Low Frequency Region Research Articles

Transient Slope: A Metric for Assessing Heterogeneity from the Dielectrophoresis Spectrum

Cellular heterogeneity, an inherent feature of biological systems, plays a critical role in processes such as development, immune response, and disease progression. Human mesenchymal stem cells (hMSCs) exemplify this heterogeneity due to their multi-lineage differentiation potential. However, their inherent variability complicates clinical use, and there is no universally accepted method for detecting and quantifying cell population heterogeneity. Dielectrophoresis (DEP) has emerged as a powerful electrokinetic technique for characterizing and manipulating cells based on their dielectric properties, offering label-free analysis capabilities. Quantitative information from the DEP spectrum, such as transient slope, measure cells’ transition between negative and positive DEP behaviors. In this study, we employed DEP to estimate transient slope of various cell populations, including relatively homogeneous HEK-293 cells, heterogeneous hMSCs, and cancer cells (PC3 and DU145). Our analysis encompassed hMSCs derived from bone marrow, adipose, and umbilical cord tissue, to capture tissue-specific heterogeneity. Transient slope was assessed using two methods, involving linear trendline fitting to different low-frequency regions of the DEP spectrum. We found that transient slope serves as a reliable indicator of cell population heterogeneity, with more heterogeneous populations exhibiting lower transient slopes and higher standard deviations. Validation using cell morphology, size, and stemness further supported the utility of transient slope as a heterogeneity metric. This label-free approach holds promise for advancing cell sorting, biomanufacturing, and personalized medicine.

Hilbert Transform Reveals Unusual Modulation in Delta Scuti Star KIC 10407873

We report a δ Scuti star, KIC 10407873, exhibiting significant amplitude modulation. Fourier analysis of Kepler long-cadence data (i.e., Q0-Q17, spanning 1471 days) reveals two distinct features: harmonic series of frequencies in the low-frequency region and the frequencies of the split triplet lines in the high-frequency region. Using the Hilbert transform method, we separated the amplitude modulation signals, obtaining precise parameters for the two modulation frequencies. For the harmonic series of frequencies in the low-frequency region, we isolated them through a prewhitening process. Based on the residual segmented spectrum and the phase-folding diagram, we propose that these harmonic series of frequencies may be caused by temperature inhomogeneity on the stellar surface and stellar rotation. The subsequent phase evolution diagrams we generated, combined with LAMOST’s vsini data, further support this hypothesis. Consequently, this suggests that the cause of amplitude modulation in the high-frequency region is unrelated to stellar rotation. Finally, we discussed the information potentially carried by the isolated modulation signals, as well as the similarities between the star’s dual-amplitude modulation and the periodically modulated Tseraskaya–Blazhko effect.

A 62Hz high-Q 4-spiral mechanical resonator fabricated of a silicon wafer.

High purity silicon is considered as the test mass material for future cryogenic gravitational-wave detectors, in particular Einstein Telescope-low frequency and LIGO Voyager [(LIGO) Laser Interferometer Gravitational-Wave Observatory]. To reduce the thermal noise of the test masses, it is necessary to study the sources of corresponding losses. Mechanical resonators with frequencies 300 Hz-6kHz are successfully used for studying, for example, losses in optical coatings of the test mass. However, the frequency range of the interferometric gravitational-wave detectors starts at 10Hz, and the investigation of different dissipation mechanisms for the test masses in the low-frequency region is relevant. We developed a design of a four-spiral mechanical resonator for studying dissipation and noise in the low frequency range. The resonator was fabricated of a 3-in. silicon wafer using an anisotropic wet etching technique. It consists of four spiral cantilevers on a common base, linked together with additional coupling beams for increasing the frequency difference between the resonator normal modes corresponding to the fundamental flexural off-plane mode of a single spiral cantilever. The measured Q-factor of the 62Hz out-of-phase mode of the four-spiral silicon resonator at room temperature is limited mainly by the thermoelastic loss. At 123K, the measured Q = (1.5 ± 0.3) × 107. The main contribution to the total loss comes from clamping and surface losses.

Single-mode wave decay

The usual approach on electrostatic wave decay process for a weak beam-plasma system considers two different wave modes interplaying, the Langmuir and ion-sound mode. In the present paper, a single-mode approach is shown to be feasible for conditions where the respective dispersion relations undergo topological changes. Numerical solutions for the dispersion relation of a beam-plasma system are presented, supporting the modeling of an analytic dispersion relation of a single wave mode. This wave mode is accounted for in the kinetic equations for particles and waves, which rule the evolution of the system. The results are compared against the two-wave mode approach using Langmuir and ion-sound waves, within the context of weak turbulence theory. It is found that the single-mode approach can account for the basic features of particles and waves, since the single mode exhibits both low and high frequency regions, which ultimately play the roles of ion-sound and Langmuir modes, respectively.

