Wave Propagation Research Articles

Tailored ultrasound propagation in microscale metamaterials via inertia design

The quasi-static properties of micro-architected (meta)materials have been extensively studied over the past decade, but their dynamic responses, especially in acoustic metamaterials with engineered wave propagation behavior, represent a new frontier. However, challenges in miniaturizing and characterizing acoustic metamaterials in high-frequency (megahertz) regimes have hindered progress toward experimentally implementing ultrasonic-wave control. Here, we present an inertia design framework based on positioning microspheres to tune responses of 3D microscale metamaterials. We demonstrate tunable quasi-static stiffness by up to 75% and dynamic longitudinal-wave velocities by up to 25% while maintaining identical material density. Using noncontact laser-based dynamic experiments of tunable elastodynamic properties and numerical demonstrations of spatio-temporal ultrasound wave propagation, we explore the tunable static and elastodynamic property relation. This design framework expands the quasi-static and dynamic metamaterial property space through simple geometric changes, enabling facile design and fabrication of metamaterials for applications in medical ultrasound and analog computing.

The Peculiarities of Acoustic Normal Waves Propagation in Thin Porous Sheets of Thermally Expanded Graphite

Thermally expanded graphite belongs to a new class of graphite materials with unique physical, chemical and mechanical properties. Acoustic wave velocity is one of the most important characteristics for study of porous materials including thin porous sheets of thermally expanded graphite. In this paper peculiarities of symmetric mode S0 Lamb wave propagation and SH-wave with horizontal polarization in sheets of thermally expanded graphite are experimentally investigated. To determine their velocities a differential measurement scheme on the base of a low-frequency acoustic flaw detector DIO1000 LF and specialized piezoelectric transducers with dry point contact was used. Additionally the longitudinal wave velocity in direction of sheet thickness was determined using piezoelectric transducers based on polyvinylidene fluoride. Indicatrices of normal wave velocities in the rolling plane were plotted and it was shown that the maximum acoustic anisotropy is characteristic for the S0-mode. The velocity minimum corresponds to the longitudinal direction of the rolling plane in which the maximum elongation of gas pores was observed. Influence of thickness and density of thermally expanded graphite sheets on the velocities of normal waves was investigated and presence of the thickness range where the minimum velocity values were observed due to the maximum inhomogeneity of layers formed in the rolling process. Method for determination of dynamic elastic moduli of porous thermally expanded graphite sheets using experimentally measured velocities of normal waves was proposed. It was shown that in the longitudinal direction of the rolling plane the Poisson's ratio took negative values which allow to attribute the specified material to auxetics ones.

A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations

Abstract. The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectral-element-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave-induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two-layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non-linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations.

Alpha Traveling Waves during Working Memory: Disentangling Bottom-up Gating and Top-down Gain Control.

While previous works established the inhibitory role of alpha oscillations during working memory maintenance, it remains an open question whether such an inhibitory control is a top-down process. Here, we attempted to disentangle this issue by considering the spatio-temporal component of waves in the alpha band, i.e., alpha traveling waves. We reanalyzed two pre-existing and open-access EEG datasets (N = 180, 90 males, 80 females, 10 unknown) where participants performed lateralized, visual delayed match-to-sample working memory tasks. In the first dataset, the distractor load was manipulated (2, 4, or 6), whereas in the second dataset, the memory span varied between 1, 3, and 6 items. We focused on the propagation of alpha waves on the anterior-posterior axis during the retention period. Our results reveal an increase in alpha-band forward waves as the distractor load increased, but also an increase in forward waves and a decrease in backward waves as the memory set size increased. Our results also showed a lateralization effect: alpha forward waves exhibited a more pronounced increase in the hemisphere contralateral to the distractors, whereas the reduction in backward waves was stronger in the hemisphere contralateral to the targets. In short, the forward waves were regulated by distractors, whereas targets inversely modulated backward waves. Such a dissociation of goal-related and goal-irrelevant physiological signals suggests the co-existence of bottom-up and top-down inhibitory processes: alpha forward waves might convey a gating effect driven by distractor load, while backward waves may represent direct top-down gain control of downstream visual areas.Significance Statement When exploring the functional role of alpha band neural oscillations during working memory, mostly amplitude modulations have been considered so far, with relatively limited exploration of spatial-temporal dynamics of this rather global brain oscillatory signature. The present study seeks to address this gap by examining the directionality of alpha wave propagation during working memory retention. Our findings offer novel insights into the well-established inhibitory role of alpha waves, demonstrating that this function is manifested differently according to their propagation directions: forward waves seem to facilitate bottom-up gating, while backward waves might mediate top-down gain control.

