High‑Entropy Layered Oxide Cathode Enabling High‑Rate for Solid‑State Sodium‑Ion Batteries

Na-ion O3-type layered oxides are prospective cathodes for Na-ion batteries due to high energy density and low-cost.Nevertheless,such cathodes usually suffer from phase transitions,sluggish kinetics and air instability,making it difficult to achieve high performance solid-state sodium-ion batteries.Herein,the high-entropy design and Li doping strategy alleviate lattice stress and enhance ionic conductivity,achieving high-rate performance,air stability and electrochemically thermal stability for Na_(0.95)Li_(0.06)Ni_(0.25)Cu_(0.05)Fe_(0.15)Mn_(0.49)O_(2).This cathode delivers a high reversible capacity(141 mAh g^(−1)at 0.2C),excellent rate capability(111 mAh g^(−1)at 8C,85 mAh g^(−1)even at 20C),and long-term stability(over 85%capacity retention after 1000 cycles),which is attributed to a rapid and reversible O3–P3 phase transition in regions of low voltage and suppresses phase transition.Moreover,the compound remains unchanged over seven days and keeps thermal stability until 279℃.Remarkably,the polymer solid-state sodium battery assembled by this cathode provides a capacity of 92 mAh g^(−1)at 5C and keeps retention of 96%after 400 cycles.This strategy inspires more rational designs and could be applied to a series of O3 cathodes to improve the performance of solid-state Na-ion batteries.

Investigation of anisotropic strength criteria for layered rock mass

Layered rock mass is a type of engineering rock mass with sound mechanical anisotropy,which is generally unfavorable to the stability of underground works.To investigate the strength anisotropy of layered rock,the Mohr-Coulomb and Hoek-Brown criteria are introduced to establish the two transverse isotropic strength criteria based on Jaeger's single weak plane theory and maximum axial strain theory,and parameter determination methods.Furthermore,the sensitivity of strength parameters(K 1,K 2,and K 3)that are used to characterize the anisotropy strength of non-sliding failure involved in the strength criteria and confining pressure are investigated.The results demonstrate that strength parameters K 1 and K 2 affect the strength of layered rock samples at all bedding angles except for the bedding angle of 90°and the angle range that can cause the shear sliding failure along the bedding plane.The strength of samples at any bedding angle decreases with increasing K 1,whereas the opposite is for K 2.Except for bedding angles of 0°and 90°and the bedding angle range that can cause the shear sliding along the bedding plane,K 3 has an impact on the strength of rock samples with other bedding angles that the specimens'strength increases with increase of K 3.In addition,the strength of the rock sample increases as confining pressure rises.Furthermore,the uniaxial and triaxial tests of chlorite schist samples were carried out to verify and evaluate the strength criteria proposed in the paper.It shows that the predicted strength is in good agreement with the experimental results.To test the applicability of the strength criterion,the strength data of several types of rock in the literature are compared.Finally,a comparison is made between the fitting effects of the two strength criteria and other available criteria for layered rocks.

Probabilistic analysis of tunnel face seismic stability in layered rock masses using Polynomial Chaos Kriging metamodel

Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.

Difficulties, strategies, and recent research and development of layered sodium transition metal oxide cathode materials for high-energy sodium-ion batteries

Energy-storage systems and their production have attracted significant interest for practical applications.Batteries are the foundation of sustainable energy sources for electric vehicles(EVs),portable electronic devices(PEDs),etc.In recent decades,Lithium-ion batteries(LIBs) have been extensively utilized in largescale energy storage devices owing to their long cycle life and high energy density.However,the high cost and limited availability of Li are the two main obstacles for LIBs.In this regard,sodium-ion batteries(SIBs) are attractive alternatives to LIBs for large-scale energy storage systems because of the abundance and low cost of sodium materials.Cathode is one of the most important components in the battery,which limits cost and performance of a battery.Among the classified cathode structures,layered structure materials have attracted attention because of their high ionic conductivity,fast diffusion rate,and high specific capacity.Here,we present a comprehensive review of the classification of layered structures and the preparation of layered materials.Furthermore,the review article discusses extensively about the issues of the layered materials,namely(1) electrochemical degradation,(2) irreversible structural changes,and(3) structural instability,and also it provides strategies to overcome the issues such as elemental phase composition,a small amount of elemental doping,structural design,and surface alteration for emerging SIBs.In addition,the article discusses about the recent research development on layered unary,binary,ternary,quaternary,quinary,and senary-based O3-and P2-type cathode materials for high-energy SIBs.This review article provides useful information for the development of high-energy layered sodium transition metal oxide P2 and O3-cathode materials for practical SIBs.