Enhancing sound transmission loss of polyurethane foams using waste soda glass filler

Sound transmission mechanisms and sound transmission losses are of great importance in providing acoustic comfort. Research has focused on developing materials and structures that will reduce sound transmission loss. The increasing amount of waste disrupts the ecological balance; this situation brings about global warming, air and soil pollution. These environmental effects negatively affect the lives of all living things, especially humans, and also harm the economy. Combating global pollution has become one of the primary goals of scientists. Recycling provides significant economic benefits as well as protecting both human health and natural resources. In this study, polyurethane foams used in the automotive industry and many other areas were produced by adding waste soda glass powder at various rates while keeping the isocyanate/polyol ratio constant. The durability of the produced foams was tested by apparent density measurement, wettability by contact angle analysis, organic bond structures by FT-IR spectroscopy and acoustic properties by sound transmission loss analysis. It was determined that soda glass powder did not react with the foams and that the produced foams exhibited hydrophobic properties. The acoustic properties of the filler foams were higher than the neat foam in almost the entire frequency range (65-6300 Hz). The sample coded PU-SG4 is the sample that exhibits the best acoustic properties by reaching 9.28 dB, 9.10 dB and 13.48 dB values in the low, medium and high frequency regions, respectively. In the high frequency range region, all of the soda glass added foam composites reached a sound transmission loss of over 13 dB.

GDTE-based crack diagnosis for planetary gear: Mechanism, validation, and advantages compared to vibration-based technology

Effective health monitoring and fault diagnosis technologies are crucial to timely grasping the operation status of the planetary gear train (PGT). In this study, the mechanism for global dynamic transmission error (GDTE)-based crack diagnosis of PGT is revealed from dynamic responses and validated through experiments, and the advantages of this new technique are compared with the commonly used vibration-based technology. Initially, a dynamic model of the PGT considering various crack degrees and transfer path effects is established, and the effectiveness of the model response is verified through experiment. Subsequently, GDTE and vibration signals under different crack conditions are statistically analyzed in time domain and frequency domain to evaluate the differences in the ability to reveal gear failure information. Ultimately, the reasons for the different distribution of fault characterization information in the two signals are explained from a dynamic perspective. The results show that GDTE-based fault diagnosis exhibits greater sensitivity to gear crack degree compared to vibration-based monitoring technology, with both time and frequency domain responses containing richer fault characteristic information, particularly in low-frequency regions. The fault characteristics concentrated in higher-frequency regions in the vibration signal are mainly caused by the modulation between gear crack shock and the gear single and double tooth alternating meshing shock. Conversely, fault frequencies in GDTE signals are mainly found in low-frequency regions, as fault shocks in GDTE signals directly correlate with the rotational frequency of the cracked gear. Modulation effects and attenuation on the transfer path are identified as the main reasons for the weaker representation of gear fault information in vibration signals compared to GDTE signals.

Phonon-mediated superconductivity in orthorhombic XS (X = Nb, Ta and W)

Abstract The unique three-dimensional (3D) orthorhombic NbS ($o$-NbS) synthesized in 1969 has recently been experimentally confirmed to be a superconductor [Ruan B B $et$ $al.$ 2023 Phys. Rev. B 108 174517]. However, there is currently no theoretical research on its superconducting mechanism. In this work, we investigate superconducting properties of $o$-NbS from first-principles calculations. Based on Eliashberg equation, it is found that the superconductivity is mainly originated from the coupling between the electrons of Nb-$4d$ orbitals and the vibrations of Nb atoms in the low-frequency region and the vibrations of S atoms in the high-frequency region. A superconducting transition temperature ($T_{c}$) of 10.7 K is obtained, which is close to the experimental value and higher than most transition-metal chalcogenides (TMCs). The calculated thermodynamic properties in the superconducting state, such as specific heat, energy gap, isotope coefficient, etc. also indicate that $o$-NbS is a conventional phonon-mediated superconductor. These results are consistent with recent experimental reports and provide a good understanding on superconducting mechanism of $o$-NbS. Furthermore, the TMCs of $o$-TaS and $o$-WS are also investigated, which belong to the same and neighboring groups as Nb, and find that $o$-$X$S ($X$ = Ta and W) are also phonon-mediated superconductors with $T_{c}$ of 8.9 K and 7.2 K, respectively.

