Propagation Of Low-frequency Waves Research Articles

Design strategies of cementitious metamaterials (CMs) with tunable bandgaps: Density customization and geometric optimization

The propagation of low-frequency elastic waves may exert significant stress on both human health and environmental safety. This study presents a new kind of cementitious metamaterials (CMs) characterized by tunable bandgaps for efficient absorption of low-frequency elastic waves. A dynamic system model is employed to examine and analyze the eigenfrequencies of these CMs. Herein, the porous alkali-activated municipal solid waste incineration fly ash (AAFMs) is modulated with customed density and then combined with rubber for generating CMs. Two distinct strategies are proposed to modulate the bandgap properties of the CMs: density customization and geometric optimization. The AAFMs' density is meticulously regulated by altering the foaming aluminum content, allowing the customization of CMs' bandgaps. Additionally, the CMs' bandgaps can also be tailored through geometric optimization, a process that involves a numerical method focused on examining the impact of varying inclined angles in inner and outer re-entrant structures. A transmission loss model is also developed to validate the bandgap characteristics of these CMs. Overall, the study explores the potential applications of these CMs, with a specific focus on their efficacy in mitigating low-frequency vibrations and attenuating noise. The successful utilization of these materials in such domains holds promising prospects for substantial advancements across diverse industrial sectors.

Improved Formulae for Low-Frequency Ultrasonic Attenuation in Metals

A range of ultrasonic techniques associated with the nondestructive evaluation of metals involves the propagation of low-frequency elastic waves. Metals that are isotropic and homogeneous in the macroscopic length scale contain elastic heterogeneities, such as grain boundaries within the microstructures. Ultrasonic waves propagating through such microstructures get scattered from the grain boundaries. As a result, the propagating ultrasound attenuates. The mass density and the elastic anisotropy in each constituent grain govern the degree of heterogeneity in the polycrystalline aggregates. Existing elastodynamic models consider first-order scattering effects from grain boundaries. This paper presents the improved attenuation formulae, for the first time, by including the next order of grain scattering effects. Results from investigating 759 polycrystals reveal a positive correlation between the effects of higher-order scattering from grain boundaries and the degree of heterogeneity. Thus, higher-order grain scattering effects are now known. These results motivate further investigation into higher frequencies and strongly scattering alloys in the future.

Downhole detection of gas kick using low-frequency elastic wave: Multiphysics modeling and its implications

Gas kick is a common and high-risk drilling trouble in geo-energy engineering, especially for deep-water drilling and ultra-deep well drilling. The most favorable way of early detection of gas kick is to move the detection from the wellhead or near surface to the downhole. In this paper, a new conception of downhole detection of gas kick using low-frequency elastic wave was put forward. The framework of coupling the multiple physic processes of gas-liquid two-phase annulus flow, bubble migration and low-frequency elastic wave propagation during gas kick was developed. The characteristic responses of low frequency elastic wave to gas kick were quantitatively analyzed based on multiphysics modeling under the ideal case and different levels of background gas (BGG), respectively. The modeling results indicated that: (i) The velocity decreases cliff-like and the attenuation coefficient increases significantly at the gas-kick bubble front. The change magnitudes of the velocity and the attenuation coefficient increase with the gas intrusion rate, and decrease with the pump displacement. The change magnitude of attenuation coefficient decreases with mud density, while the increase of velocity is not sensitive to the mud density. (ii) For the ideal case of the vertical well, the effective detection within the depth section of (2014–2568) meter could identify gas kick about (14.3–29.2) minutes earlier than the conventional pit-gain method. The gas kick could be identified earlier when the deviation angle is smaller and/or the monitoring point goes deeper. (iii) The changing magnitudes and rates of the velocity and the attenuation coefficient decrease with the BGG. The downhole detection of gas kick using low-frequency elastic wave should be reliable when the BGG is lower than 5%. The effects of rock cuttings, phase transition of the gas, and drill-string vibrations should be further investigated in future study.

Low frequency dust acoustic drift instability in the equatorial electrojet

The dust acoustic drift instability has been investigated at the lower electrojet region of the dusty ionosphere by considering a linearized fluid model. The effect of dust-neutral collisions, electron–ion recombination at the surface of the dust particles, and electron and ion inertia on the onset and growth of the instability have been explored in minutiae. The perturbed densities are gleaned from the electron, ion, and dust dynamics, which engendered generalized dispersion relations. The generalized dispersion relation delineates the propagation of low-frequency dust acoustic drift waves. The dispersion relation is solved numerically for various cases of interest at the two different altitudes(∼90km and ∼100km) of the lower electrojet region. It has been found that the instability is unlikely to develop due to recombination alone, similar as observed in the case of laboratory dusty plasma. A significant reduction of the growth rate has been observed in the low-frequency mode due to the dust-neutral collision both in the presence and absence of an equilibrium electron density gradient. However, the effect of dust-neutral collision is not discernible in the relatively higher frequency mode, which exists at an altitude of 100km. Moreover, the presence of electron and ion inertia has a stabilizing effect on the instability. The analysis presented here is germane to the lower ionospheric dusty electrojet region in which electrons are magnetized, but ions and dust particles are unmagnetized.