Dynamic response and failure process of horizontal-layered fractured structure rock slope under strong earthquake

Rock slope with horizontal-layered fractured structure(HLFS)has high stability in its natural state.However,a strong earthquake can induce rock fissure expansion,ultimately leading to slope failure.In this study,the dynamic response,failure mode,and spectral characteristics of rock slope with HLFS under strong earthquake conditions were investigated based on the large-scale shaking table model test.On this basis,multiple sets of numerical calculation models were further established by UDEC discrete element program.Five influencing factors were considered in the parametric study of numerical simulations,including slope height,slope angle,bedding-plane spacing and secondary joint spacing as well as bedrock dip angle.The results showed that the failure process of rock slope with HLFS under earthquake action is mainly divided into four phases,i.e.,the tensile crack of the slope shoulder joints and shear dislocation at the top bedding plane,the extension of vertical joint cracks and increase of shear displacement,the formation of step-through sliding surfaces and the instability,and finally collapse of fractured rock mass.The acceleration response of slopes exhibits elevation amplification effect and surface effect.Numerical simulations indicate that the seismic stability of slopes with HLFS exhibits a negative correlation with slope height and angle,but a positive correlation with bedding-plane spacing,joint spacing,and bedrock dip angle.The results of this study can provide a reference for seismic stability evaluation of weathered rock slopes.

Layered Structural PBAT Composite Foams for Efficient Electromagnetic Interference Shielding

The utilization of eco-friendly,lightweight,high-efficiency and high-absorbing electromagnetic interference(EMI)shielding composites is imperative in light of the worldwide promotion of sustainable manufacturing.In this work,magnetic poly(butyleneadipate-coterephthalate)(PBAT)microspheres were firstly synthesized via phase separation method,then PBAT composite foams with layered structure was constructed through the supercritical carbon dioxide foaming and scraping techniques.The merits of integrating ferroferric oxideloaded multi-walled carbon nanotubes(Fe3O4@MWCNTs)nanoparticles,a microcellular framework,and a highly conductive silver layer have been judiciously orchestrated within this distinctive layered configuration.Microwaves are consumed throughout the process of“absorption-reflection-reabsorption”as much as possible,which greatly declines the secondary radiation pollution.The biodegradable PBAT composite foams achieved an EMI shielding effectiveness of up to 68 dB and an absorptivity of 77%,and authenticated favorable stabilization after the tape adhesion experiment.

Enhancing the stability of Ni Fe-layered double hydroxide nanosheet array for alkaline seawater oxidation by Ce doping

Electrocatalytic hydrogen production from seawater holds enormous promise for clean energy generation.Nevertheless,the direct electrolysis of seawater encounters significant challenges due to poor anodic stability caused by detrimental chlorine chemistry.Herein,we present our recent discovery that the incorporation of Ce into Ni Fe layered double hydroxide nanosheet array on Ni foam(Ce-Ni Fe LDH/NF)emerges as a robust electrocatalyst for seawater oxidation.During the seawater oxidation process,CeO_(2)is generated,effectively repelling Cl^(-)and inhibiting the formation of Cl O-,resulting in a notable enhancement in the oxidation activity and stability of alkaline seawater.The prepared Ce-Ni Fe LDH/NF requires only overpotential of 390 m V to achieve the current density of 1 A cm^(-2),while maintaining long-term stability for 500 h,outperforming the performance of Ni Fe LDH/NF(430 m V,150 h)by a significant margin.This study highlights the effectiveness of a Ce-doping strategy in augmenting the activity and stability of materials based on Ni Fe LDH in seawater electrolysis for oxygen evolution.