How good are the dynamical results obtained through different terminators of a continued fraction approach?

Extrapolation procedures for obtaining higher order recurrants within the Method of Recurrence Relation have been analyzed considering one-dimensional spin-1/2 quantum systems comprising the isotropic XY model, the random transverse Ising model, and the isotropic Heisenberg model. The first six recurrants have already been computed for the XY model, as well as nine recurrants for the random transverse Ising model, and fourteen recurrants for the Heisenberg model. Nevertheless, from the exact solution of the autocorrelation function and its spectral density, it has been possible here to exactly compute all orders of the moments and recurrants for the XY model. An analytical expression for the recurrants of the XY model has also been proposed, which is able to furnish all of the recurrants, of any order, to within only 0.03 percent error. An extrapolation process has then been employed to analyze the autocorrelation functions and their spectral densities for all three models. It has been noticed that, as expected, the more recurrants are estimated the longer is the timespan of the computed autocorrelation function. However, the timespan saturates and becomes insensitive as more recurrants are taken into accout. On the other hand, the autocorrelation function needs a high number of recurrants in order to obtain a quantitative account of the spectral function. Even so, the behavior of the spectral density still remains, in cases where just a few recurrants are exactly known, not completely clear in the low frequency region.

Multi-exposure image fusion for phase enhancement in digital holographic microscopy

Phase information in single exposure images is often lost for specimens with non-uniform transmittance. To address this issue, we propose a multi-exposure image fusion phase enhancement technique for holographic images. In this process, exposure time is varied to acquire 11 groups of four-step phase-shifted holographic images from a common sampling area. The resulting images are then decomposed using a wavelet transform. Maximum phase information from the low-frequency regions and regional features from the high-frequency regions were employed to avoid discontinuities in subsequent reconstructions, caused by regional truncation. Holographic images were then obtained after multi-exposure image fusion using a wavelet fusion method. Corresponding phase information was acquired by reconstructing fused holographic images using a four-step phase shifting technique. Experimental results showed that for specimens with non-uniform transmittance, this approach increased information entropy by 4.2%, edge density by 5%, and contrast by 3.8%, in comparison with the single-exposure digital holography phase reconstruction method. This result suggests that clarity and information content are improved, thereby enhancing the reconstructed phase.

A straight-arch-straight beam tandem quasi-zero stiffness structure

Extremely low dynamic stiffness is essential for the successful utilization of quasi-zero stiffness (QZS) structures for vibration isolation, energy harvesting, and micromechanical sensing. However, most conventional QZS structures are based on a parallel connection of positive and negative stiffness mechanisms, which poses challenges for stiffness matching, structure design, and fabrication. We propose a QZS structure based on a straight-arch-straight (SAS) tandem connection, in which the integrated design of the structure overcomes the problem of stiffness matching, and more importantly, the simple design of the structure greatly reduces the difficulty of fabrication and enables the design of a wide range of load-carrying capacity by only adjust the ratio of the length of the straight beam to the arch and the ratio of the height of the arch to the thickness. The symmetric deformation of the SAS structure extends the working range of the QZS structure, which can be further extended several times or divided into several different QZS intervals by connecting several identical or different SAS units in parallel. The experimental results show that the SAS structure has excellent vibration isolation performance in the low-frequency region, and more importantly, the low preload requirement also provides an important reference for structural design in the field of micromechanical sensing.

Effects of mooring failure on the dynamic behavior of the power capture platforms

In recent years, for enhancing the ocean energy capture, it has been prevail to combine multiple wave energy converters (WECs) with the floating platforms. A power capture platform concepts is proposed in this paper based on the point-absorber WEC array and the SPIC semi-submersible platform. The present study conducts the time-domain dynamic analysis on the performance of the power capture platforms with mooring failure. After the validation of the numerical models, ANSYS-AQWA is employed to investigate the platform motion response, the remaining mooring lines' tension response, and the WEC array's power output. The results show that the platform motion and the remaining mooring lines' tension appear significant transient overshoots after mooring failure. The mean motion response of the platform increases because of the reduction of mooring stiffness. Meanwhile, the energy distribution of the platform slow-drift and roll motions at the low-frequency region increases as well. Moreover, the mooring line tension adjacent to the failed mooring line increases significantly, while that of other mooring lines decreases. Notably, mooring failure has slight effects on the WEC array's energy conversion performance, and the total absorbed power among Model 2 is more than that among Model 1. These important findings provide some insights into the design of power capture platforms. Moreover, to ensure the floating system stable and reliable, the effects of mooring failure and the resulting changes should be evaluated in advance.