Enhancing Fault Location Accuracy in Transmission Lines Using Transient Frequency Spectrum Analysis: An Investigation into Key Factors and Improvement Strategies

Fault location estimation in transmission lines is critical for power system reliability. Various methods have been developed for this purpose, among which transient frequency spectrum analysis (TFSA) stands out as a recent method based on travelling wave (TW) theory. TFSA determines the fault location by analyzing the frequency spectrum of transient currents and/or voltages at the instant of the fault, offering advantages such as independence from fault impedance and the ability to locate faults with one-side measurements. Despite its success in fault location, TFSA has several considerations that warrant detailed investigation. This study explores the effects of source inductance, series compensation, fault arc, and current transformer (CT) characteristics on transient frequencies. Additionally, the impact of noise on TFSA results is examined. The new proposed source inductance compensation method can reduce the error of 6.55% to 0.88%, where the same error can be reduced to 3.45% with the compensation method given in previous study. Strategies to enhance accuracy are discussed and compared to previous studies, including a proposed detection approach providing appropriate data size and precise wave propagation speed calculations. These findings contribute to a deeper understanding of TFSA’s limitations and inform practical improvements for fault location accuracy in power transmission systems.

Investigating the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation: An iterative framework for nonlinear wave dynamics

Abstract This paper addresses the solution of the fractional Caudrey Dodd Gibbon Sawada Kotera (CDGSK) equation using the Conformable Laplace Decomposition Method (CLDM). The CDGSK equation, a fundamental model in wave dynamics and fluid mechanics, is explored for its applications in quantum mechanics and nonlinear optics. By employing fractional calculus, we demonstrate how fractional derivatives influence the physical characteristics of wave propagation in both optical and quantum systems. The exact solutions obtained provide insight into soliton behavior, essential for understanding wave-particle interactions in quantum fields and light-matter interactions in optics. The fractional nature of the equation allows for more accurate modeling of non-integer order dynamics commonly found in optical fibers and quantum waveguides. The CLDM method proves to be highly effective, providing approximate solutions with minimal computational effort. These findings offer significant contributions to the fields of quantum mechanics and nonlinear optics, where the fractional CDGSK equation can be applied to solve complex wave equations with great accuracy.

Propagation, reflection, and transmission of nonlocal waves at the interface between semiconductor isotropic and diffusive porous semiconductors through a higher-order fractional derivative study

The current research paper investigates the transmission of nonlocal waves occurring at the interface between a semiconductor isotropic medium and a diffusive porous solid. A higher-order fractional-order derivative heat conduction model is utilized to account for thermal effects on wave propagation, reflection, and transmission. The interface generates five coupled and one independent transmitted wave in the lower medium, along with three coupled transmitted waves and one independent SV wave. Graphical analyses are conducted to examine the propagation speed of reflected waves in both porous and non-porous media. The impact of elastic non-locality and the fractional-order parameter on the propagation speed of all waves within the media is also assessed. The amplitude ratios are computed for the incident longitudinal displacement wave at the free boundary. The research explores the influence of physical parameters on reflection and transmission coefficients, and the results are validated through the conservation of energy. Additionally, the analysis yields deductions for certain special cases.

Analysis of Influence of Excitation Source Direction on Sound Transmission Loss Simulation Based on Alloy Steel Phononic Crystal

As a type of locally resonant phononic crystal, alloy steel phononic crystals have achieved notable advancements in vibration and noise reduction, particularly in the realm of low-frequency noise. Their exceptional band gap characteristics enable the efficient reduction of vibration and noise at low frequencies. However, the conventional transmission loss (TL) simulation of finite structures remains the benchmark for plate structure TL experiments. In this context, the TL in the XY-direction of phononic crystal plate structures has been thoroughly investigated and analyzed. Given the complexity of sound wave incident directions in practical applications, the conventional TL simulation of finite structures often diverges from reality. Taking tungsten steel phononic crystals as an example, this paper introduces a novel finite element method (FEM) simulation approach for analyzing the TL of alloy steel phononic crystal plates. By setting the Z-direction as the excitation source, the tungsten steel phononic crystal plate exhibits distinct responses compared to excitation in the XY-direction. By combining energy band diagrams and modes, the impact of various excitation source directions on the TL simulations is analyzed. It is observed that the tungsten steel phononic crystal plate exhibits a more pronounced energy response under longitudinal excitation. The TL map excited in the Z-direction lacks the flat region present in the XY-direction TL map. Notably, the maximum TL in the Z-direction is 131.5 dB, which is significantly lower than the maximum TL of 298 dB in the XY-direction, with a more regular peak distribution. This indicates that the TL of alloy steel phononic crystals in the XY-direction is closely related to the acoustic wave propagation characteristics within the plate, whereas the TL in the Z-direction aligns more closely with practical sound insulation and noise reduction engineering applications. Therefore, future research on alloy steel phononic crystal plates should not be confined to the TL in the XY-direction. Further investigation and analysis of the TL in the Z-direction are necessary. This will provide a novel theoretical foundation and methodological guidance for future research on alloy steel phononic crystals, enhancing the completeness and systematicness of studies on alloy steel phononic crystal plates. Simultaneously, it will advance the engineering application of alloy steel phononic crystal plates.