Pile foundation in alternate layered liquefiable and non-liquefiable soil deposits subjected to earthquake loading

Pile foundations are still the preferred foundation system for high-rise structures in earthquake-prone regions.Pile foundations have experienced failures in past earthquakes due to liquefaction.Research on pile foundations in liquefiable soils has primarily focused on the pile foundation behavior in two or three-layered soil profiles.However,in natural occurrence,it may occur in alternative layers of liquefiable and non-liquefiable soil.However,the experimental and/or numerical studies on the layered effect on pile foundations have not been widely addressed in the literature.Most of the design codes across the world do not explicitly mention the effect of sandwiched non-liquefiable soil layers on the pile response.In the present study,the behavior of an end-bearing pile in layered liquefiable and non-liquefiable soil deposit is studied numerically.This study found that the kinematic bending moment is higher and governs the design when the effect of the sandwiched non-liquefied layer is considered in the analysis as opposed to when its effect is ignored.Therefore,ignoring the effect of the sandwiched non-liquefied layer in a liquefiable soil deposit might be a nonconservative design approach.

Interception of Layered LP-N and HLP-N at Ambient Conditions by Confined Template

We propose a feasible strategy of intercepting the layered polymeric nitrogen(LP-N)and hexagonal layered polymeric nitrogen(HLP-N)at ambient conditions by using the confinement templates.The stable mechanism of confined LP-N and HLP-N at ambient conditions is revealed.

Defective Nickel-Iron Layered Double Hydroxide for Enhanced Photocatalytic NO Oxidation with Significant Alleviation of NO2 Production

Photocatalysis offers a sustainable means for the oxidative removal of low concentrations of NOx(NO,NO2,N2O,N2O5,etc.)from the atmosphere.Layered double hydroxides(LDHs)are promising candidate photocatalysts owing to their unique layered and tunable chemical structures and abundant surface hydroxide(OH)moieties,which are hydroxyl radical(OH)precursors.However,the practical applications of LDHs are limited by their poor charge-separation ability and insufficient active sites.Herein,we developed a facile N_(2)H_(4)-driven etching approach to introduce dual Ni^(2+)and OHvacancies(Niv and OHv,respectively)into NiFe-LDH nanosheets(hereafter referred to as NiFe-LDH-et)to facilitate improved charge-carrier separation and active Lewis acidic site(Fe^(3+)and Ni^(2+)exposed at OHv)formation.In contrast to inert pristine LDH,NiFe-LDH-et actively removed NO under visible-light illumination.Specifically,Ni_(76)Fe_(24)-LDH-et etched with 1.50 mmol·L^(-1)N_(2)H_(4)solution removed 32.8%of the NO in continuously flowing air(NO feed concentration:500 parts per billion(ppb))under visible-light illumination,thereby outperforming most reported catalysts.Experimental and theoretical data revealed that the dual vacancies promoted the production of reactive oxygen species(O_(2)·^(-)andOH)and the adsorption of NO on the LDH.In situ spectroscopy demonstrated that NO was preferentially adsorbed at Lewis acidic sites,particularly exposed Fe^(3+)sites,converted into NO+,and subsequently oxidized to NO3without the notable formation of the more toxic intermediate NO2,thereby alleviating risks associated with its production and emission.

Impact of Transition Metal Layer Vacancy on the Structure and Performance of P2 Type Layered Sodium Cathode Material

This study explores the impact of introducing vacancy in the transition metal layer of rationally designed Na_(0.6)[Ni_(0.3)Ru_(0.3)Mn_(0.4)]O_(2)(NRM)cathode material.The incorporation of Ru,Ni,and vacancy enhances the structural stability during extensive cycling,increases the operation voltage,and induces a capacity increase while also activating oxygen redox,respectively,in Na_(0.7)[Ni_(0.2)V_(Ni0.1)Ru_(0.3)Mn_(0.4)]O_(2)(V-NRM)compound.Various analytical techniques including transmission electron microscopy,X-ray absorption near edge spectroscopy,operando X-ray diffraction,and operando differential electrochemical mass spectrometry are employed to assess changes in the average oxidation states and structural distortions.The results demonstrate that V-NRM exhibits higher capacity than NRM and maintains a moderate capacity retention of 81%after 100 cycles.Furthermore,the formation of additional lone-pair electrons in the O 2p orbital enables V-NRM to utilize more capacity from the oxygen redox validated by density functional calculation,leading to a widened dominance of the OP4 phase without releasing O_(2) gas.These findings offer valuable insights for the design of advanced high-capacity cathode materials with improved performance and sustainability in sodium-ion batteries.