Image inpainting for periodic discrete density defects via frequency analysis and an adaptive transformer-GAN network

Image inpainting based on deep learning has made significant progress in addressing regular and coherent irregular defects. However, little has been studied on periodic discrete density (PDD) defects that are prevalent in microscopic images obtained by advanced instruments like transmission electron microscopes (TEM) and scanning tunneling microscopes (STM). The PDD defects usually introduce low-frequency noise in the fast Fourier transform (FFT) images, preventing the extraction of useful information particularly in the low-frequency regions. Despite its significant impact, no method has been reported to date to efficiently remove the PDD-induced noise from the FFT of high-resolution microscopic images. In this study, we introduced a novel GAN-based two-stage network (FGTNet), a novel coarse-to-fine inpainting framework, which is built upon the architecture of Generative Adversarial Networks (GAN) and transformer blocks. By integrating the information from both frequency and spatial domains, contextual structures are preserved and high-frequency details are generated in our method. We also proposed an adaptive-window transformer block (A-LeWin) to enhance the spatial feature representation and to fully use the information around the defects. To validate our approach, we constructed a specialized microscopic image dataset with 2730 training samples and 105 testing samples. For comparison, we also extended the experiments to the public Describable Texture Dataset (DTD) and coherence defects that are often discussed in the field of image inpainting. The experiment results indicate that our method performs well on six pixel-level and perceptual-level metrics, and shows the best performance and visual effect of coherent texture.

Theoretical exploration on the combined effect of isoelectron B-N bonds and B-N resonance skeleton on the thermally activated delayed fluorescence property

The multiple resonance thermally activated delayed fluorescence (MR-TADF) materials has become a hot spot in recent years depending on their potential in achieving an internal quantum efficiency of 100 %. The combined effect of para B-N resonance skeleton and isoelectron B-N bonds on the TADF property was investigated in details by employing density functional theory/time-dependent density functional theory (DFT/TDDFT) in this work based on four polycyclic aromatic molecules. The results show that isoelectron B-N bonds are favorable to the enhancement of spin orbital coupling (SOC) constants between the first singlet state (S1) and the first triplet state (T1), while para B-N resonance skeleton is more conducive to reducing the energy gap between S1 and T1 (ΔEST) through realizing short-range charge transfer character and keeping electron and hole localized at different atoms. Accordingly the combination of isoelectron B-N bonds and para B-N resonance skeleton in m[B-N]N1 and m[B-N]N2 could realize faster intersystem crossing (ISC) and reverse intersystem crossing (RISC) processes through larger SOC and lower ΔEST compared with BCz-BN and NBN-2 which only contain para B-N resonance skeleton and isoelectron B-N bonds, respectively. At the same time, the para B-N resonance skeleton help to stabilize the structure of polycyclic aromatic hydrocarbons and localize the vibration in low frequency region during emission from S1 to ground state. Thus larger nonradiative rates induced by the rotation of carbazole and tert-butyl carbazole in low frequency region in m[B-N]N1 and m[B-N]N2 could be easily reduced by replacing them by small functional group such as electron-donating (-CH3) and electron-withdrawing (-CN) groups. Therefore, we can obtain high TADF efficiency through combining para B-N resonance skeleton and isoelectron B-N bonds and suppressing low-frequency vibrations as in our designed molecules m[B-N]CH3 and m[B-N]CN.

Attenuation enhancement for the inertial amplification metamaterial using multiple local resonators