An Implementation Method of the Complex Frequency-Shifted Uniaxial/Multi-Axial PML Technique for Viscoelastic Seismic Wave Propagation

ABSTRACT A numerical implementation method of the complex frequency-shifted uniaxial/multi-axial PML (CFS UPML/MPML) is developed for modeling half-space viscoelastic wave propagation. A mixed CFS PML combining CFS UPML and CFS MPML is designed to improve PML’s performances in avoiding evanescent waves at grazing incidence and stabilizing long-time simulation of low-frequency viscoelastic wave propagation. Two numerical examples’ results showed that the developed method for the mixed CFS PML can implement elimination of evanescent waves at grazing incidence near the PML interface, long-time accurate simulation of low-frequency viscoelastic wave propagation and efficient absorption of the near-fault outgoing seismic waves in homogeneous earth medium.

Low frequency band gap and wave propagation mechanism of resonant hammer circular structure

The two circular structures with local resonance resonant hammers proposed in this paper have the comprehensive performance of small size, easy fabrication and low frequency vibration and sound damping. In the study, Bloch’s theorem is used to calculate the energy band curves of the two structures and to analyze the vibration forms of the structures at the edge of the band gap. At the same time, the integrated analysis means of phase constant surface, group velocity and phase velocity are innovatively used to explore the real propagation path of waves and provide experience for topology optimization. The position of resonant hammers, the mirror symmetry structure and the size of resonant hammers are adjusted to optimize the band gap for both structures. Finally, the vibration transmission characteristics of the finite period structure are calculated to verify the band gap and evaluate the vibration isolation performance. The results show that the new structure has low-frequency noise reduction performance, and the band gap frequency can be further reduced by topology optimization. This study presents an innovative approach for achieving low-frequency noise reduction, analysis of wave propagation paths and lightweight design.

A study of the propagation of magnetoacoustic waves in small-scale magnetic fields using solar photospheric and chromospheric Dopplergrams: HMI/SDO and MAST observations

In this work, we present a study of the propagation of low-frequency magneto-acoustic waves into the solar chromosphere within small-scale inclined magnetic fields over a quiet-magnetic network region utilizing near-simultaneous photospheric and chromospheric Dopplergrams obtained from the HMI instrument onboard SDO spacecraft and the Multi-Application Solar Telescope (MAST) operational at the Udaipur Solar Observatory, respectively. Acoustic waves are stochastically excited inside the convection zone of the Sun and intermittently interact with the background magnetic fields resulting into episodic signals. In order to detect these episodic signals, we apply the wavelet transform technique to the photospheric and chromospheric velocity oscillations in magnetic network regions. The wavelet power spectrum over photospheric and chromospheric velocity signals show a one-to-one correspondence between the presence of power in the 2.5–4 mHz band. Further, we notice that power in the 2.5–4 mHz band is not consistently present in the chromospheric wavelet power spectrum despite its presence in the photospheric wavelet power spectrum. This indicates that leakage of photospheric oscillations (2.5–4 mHz band) into the higher atmosphere is not a continuous process. The average phase and coherence spectra estimated from these photospheric and chromospheric velocity oscillations illustrate the propagation of photospheric oscillations (2.5–4 mHz) into the solar chromosphere along the inclined magnetic fields. Additionally, chromospheric power maps estimated from the MAST Dopplergrams also show the presence of high-frequency acoustic halos around relatively high magnetic concentrations, depicting the refraction of high-frequency fast mode waves around vA≈vs layer in the solar atmosphere.