Comparative analysis of methods for predicting train-induced vibrations

Railway systems cause more severe vibration pollution than road systems, and the vibration pollution caused by railway systems has been increasing annually over the past two decades. Despite this, there is limited investigation into the accuracy of train-induced vibration prediction methods. Therefore, the present study investigated the accuracy of the detailed and general procedures proposed by the US Federal Transit Administration (FTA) for predicting train-induced vibrations. The accuracy of these methods was determined by evaluating their predictions against in-situ measurements of ground vibration levels induced by passing trains. The field experiments conducted in this study involved the measurement of train-induced vibration levels, the estimation of line-source transfer mobility (LSTM) by dropping a weight on rail sleepers, the evaluation of force density levels, and the determination of ground LSTM by dropping a weight on the ground. In addition, graphs were plotted to determine the relationships of train-induced vertical vibration levels with train speed, distance from the track centreline, and train length. The study compared measured and predicted vibration levels to assess the accuracy of the FTA’s detailed and general prediction methods. Results indicate that detailed assessments tend to overestimate vibration levels, while an optimized general vibration assessment curve offers a more precise estimate. Additionally, on the basis of the measurement data, the study explored the impact of train length on ground vibration and demonstrated that track ballast can absorb vibration energy along the wave propagation path. A frequency propagation contour plot was also created to analyse vibration energy across different frequencies. These findings enhance the reliability of train-induced vibration prediction methods and provide insights for improving vibration mitigation strategies in urban railway systems.

Hydrodynamic simulation of coastal reservoir in response to flow control: a numerical study of the Saemangeum reservoir

Coastal reservoirs (CRs) are important water resources worldwide, but environmental problems can arise due to limited material mixing caused by the blocked propagation of tidal waves. The Saemangeum Reservoir is a large brackish reservoir in South Korea; owing to its complex fluctuation characteristics, accurate reproduction of its three-dimensional (3D) circulation and material distribution characteristics remains a challenge. Here, we aimed to improve the reproducibility of the Delft3D model through long-term precision monitoring and analyze problems occurring in CRs. The model reproduced the hydraulic flow and stratification phenomena in CRs. The Richardson number ( R i ) was higher than 100, and the Stratification Index ( SI ) was higher than 1 due to the density difference between the surface and bottom layers. The stratification strength of the Saemangeum Reservoir was, therefore, considered high. Moreover, a two-layer circulation occurred due to the strength of the eddy and the horizontal gradient of salinity. When the sluice gate was expanded, the area and number of days where hypoxia occurred decreased. It would also mitigate the retention of materials caused by the eddy and improve circulation. The findings of this study can be used as foundational data for solving and managing hydraulic problems within CRs.

The generalized soliton wave structures and propagation visualization for Akbota equation

Abstract This paper explores in detail the integrable Akbota equation, a Heisenberg ferromagnet-type problem that is essential to the study of surface and curve geometry. A variety of soliton families are represented by the generalized solitonic wave profiles that are produced using the improved modified Sardar sub-equation technique, which is renowned for its accuracy and dependability. There has never been a study that used this technique before the current one. As a result, the solitonic wave structures have kink, dark, brilliant, king-singular, dark-singular, dark-bright, exponential, trigonometric, and rational solitonic structures, among other characteristics. In order to check the energy conservation, the Hamiltonian function is created and energy level demonstrated. The sensitivity analysis is also presented at various initial conditions. The graphical representation is also depicted along with the appropriate parametric values.