The bandgap generated by inertial amplification metamaterial (IAM) features broad width and low-frequency, but weak attenuation strength within a large part of the bandgap. Introducing local resonators is the most common way to enhance low-frequency vibration attenuation characteristics. However, discrete bandgaps are usually observed for the metamaterials containing non-uniform resonators. In this paper, two resonators are attached to the baseline mass and the inertial amplifier of IAM, respectively. The merging of locally resonant bandgaps is realized by coupling them with the inertial amplification bandgap. The attenuation characteristics of the coupled bandgap are first studied, including the number and positions of attenuation peaks. Then, the methods to enhance the attenuation strength are explored. It is found that two attenuation peaks are attributed to zero effective stiffness while another one is induced by infinite effective mass. The conditions for the triple peaks occurring in a single bandgap are derived according to the rational polynomial form of the dispersion relation. Additionally, the attenuation strength within the coupled triple-peak bandgap is enhanced by increasing the mass of the resonator on the baseline mass and adjusting the coupling degree between the inertial amplification and the resonance of the local resonator on the inertial amplifier. Finally, to overcome the decrease in attenuation level when the attenuation-enhanced region widened, a supercell with high attenuation strength is designed by combining unit cells with different attenuation peaks. Compared to the IAM with double-peak bandgap in the previous study, the minimum attenuation level in the enhanced region is increased by 84%. This study gives guidance to enhance the attenuation characteristics of metamaterials in the low-frequency region.

Comparison Study on the Fatigue Damage of a Container Ship Applying Hydroelastic Fatigue Analysis Procedures of LR and BV Classification Societies

<i>Container ships, which have hatch openings, are subject to low natural frequencies and exhibit elastic behavior due to wave loads, a phenomenon referred to as the hydroelastic effect. Classification societies have established hydroelastic fatigue analysis procedures to address the increased fatigue damage caused by this effect. This study compares the fatigue damage increase ratios at the hatch coaming top corners according to the procedures provided by Lloyd's Register (LR) and Bureau Veritas (BV). The weight distribution was adjusted using mass and interpolation elements, and normal mode analysis was conducted to obtain the natural frequencies and mode shapes of the ship, which were then used in frequency-domain hydroelastic motion analysis. The fatigue analysis was performed based on LR and BV procedures, using mode response amplitude operators (RAOs) and hydrodynamic coefficients derived from the hydroelastic motion analysis. Despite the differing methodologies between LR and BV, similar stress RAOs were obtained, with the midship showing a higher fatigue damage increase ratio than the forward and aft ends. For the LR procedure, more modes are needed for greater accuracy at the aft end, and for the BV procedure, further investigation is required to address the unreasonable response of the dynamic stress RAO in the low-frequency region, which is distant from the resonance frequency.</i>

Electric Response of a Negative Dielectric Anisotropy Nematic Liquid Crystal Doped with Ionic Dopant

The electrical properties measurements have been performed in a homogeneous alignment parallelepiped cell containing 4-methoxy benzylidene- 4-butylaniline (MBBA) liquid crystal doped with 0.02%wt tetrabutylammonium bromide (TBAB). The measurement of the complex permittivity was conducted in the nematic phase, covering a frequency range of 42 Hz to 5 MHz. A new relaxation mode was observed in the low-frequency region, which was not present in pure MBBA. The obtained dielectric dispersion could be fitted using the double Cole–Cole formula to determine the relaxation frequencies. The steady-state current exhibited a nonlinear dependence on the applied voltage, and hysteresis was observed in the transient current-voltage characteristic curve.

Synthesis, Characterization and Biological Studies of Gemifloxacin Mesylate with Nickel(II) and Copper(II)

Gemifloxacin mesylate, a fourth-generation fluoroquinolone-type antibiotic, is widely used for community treatment of acquired pneumonia and severe bacterial infections. The Cu(II) and Ni(II) complexes of gemifloxacin mesylate were synthesized by refluxing an aqueous solution of the ligand with the required amount of metal(II) salts in a round bottom flask with 2:1 (L:M) ratio in an oil bath at 90 ºC with a continuous stirring for 4 h. The mixture was kept overnight to obtain a coloured solid complex. The synthesized metal(II) complexes were characterized by physico-chemical parameters and spectral analyses, including UV-Vis, FT-IR and 1H NMR. The structures of the complexes were further confirmed by elemental (CHNS) and TG-DTA analyses. The spectral findings revealed that metal-ligand interaction has successfully occurred where the ligand acted as a bidentate chelate in the synthesized metal(II) complexes. The IR studies showed that upon complexation the characteristic carboxylic stretching frequency at 1714 cm-1 disappeared and the pyridone stretching frequency shifted to a lower frequency region. The 1H NMR data of the complexes confirm the effective interaction between the metal and the ligand via 3-carboxyl group and 4-oxo groups. The thermal and elemental analyses data were also in agreement with the proposed interaction. The ligand as well as its metal(II) complexes showed significant activity against all the studied 11 bacterial strains and one of the fungal strains, Candida sp.