Empirical Parameterization of Broadband VLF Attenuation in the Earth‐Ionosphere Waveguide

AbstractThe Earth‐ionosphere waveguide (EIW) determines the propagation of Very Low Frequency (VLF; ∼3−30 kHz) waves. Characterizing the waveguide is a longstanding challenge due to its large spatial scale and the complex variability of the lower ionosphere. Here we apply a novel linear basis function regression technique to characterize attenuation in the EIW using broadband measurements of lightning‐generated radio waves. The process begins with defining a basis function set, which ideally encompasses a feature set that can predict the variability seen in VLF attenuation properties. With this basis set defined, a system of linear equations is then constructed using sensor pair observations to eliminate the dependency on source amplitude in each observation. Using this formalism, an empirical attenuation model for broadband signals from lightning is constructed and the dependence on attenuation properties with the boundary conditions is explored. The empirically derived results show attenuation rates over ice that are 12 dB/Mm higher compared to paths over saltwater. Well‐known east/west attenuation rate asymmetry stemming from anisotropic reflection coefficients of the ionosphere is also demonstrated and investigated. For example, under a daytime ionosphere, westward‐propagating waves suffer up to 2.8 dB/Mm greater attenuation compared to eastward‐propagating waves. The trained model is used for propagation corrections in a global lightning locating system (LLS), but this technique can be expanded to further study VLF attenuation rates by employing different sets of basis functions.

Effects of the reef roughness on the harbor oscillations induced by low-frequency waves

Low-frequency waves can be captured and amplified within harbors and present a prevalent inducing factor of harbor oscillations. Effects of the rough reef surface and the possible inhomogeneity of the roughness on the oscillating behaviors within an elongated harbor on reef topography are investigated based on numerical simulations. The reef roughness is applied via hydraulic roughness coefficient within the well-recognized empirical range and the inhomogeneity is arranged following the probable location of the coral covers and the possible engineering inventions. With wavelet transformation analysis and bispectral analysis for inspecting energy distribution of oscillating components and their interactions, the lowest oscillation mode is found to be more influenced by the rough extents of the reef surface whereas higher modes, by the location of roughness. The friction induced by rough surface in the vicinity of reef crest is revealed to be effective in reducing the oscillating behaviors by acting on the generation of low-frequency waves on the reef by the incident short ones. In addition to the damping effects of the reef roughness, the transition from smooth reef surface to rougher one may also lead to evolutions of coupling between different oscillating components and consequently affect oscillating energy distributions.

Opera 2015 Project: Accurate Measurement Equipment for Earthquake Electromagnetic Emissions and Radio Seismic Indicator.

Electromagnetic emissions from earthquakes are known as precursors and are of considerable importance for the purpose of early alarms. The propagation of low-frequency waves is favored, and the range between tens of mHz to tens of Hz has been heavily investigated in the last thirty years. This work describes the self-financed Opera 2015 project that initially consisted of six monitoring stations over Italy, equipped with electric and magnetic field sensors, among others. Insight of the designed antennas and low-noise electronic amplifiers provides both characterization of performance (similar to the best commercial products) and the elements to replicate the design for our own independent studies. Measured signals through data acquisition systems were then processed for spectral analysis and are available on the Opera 2015 website. Data provided by other world-known research institutes have also been considered for comparison. The work provides examples of processing methods and results representation, identifying many exogenous noise contributions of natural or human-made origin. The study of the results occurred for some years and led us to think that reliable precursors are confined to a short area around the earthquake due to the significant attenuation and the effect of overlapping noise sources. To this aim, a magnitude-distance indicator was developed to classify the detectability of the EQ events observed during 2015 and compared this with some other known earthquake events documented in the scientific literature.

Effect of trapping in coupled kinetic Alfven-acoustic waves in a partially degenerate plasma with quantizing magnetic field

Inclusion of a quantizing magnetic field in a partially degenerate plasma has interesting effects on the propagation of solitary and nonlinear periodic structures in coupled kinetic Alfven acoustic waves. In this paper, we use two-potential theory to investigate the nonlinear structures using Sagdeev potential approach and further analyze it using nonlinear dynamical methods. It is shown that the existence of solitary structure is sensitive to small temperature effects and quantizing magnetic field in a dense plasma with adiabatically trapped electrons. The work presented here is useful in understanding the low frequency wave propagation in a dense astrophysical environment like white dwarf stars and in low beta laboratory plasmas e.g. intense laser-plasma interactions.

Novel periodic pile barrier with low-frequency wide bandgap for Rayleigh waves

This paper aims to investigate the propagation of low-frequency seismic surface waves in periodic in-filled barriers from the viewpoint of bandgaps. Based on Bloch-Flouquet theory, four configurations of periodic pile barriers with the same filling rate but different cross sections are studied. The periodic boundary conditions are imposed to derive the characteristics equation. Simultaneously, the finite element method is used to calculate the numerical dispersion relation and vibration modes of four types of periodic pile barriers with various inclusions. The sound cone and the energy parameter method are introduced to identify the surface wave modes further. Additionally, the mitigation effectiveness of a finite number of periodic barriers is evaluated using a three-dimensional transmission model. The results show that the initial frequency and bandwidth of the surface bandgaps are sensitive to the shape of the cross-section and mechanical parameters of the inclusions. The surface wave bandgaps within 9.64 ∼ 13.92 Hz are observed for the periodic barrier composed of cross-like polyfoam sections. Moreover, the radiation modes formed by the leakage of some surface waves into the sound cone are expected to widen the attenuation zones of the periodic barriers. The numerical results in frequency and time domains further validate the attenuation effect of finite barrier in the bandgap and the attenuation widening phenomenon caused by the dissipation of the leak modes into the bulk. This study provides new insights into the design of periodic pile barriers. In the future, it is expected to mitigate the low-frequency ground motion by fully designing the section shape and filling materials of pile barriers.