Comparison and parametric study of characteristics of eleven types of anisotropic woods based on the behaviour of Lamb wave propagation

AbstractKnowledge in advance of the nine orthotropic independent elastic constants (Cij) of the wood medium is essential for evaluating its mechanical properties. The most prominent technique to retrieve Cij is the ultrasonic testing technique. This technique uses guided waves that can propagate through the material under test. Accordingly, it is worth noting that the numerical modelling of the phase and group velocities of guided waves is an unavoidable preliminary step before experimentally producing guided wave modes. Therefore, the main goal of the present work is to numerically calculate the phase velocity, group velocity and the relevant optimal incidence angles of Lamb waves in anisotropic wood that can be used as a numerical parametric study for any future experimental setup. Here, Lamb dispersion curves are calculated for eleven types of woods, where the Legendre polynomial method is employed to solve the wave equations. Moreover, the optimal incidence angle for each Lamb mode is calculated according to the Snell–Descartes law. By calculating out the three parameters of phase velocity, group velocity and optimal incidence angle of Lamb modes in eleven types of anisotropic woods, we hope to fast-track the researchers in considering the present work to facilitate their experimental measurements.

SH‐waves in a complex fluid composite structure with spring membrane imperfect interfaces

AbstractComplex fluids are of nobleness due to their unique mechanical responses to applied stress, which are different from simple fluids. Therefore, the current study encapsulated the behavior of SH‐wave in a complex fluid layer overlying a fiber‐reinforced half‐space with six different cases considered at the common interface. These cases involve various interface conditions, including perfect bonding, a spring layer, an infinitely thin membrane layer, loose bonding, a combined spring‐membrane layer, and a membrane layer with loose bonding. Precisely, the effect of loose bonding, membrane strength, and spring stiffness at the common interface on the propagation of SH (Shear Horizontal) wave is studied in detail. The problem is mathematically formulated for all the aforementioned six models followed by their solution with the aid of appropriate boundary conditions. Numerical computations are performed with a view to study the effect of stiffness of spring and membrane, as well as loose bonding at the common interface of the media. It is demonstrated that membrane strength impedes wave propagation, while increased spring stiffness supports it. Notably, the combined spring‐membrane interface has a more pronounced effect than a spring layer alone. The findings of this study may be utilized in the development of membrane technology, including the study of fluid membranes and it has significant importance in seismic engineering and vibration isolation systems.

Peculiarities of flexural wave propagation in a notched bar

The results of numerical modeling and experimental studies of the propagation of flexural elastic waves in a metal notched bar approximates the effect of an acoustic black hole are presented. The sample is a bar with notches, the depth of which increases according to the power law with an exponent equal to (4/3). It has been confirmed experimentally and with the simulation results, that such bars slow down the propagation of an elastic wave to the end of the bar. It is shown in such structures flexural waves have dispersion and their localization at the end of the bar is higher for some natural frequencies than that of a solid rod. The natural oscillations of the whole and notched bars are compared, i.e. the shape of the amplitude of the flexural wave along the rods. The dependence of the flexural wave length in a notched bar on the frequency is investigated as a wave propagates to the end of the bar.

Dynamic characterization of plasma and combustion wave interactions during millisecond-nanosecond combined laser-induced enhanced damage on fused silica

Fused silica, which is widely used in optical systems, limits the load capacity of the optical system when it is damaged by laser irradiation. In this paper, a combined millisecond-nanosecond pulsed laser induced triple combustion wave dynamics model for fused silica generation is developed. The relationship between pulse delay and the dynamic propagation of plasma and combustion waves induced by combined laser-induced fused silica was studied from three aspects: theory, simulation, and experiment. The results show that the energy deposition of the nanosecond laser injects energy into the dilute plasma, which increases the speed of the double-burning wave to form a triple-burning wave. In addition, it was found that the combined effect of viscous shear between the plasma plume and the air exacerbates the degree of imbalance in the Knudsen layer instantaneously releasing pressure and increasing the complexity of plasma and combustion wave propagation, recoil pressure produces a more complex crack network on the fused silica surface. The results provide a better understanding of the propagation properties of plasma and triple-burning waves during combined millisecond-nanosecond induced fused silica damage.

The Improved tan (\(\frac{\Phi(\xi)}{2}\)) -Expansion Method for The Non-dissipative Double Dispersive Equation in Microstructured Solids

In microstructured solids, the non-dissipative double dispersive equation is a fourth-order non-linear partial differential equation that arises in the study of non-dissipative strain wave propagation. Seeking the exact solution of a nonlinear partial differential equations with a physical background is helpful to understand the motion law of matter and to explain the corresponding physical phenomena scientifically. This equation has been studied widely, and there have been a lot of research methods to find exact solutions to this equation. In this manuscript, we try to study the non-dissipative double dispersive equation by the improved tan (\(\frac{\Phi(\xi)}{2}\)) -expansion method. As far as our known, no one has used this method to study the non-dissipative double dispersive equation, partly because of the complicated calculation. We obtain a lot of exact traveling wave solutions, including hyperbolic function solutions, trigonometric function solutions, exponential function solutions, and rational function solutions. Compared with the other methods, some solutions obtained in this manuscript are consistent with existing solutions, which shows the effectiveness of the improved tan (\(\frac{\Phi(\xi)}{2}\)) -expansion method. Through this method, Our manuscript obtains more general and new exact solutions. These solutions may play an important role in engineering and physics. What's more, we plot the 3D graphs of some of the solutions obtained in this manuscript, which helps us understand the physical phenomenon of the non-dissipative double dispersive equation. In the future, we will continue to explore its physical significance from the new analytical solution we have obtained.