Structural, Microstructural, Dielectric and Ac-conductivity of CaTi1-xFexO3 Multiferroic Materials Synthesized by Solid State Method

In this study, the structural, microstructural, dielectric and conductivity properties of Fe-doped CaTiO3 (CT) ceramic were investigated. These ceramics were successfully synthesized using the conventional solid-state method. The X-ray diffraction and Rietveld refinement results showed that the ceramics at x=0.0, 0.1, 0.2 and 0.3 crystalized in the orthorhombic phase with the Pmmm space group. While for x=0.4, 0.5 and 0.6, the phase formation changes from orthorhombic to tetragonal phase with P4/mmm group space. The SEM results revealed a semi-spherical shape of grain for lower Fe content (≤0.4), while at x=0.5 and 0.6 an agglomeration phenomenon is observed and the observed density of the sample at x=0.5 is higher than the other ceramics. The dielectric properties were studied as function of frequency and temperature. The dielectric permittivity (ɛ’r) decreases as function of frequency at lower frequency region and remain almost independent of frequency at high frequency region in the whole temperature range of R.T–520 °C. Each converges at high frequency (>105 Hz) for all the temperatures. The evolution of ɛ’r as function of temperature for pure CT ceramic showed a stability at large range of temperature (from R.T to 250°C). For substituted ceramics, we obtained a phase transition which shifted to the lower temperature with the increase of Fe content. And the value of ɛ’r, increases for Fe-doped CT ceramics and reaches a maximal value for x=0.5 which is 50 time bigger than the pure ceramic. The AC conductivity, σAC, is found to increase rapidly as a function of frequency, at low frequency region, and increases linearly at high frequency region, which confirms the hopping of electrons related to the conduction mechanism. The σAC evolution is found to follow the Jonscher’s law and the s exponent decreased with the increasing temperature which is related to the correlated barrier height (CBH) model. And the σAC values increase with the increases of Fe content.

Research on the Electrochemical Impedance Spectroscopy Evolution of Sodium-Ion Batteries in Different States.

Sodium-ion batteries (SIBs) have emerged as a promising alternative to lithium-ion batteries (LIBs) due to the abundant availability of sodium, lower costs, and comparable electrochemical performance characteristics. A thorough understanding of their performance features is essential for the widespread adoption and application of SIBs. Therefore, in this study, we investigate the output characteristics and electrochemical impedance spectroscopy (EIS) features of sodium-ion batteries (SIBs) under various states. The research results show that, unlike conventional lithium iron phosphate (LFP) batteries, SIBs exhibit a strong linear relationship between state of charge (SOC) and open-circuit voltage (OCV) across various SOC and temperature conditions. Additionally, the discharge capacity of the battery remains relatively stable within a temperature range of 15 °C to 35 °C; when the temperatures are outside this range, the available capacity of the sodium-ion battery reduces significantly. Moreover, the EIS profiles in the high-frequency region are predominantly influenced by the ohmic internal resistance, which remains largely unaffected by SOC variations. In contrast, the low-frequency region demonstrates a significant correlation between SOC and impedance, with higher SOC values resulting in reduced impedance, indicated by smaller semicircle radii in the EIS curves. This finds highlights that EIS profiling can effectively monitor SOC and state of health (SOH) in SIBs, offering a clear correlation between impedance parameters and the battery's operational state. The research not only advances our understanding of the electrochemical properties of SIBs but also provides a valuable reference for the design and application of sodium-ion battery systems in various scenarios.

“Borrow-force-attack-force” by multi-scale elastic metamaterial with nonlinear damping

The powerful energy carried by low-frequency vibration is often challenging to be effectively attenuated using traditional damping materials. If low-frequency vibration can be controlled through the energy carried by the excitation itself, the cost of achieving ultra-wide low-frequency vibration control would be significantly reduced. To this end, this paper constructs a multi-scale elastic metamaterial with nonlinear damping (MEMND) to achieve the efficient suppression of ultra-wide low-frequency vibration through its unique transmission characteristics and the effect of “borrow-force-attack-force” (leveraging the excitation to dampen vibration), which is amplified with increasing external excitation. Theoretical, simulation, and experimental results demonstrate that MEMND can achieve over 10 dB damping enhancement at the expense of losing a small amount of the bandgap effect. It exhibits high sensitivity to external excitation in the low-frequency region, offering a promising opportunity for “borrow-force-attack-force”. This work integrates a natural nonlinear damping element into elastic metamaterials and leverages the nonlinear action mechanism of external excitation, presenting a different approach for nonlinear metamaterial design with potential engineering applications.