Layered metastructure containing freely-designed local resonators for wave attenuation

Combining periodic layered structure with three-dimensional cylindrical local resonators,a hybrid metastructure with improved wave isolation ability was designed and investigated through theoretical and numerical approaches.The metastructure is composed of periodic rubber layers and concrete layers embedded with three-dimensional resonators,which can be freely designed with multi local resonant frequencies to attenuate vibrations at required frequencies and widen the attenuation bandgap.The metastructure can also effectively attenuate seismic responses.Compared with layered rubber-based structures,the metastructure has more excellent wave attenuation effects with greater attenuation and wider bandgap.

Phase engineering of Ni-Mn binary layered oxide cathodes for sodiumion batteries

Nickel-manganese binary layered oxides with high working potential and low cost are potential candidates for sodium-ion batteries,but their electrochemical properties are highly related to compositional diversity.Diverse composite materials with various phase structures of P3,P2/P3,P2,P2/O3,and P2/P3/O3 were synthesized by manipulating the sodium content and calcination conditions,leading to the construction of a synthetic phase diagram for Na_(x)Ni_(0.25)Mn_(0.75)O_(2)(0.45≤x≤1.1).Then,we compared the electrochemical characteristics and structural evolution during the desodiation/sodiation process of P2,P2/P3,P2/03,and P2/P3/O3-Na_(x)Ni_(0.25)Mn_(0.75)O_(2).Among them,P2/P3-Na0.75Ni0.25Mn0.75O2exhibits the best rate capability of 90.9 mA h g^(-1)at 5 C,with an initial discharge capacity of 142.62 mA h g^(-1)at 0.1 C and a capacity retention rate of 78.25%after 100 cycles at 1 C in the voltage range of 2-4.3 V.The observed superior sodium storage performance of P2/P3 hybrids compared to other composite phases can be attributed to the enhanced Na^(+)transfer dynamic,reduction of the Jahn-teller effect,and improved reaction reversibility induced by the synergistic effect of P2 and P3 phases.The systematic research and exploration of phases in Na_(x)Ni_(0.25)Mn_(0.75)O_(2)provide new sights into high-performance nickel-manganese binary layered oxide for sodium-ion batteries.

Surface encapsulation of layered oxide cathode material with NiTiO_(3) for enhanced cycling stability of Na-ion batteries

In Na-ion batteries,O3-type layered oxide cathode materials encounter challenges such as particle cracking,oxygen loss,electrolyte side reactions,and multi-phase transitions during the charge/discharge process.This study focuses on surface coating with NiTiO_(3) achieved via secondary heat treatment using a coating precursor and the surface material.Through in-situ x-ray diffraction(XRD)and differential electrochemical mass spectrometry(DEMS),along with crystal structure characterizations of post-cycling materials,it was determined that the NiTiO_(3) coating layer facilitates the formation of a stable lattice structure,effectively inhibiting lattice oxygen loss and reducing side reaction with the electrolyte.This enhancement in cycling stability was evidenced by a capacity retention of approximately 74%over 300 cycles at 1 C,marking a significant 30%improvement over the initial sample.Furthermore,notable advancements in rate performance were observed.Experimental results indicate that a stable and robust surface structure substantially enhances the overall stability of the bulk phase,presenting a novel approach for designing layered oxide cathodes with higher energy density.

Moiré superlattices arising from growth induced by screw dislocations in layered materials

Moiré superlattices(MSLs) are modulated structures produced from homogeneous or heterogeneous two-dimensional layers stacked with a twist angle and/or lattice mismatch. Enriching the methods for fabricating MSL and realizing the unique emergent properties are key challenges in its investigation. Here we recommend that the spiral dislocation driven growth is another optional method for the preparation of high quality MSL samples. The spiral structure stabilizes the constant out-of-plane lattice distance, causing the variations in electronic and optical properties. Taking SnS_(2) MSL as an example, we find prominent properties including large band gap reduction(~ 0.4 e V) and enhanced optical activity. Firstprinciples calculations reveal that these unusual properties can be ascribed to the locally enhanced interlayer interaction associated with the Moiré potential modulation. We believe that the spiral dislocation driven growth would be a powerful method to expand the MSL family and broaden their scope of application.