Efficient layerwise multiphysics spectral element model for delaminated composite strips with PWAS transducers

Efficient structural element-based models are essential for fast simulations of wave propagation in composite structures for model-based and physics-informed data-driven structural health monitoring. This article introduces the first efficient multiphysics time-domain spectral structural element for wave propagation analysis of beam and panel-type composite structures with piezoelectric transducers (patch or full layers) containing delaminations. A general framework is presented to model multiple delaminations and transducer patches located arbitrarily. The intact host and patch transducer-bonded laminates and sub-laminates between delaminations are modelled separately using an electromechanically coupled efficient layerwise zigzag theory (ZIGT) for kinematics and a piecewise quadratic variation for the electric potential across piezoelectric layers. The high-order spectral element (SE) features a virtual electric node to model equipotential surfaces of piezoelectric transducers apart from the usual physical nodes having mechanical and internal electric degrees of freedom. A hybrid point-least squares continuity approach is employed to maintain continuity at the intersections of delaminated sub-laminates or the patch-bonded laminate with the host laminate. The model’s performance in capturing electroelastic waves’ interaction with delamination is examined with reference to the conventional finite element (FE) solution based on the ZIGT, continuum-based FE solutions, and the SE solution based on a non-layerwise version of the laminate theory. Finally, the model is used to examine the impact of interfacial location and size of delaminations on wave propagation behaviour.

Influence of Gravity and Hydrostatic Initial Stress on Wave Propagation in Context of Three Phase Lag Thermoelasticity

Influence of Gravity and Hydrostatic Initial Stress on Wave Propagation in Context of Three Phase Lag Thermoelasticity

Reconfigurable magnonic crystals: Spin wave propagation in Pt/Co multilayer in saturated and stripe domain phase

To control the spin wave (SW) propagation, external energy sources such as magnetic fields, electric currents, or complex nanopatterning are used, which can be challenging at the deep nanoscale level. In this work, we overcome such limitations by demonstrating SW propagation in Pt/Co multilayers at a remanent state controlled by stripe domain patterns, using Brillouin light scattering and micromagnetic simulations. We show that parallel stripes with a periodicity around 100 nm exhibit reconfigurability, as the stripes can be rotated by applying the in-plane field without damaging their shape. This allows us to study SW propagation perpendicular and parallel to the stripes. We observe multimodal SW spectra—three bands in perpendicular and five in parallel geometry. Numerical results allow us to identify all observed modes and to explain the differences between two configurations by the unequal contribution of all three magnetization components in the SW dynamics. We find that the experimentally measured non-reciprocal dispersion (for the wavevector perpendicular to the stripes) is not the breaking of time-symmetry but the asymmetry in intensity of the measured signals of two different low-frequency modes, which is due to the inhomogeneous SW amplitude distribution over the multilayer thickness and the limited light penetration depth. Our results pave the way for easy reprogrammability and high energy efficiency in nanomagnonics.

Dam break flow through rigid-emergent vegetation

Abstract Dam failures pose a significant threat to life and property. This study investigates the potential of rigid emergent vegetation to attenuate dam break waves, reducing their destructive impact. Experiments explored the effect of varying vegetation field lengths on wave propagation. Wooden cylinders with consistent diameter (1.0 cm) and density (0.067) simulated the rigid vegetation in a straight, flat rectangular channel. Four different vegetation lengths and three bore conditions for different reservoir and tailwater depths were examined to analyze their influence on dam break wave behavior. The results demonstrate the effectiveness of vegetation in dissipating wave energy, leading to a rapid decrease in wave height and celerity. Interestingly, increasing vegetation length significantly attenuates the wave height downstream of the vegetation zone, while having no significant impact on the reflection wave height upstream of the vegetation. This finding highlights the targeted effectiveness of strategically placed vegetation in shielding downstream areas. The study also clarifies that celerity can be calculated using shallow water equations for both upstream and downstream regions with wave height and tailwater depth. However, within the vegetation, drag forces significantly reduce celerity. A novel equation, derived from wavefront profiles, was proposed and validated to accurately calculate celerity within the vegetation field. These findings provide valuable data for validating numerical models simulating dam break wave interactions with vegetation. Graphical abstract