Modeling of Diurnal Variation Characteristics of VLF Wave Propagation in Earth-Ionosphere Waveguide With FDTD Method

In this letter, Wait's exponential (EXP) model and international reference ionosphere (IRI) model are combined to study the diurnal variation characteristics of very low frequency (VLF) wave propagation. The EXP model is used below the IRI model to compensate for the subionosphere electron density lack of the IRI. The major EXP parameters are reconstructed from the lower IRI electron density for different times of the day. Being capable of characterizing the subionosphere details, the combined IRIEXP model gets higher accuracy than the pure IRI model for VLF diurnal variation prediction. The measurement result is replicated by using the finite-difference time-domain method to validate the presented model.

Analysis of low frequency vibration attenuation and wave propagation mechanism of graded maze structure

In this paper, a new graded maze metamaterial with a single phase is proposed. Based on the finite element method and Bloch's theorem, the bandgap characteristics of graded maze structures in different regions are analyzed, and the mechanism of bandgap opening and closing is explored by vibration patterns. Subsequently, the mechanism of elastic wave propagation within different structures is comprehensively analyzed from four perspectives, such as group velocity and phase velocity. And the damping performance is further verified by frequency response spectra. The results show that the new structure has excellent low-frequency bandgap and damping performance, the local resonance of the graded maze plays an important role in the expansion of the bandgap, and there is directionality and regionality of wave propagation within the structure. This paper provides a new idea for wave propagation control and analysis, and low frequency damping of single-phase materials.

Folding-angle framework for structural modeling of rigid triangulated Miura-ori lattices

Abstract Origami is rapidly gaining prominence in the research of metamaterials as it allows for tuning the properties of interest by change in the folded state. Origami-based lattices that allow low-frequency wave-propagation can potentially find use as acoustic metamaterials. Rigid panel origami tessellations have lattice modes which are exclusively due to the low-energy folding deformations at creases and hence will be suitable for low-frequency wave-propagation applications. Modeling frameworks like bar-and-hinge that are typically used to study origami lattice mechanics allow for panel stretching behavior which is forbidden and redundant in rigid panel origami lattices. This drives the necessity for an efficient analysis framework dealing exclusively with folding-angles for study of origami lattices with rigid panels. As a first step in this direction, in this paper, we propose a folding-angle-based analytical framework for structural modeling of infinite lattices of triangulated Miura-ori with rigid panels. We assign rotational stiffness to the creases and analytically derive the stiffness matrix for the lattices based on a minimal number of folding-angle degrees of freedom. Finally, we study the influence of the equilibrium folded state and the relative crease stiffness on the modal energies, to demonstrate the tunable and programmable nature of the structure. The framework proposed in our work could enable the study of wave dynamics in rigid panel Miura-ori-based lattices and our findings show significant promise for the future use of 1D origami with rigid panels as acoustic metamaterials.

Low Frequency Band Gap and Wave Propagation Properties of a Novel Fractal Hybrid Metamaterial

In order to achieve the attenuation of low‐frequency sound, in this paper, a hybrid metamaterial structure with a complete band gap below 500 Hz is proposed, which is subjected to second‐order fractal, series fusion, and whether the structure is framed or not to form 8 different structures. Based on the finite element method and Bloch's theorem, the bandgap and transport properties of all model structures are evaluated, and the bandgap and propagation properties of metamaterial structures with different fractal levels are elucidated in terms of band structure and group velocity. In addition, the third‐order fractal structure and the dependence of the band gap on the material are also studied. The results show that the structure has a superior band gap width, and the complete band gap of its tandem fusion structure accounts for up to 45.502% in the range of 500 Hz, and the second‐order fractal has a complete band gap of 45.588% in the range of 1000 Hz. Compared with other structures, it can produce lower and better band gap. The research in this paper provides a new strategy for realizing acoustic metamaterial structures with low frequency band gaps.

