequency response. The second band gap, caused by local resonance, exhibits better attenuation over a relevant part of its frequency range; its lower/upper edge frequencies and amplitude may be suitably changed depending on the parameters of the inerter-based resonant supports, and very considerable amplitudes can be obtained thanks to the large inertia effects warranted by the grounded inerter. The influence on the band gaps of key parameters such as fluid velocity and ratio of fluid mass to total pipe mass is assessed. Moreover, the effect of damping is considered, assuming a Kelvin–Voigt viscoelastic behavior for the pipe material and including viscous dashpots in parallel with the springs within the inerter-based resonant supports. An original exact dynamic-stiffness method is formulated for computational purposes, targeting wave dispersion analysis of the infinite pipe as well as frequency-domain analysis of the finite pipe. In particular, the main novelty is the derivation of the exact dynamic-stiffness matrix and exact load vector of the unit cell of the Timoshenko pipe with Kelvin–Voigt viscoelastic behavior. Remarkably, the transmittance of the finite pipe confirms the predictions from wave dispersion analysis of the infinite pipe and substantiates the effectiveness of the proposed concept of locally resonant fluid-conveying pipe.

Deep learning‐based extraction of surface wave dispersion curves from seismic shot gathers

AbstractMulti‐channel analysis of surface waves is a seismic method employed to obtain useful information about shear‐wave velocities in the near surface. A fundamental step in this methodology is the extraction of dispersion curves from dispersion spectra, with the latter usually obtained by applying specific processing algorithms onto the recorded shot gathers. Although the extraction process can be automated to some extent, it usually requires extensive quality control, which can be arduous for large datasets. We present a novel approach that leverages deep learning to identify a direct mapping between seismic shot gathers and their associated dispersion curves (both fundamental and first higher order modes), therefore by‐passing the need to compute dispersion spectra. Given a site of interest, a set of 1D compressional and shear velocities and density models are created using prior knowledge of the local geology; pairs of seismic shot gathers and Rayleigh‐wave phase dispersion curves are then numerically modelled and used to train a simplified residual network. The proposed approach is shown to achieve high‐quality predictions of dispersion curves on a synthetic test dataset and is, ultimately, successfully deployed on a field dataset. Various uncertainty quantification and convolutional neural network visualization techniques are also presented to assess the quality of the inference process and better understand the underlying learning process of the network. The predicted dispersion curves are inverted for both the synthetic and field data; in the latter case, the resulting shear‐wave velocity model is plausible and consistent with prior geological knowledge of the area. Finally, a comparison between the manually picked fundamental modes with the predictions from our model allows for a benchmark of the performance of the proposed workflow.

Development of a piezo stack – Laser doppler vibrometer sensing approach for characterizing shear wave dispersion and local viscoelastic property distributions

Laser Doppler vibrometry and wavefield analysis have recently shown great potential for nondestructive evaluation, structural health monitoring, and studying wave physics. However, there are limited studies on these approaches for viscoelastic soft materials, especially, very few studies on the laser Doppler vibrometer (LDV)-based acquisition of time–space wavefields of dispersive shear waves in viscoelastic materials and the analysis of these wavefields for characterizing shear wave dispersion and evaluating local viscoelastic property distributions. Therefore, this research focuses on developing a piezo stack-LDV system and shear wave time–space wavefield analysis methods for enabling the functions of characterizing the shear wave dispersion and the distributions of local viscoelastic material properties. Our system leverages a piezo stack to generate shear waves in viscoelastic materials and an LDV to acquire time–space wavefields. We introduced space-frequency-wavenumber analysis and least square regression-based dispersion comparison to analyze shear wave time–space wavefields and offer functions including extracting shear wave dispersion relations from wavefields and characterizing the spatial distributions of local wavenumbers and viscoelastic properties (e.g., shear elasticity and viscosity). Proof-of-concept experiments were performed using a synthetic gelatin phantom. The results show that our system can successfully generate shear waves and acquire time–space wavefields. They also prove that our wavefield analysis methods can reveal the shear wave dispersion relation and show the spatial distributions of local wavenumbers and viscoelastic properties. We expect this research to benefit engineering and biomedical research communities and inspire researchers interested in developing shear wave-based technologies for characterizing viscoelastic materials.

Multi‐mode non‐linear inversion of Rayleigh wave dispersion curves with grey wolf optimization and cuckoo search algorithm

AbstractDispersion curve inversion is one of the core contents of Rayleigh wave data processing. However, the dispersion curve inversion has the characteristics of multi‐parameter, multi‐extremum as well as nonlinearity. In the face of Rayleigh wave data processing under complex seismic‐geological conditions, it is difficult to reconstruct an underground structure quickly and accurately apply a single global‐searching non‐linear inversion algorithm. For this reason, we proposed a strategy to invert multi‐order mode Rayleigh wave dispersion curves by combining with grey wolf optimization (GWO) and cuckoo search (CS) algorithms. On the basis of introducing the mechanism of iterative chaotic map with infinite collapses (ICMIC) and the strategy of dimension learning–based hunting (DLH), an improved GWO was developed that was called IDGWO (ICMIC and DLH GWO). After searching the near‐optimal region through IDGWO, the CS with a variable step‐size Lévy flight search mechanism was switched adaptively to complete the final inversion. The correctness of our method was verified by the multi‐order mode dispersion curve inversion of a six‐layer high‐velocity interlayer model. Then it was further applied to the processing of real seismic datasets. The research results show that our method fully utilizes the advantages of each of the two global‐searching non‐linear algorithms after integrating IDGWO and CS, while effectively balancing the ability between global search and local exploitation, further improving the convergence speed and inversion accuracy and having good anti‐noise performance.

Use of periodic 2D pillar array for performance enhancement of AlN-based SMR BAW resonators

This paper discusses the applicability of a two-dimensional (2D) periodic pillar array as the first layer of an acoustic mirror for AlN-based solidly mounted resonators of bulk acoustic waves. It is based on the idea that the periodic pillar array behaves like a uniform layer when the period is much smaller than the wavelength and its behavior is given by the ensemble average of pillar materials. The simulation shows that the effective electromechanical coupling factor can be enhanced close to that of AlN-based film bulk acoustic resonators when the slot ratio is large. It is also shown that the use of a 2D pillar array can enhance the reflectivity of the Bragg reflector. It should be noted that the periodic 2D pillar array can also control the anisotropy of wave propagation along the surface. Owing to this, transverse mode resonances can be suppressed well by adjusting the wave dispersion curve properly.

Resonant Absorption of Magnetohydrodynamic Body Modes under Photospheric Conditions

Observations reveal that surface and body modes exist in solar pores under photospheric conditions. While the effects of resonant absorption on photospheric surface modes are well established, its effect on body modes is not known yet. In this paper, we investigate resonant absorption for the body modes under photospheric conditions. We numerically solve the dispersion relation induced by thin boundary approximation and obtain the wave dispersion curves and damping rates of three arbitrarily chosen body modes for sausage and kink waves, respectively. The results show that resonant absorption for the body modes is weaker than for the slow surface modes in both cusp and Alfvén continua. The damping behavior of body modes is similar to slow surface modes while the higher body mode has stronger resonant absorption.