Design of low-frequency and broadband acoustic metamaterials with I-shaped antichiral units

Controlling the propagation of low-frequency sound waves on the sub-wavelength scale is still a challenging problem. For the design of low frequency sound reduction materials, this paper introduces the I-shaped antichiral unit to the acoustic metamaterials with Mie resonance, which can manipulate the sub-wavelength acoustic waves and achieve effective low-frequency and broadband sound isolation. By adjusting the width of the ligament, the proportion of the omnidirectional bandgap is 65.6 % in the subwavelength range. Firstly, the designed acoustic metamaterials are constructed by rotating the I-shaped units with mutually orthogonal periodic distribution. The parametric geometric model of metamaterials is established, and the low-frequency and wide bandgap can be effectively realized by adjusting the ligament width. Then, the investigation of sound pressure and phase reveals that the bandgaps attribute to the Mie resonant mode. Furthermore, based on the transfer matrix method, the effective bulk modulus and effective mass density of acoustic metamaterials are derived. The results show that the frequency range of the negative effective parameters obtained is consistent with that of the band gap. Finally, experimental tests are carried out, the region where attenuation occurs is in good agreement with the bandgap range (1158–2500 Hz) predicted by eigenfrequency analysis. The experimental tests verify the effectiveness of the designed antichiral acoustic metamaterials for low frequency sound reduction. The introduction of the antichiral unit provides a broad space for the application of acoustic metamaterials in low-frequency sound reduction.The low-frequency and broadband can be effectively realized by adjusting the ligament width.The low-frequency can be effectively realized by adjusting the ligament width.The experimental tests verify the effectiveness of the designed antichiral unit.

The low-frequency and broadband pendulum metamaterials based on inertial amplification mechanism

Pendulum has recently been introduced into the field of elastic metamaterials because of its low-frequency vibration characteristic, which further expands the application value of such structure. However, the low-frequency and broadband performance of traditional pendulum (TB) metamaterials still need to be further improved. In this paper, a new low-frequency pendulum metamaterial is proposed, and the low-frequency elastic wave propagation characteristics of the metamaterial are studied. The study shows that compared with the TB metamaterial, it can effectively lower the bandgap (BG) of metamaterial, but greatly narrow the BG. To solve this problem, the negative inertial amplification mechanism is further proposed, and the variation law of the metamaterial BG under this mechanism is investigated. It is found that the mechanism can effectively broaden the metamaterial BG and in specific cases make it have infinite width. Meanwhile, the constraint relationship between the frequency response function of unit-cell structure and the wave vector of metamaterial is established, which is used to reveal the broadening rationale of the BGunder the negative inertial amplification mechanism. Finally, depending on the negative inertial amplification mechanism, a novel broadband pendulum metamaterial is designed based on the low-frequency pendulum metamaterial. The relationship between the broadband attenuation behavior of the metamaterial and the frequency response function of unit-cell structure is analyzed, the working mechanism of negative inertial amplification to broadband pendulum metamaterial is also discussed, and the relevant optimization design method is given at the end.

Pressure attenuation due to radiative exchange in fluid-filled boreholes

The paper deals with the propagation of low-frequency waves in fluid-filled boreholes surrounded by an infinite solid media. Its purpose is to give a better understanding of the pressure attenuation of the acoustic wave due to radiative exchange with the solid in the low frequency range applied to the study of hydraulic facilities prone to earthquakes and sizing of hydromechanical components. We consider the case of low frequency pressure waves generated in a reservoir lake under seismic loading in the frequency range [0–20 Hz] and propagating through the duct mouth in a borehole. At theses frequencies, the radiative exchanges between soil and fluid contained into the bore are very weak, thus modelling and quantifying them constitute a challenge. A semi-analytical model based on the derivation of the equations of motion in solid and of wave propagation in fluid is developed and its results are compared with a FEM modelling. Both methods are applied to the case of a semi-infinite cylindrical buried bore and lead to close results: the strong relationship between soil properties and pressure attenuation and the influence of the Stoneley boundary wave on the acoustic pressure wave celerity. Finally, a study implementing the FEM model highlights the influence of heterogeneous solid medium and non-axisymmetric boreholes sections on the radiative exchange.

Computational Verification and Experimental Validation of the Vibration-Attenuation Properties of a Geometrically Nonlinear Metamaterial Design

Metamaterials continue to be conceptually intriguing for the manipulation of propagating waves. However, preventing low-frequency wave propagation proves to be challenging, due to limited metamaterial dimensions and mass. This study focuses on a metamaterial lattice featuring geometrically nonlinear behavior that can lead to negative stiffness, aimed at overcoming the requirement of large mass for low-frequency vibration attenuation. This approach can find application in structural engineering to protect against low-frequency excitations---such as earthquakes.