Cationic ordering transition in oxygen-redox layered oxide cathodes

Understanding the structural origin of the competition between oxygen 2p and transition-metal 3d orbitals in oxygen-redox(OR)layered oxides is eminently desirable for exploring reversible and high-energy-density Li/Na-ion cathodes.Here,we reveal the correlation between cationic ordering transition and OR degradation in ribbon-ordered P3-Na_(0.6)Li_(0.2)Mn_(0.8)O_(2) via in situ structural analysis.Comparing two different voltage windows,the OR capacity can be improved approximately twofold when suppressing the in-plane cationic ordering transition.We find that the intralayer cationic migration is promoted by electrochemical reduction from Mn^(4+)to Jahn–Teller Mn^(3+)and the concomitant NaO_(6) stacking transformation from triangular prisms to octahedra,resulting in the loss of ribbon ordering and electrochemical decay.First-principles calculations reveal that Mn^(4+)/Mn^(3+)charge ordering and alignment of the degenerate eg orbital induce lattice-level collective Jahn–Teller distortion,which favors intralayer Mn-ion migration and thereby accelerates OR degradation.These findings unravel the relationship between in-plane cationic ordering and OR reversibility and highlight the importance of superstructure protection for the rational design of reversible OR-active layered oxide cathodes.

Mg/Fe site-specific dual-doping to boost the performance of cobalt-free nickle-rich layered oxide cathode for high-energy lithium-ion batteries

Layer-type LiNi0.9Mn0.1O2is promising to be the primary cathode material for lithium-ion batteries(LIBs)due to its excellent electrochemical performance.Unfortunately,the cathode with high nickel content suffers from severely detrimental structural transformation that causes rapid capacity attenuation.Herein,site-specific dual-doping with Fe and Mg ions is proposed to enhance the structural stability of LiNi0.9Mn0.1O2.The Fe3+dopants are inserted into transition metal sites(3b)and can favorably provide additional redox potential to compensate for charge and enhance the reversibility of anionic redox.The Mg ions are doped into the Li sites(3a)and serve as O_(2)^(-)-Mg^(2+)-O_(2)^(-)pillar to reinforce the electrostatic cohesion between the two adjacent transition-metal layers,which further suppress the cracking and the generation of harmful phase transitions,ultimately improving the cyclability.The theoretical calculations,including Bader charge and crystal orbital Hamilton populations(COHP)analyses,confirm that the doped Fe and Mg can form stable bonds with oxygen and the electrostatic repulsion of O_(2)^(-)-O_(2)^(-)can be effectively suppressed,which effectively mitigates oxygen anion loss at the high delithiation state.This dual-site doping strategy offers new avenues for understanding and regulating the crystalline oxygen redox and demonstrates significant potential for designing high-performance cobalt-free nickel-rich cathodes.

A whole process damage constitutive model for layered sandstone under uniaxial compression based on Logistic function

Bedding structural planes significantly influence the mechanical properties and stability of engineering rock masses.This study conducts uniaxial compression tests on layered sandstone with various bedding angles(0°,15°,30°,45°,60°,75°and 90°)to explore the impact of bedding angle on the deformational mechanical response,failure mode,and damage evolution processes of rocks.It develops a damage model based on the Logistic equation derived from the modulus’s degradation considering the combined effect of the sandstone bedding dip angle and load.This model is employed to study the damage accumulation state and its evolution within the layered rock mass.This research also introduces a piecewise constitutive model that considers the initial compaction characteristics to simulate the whole deformation process of layered sandstone under uniaxial compression.The results revealed that as the bedding angle increases from 0°to 90°,the uniaxial compressive strength and elastic modulus of layered sandstone significantly decrease,slightly increase,and then decline again.The corresponding failure modes transition from splitting tensile failure to slipping shear failure and back to splitting tensile failure.As indicated by the modulus’s degradation,the damage characteristics can be categorized into four stages:initial no damage,damage initiation,damage acceleration,and damage deceleration termination.The theoretical damage model based on the Logistic equation effectively simulates and predicts the entire damage evolution process.Moreover,the theoretical constitutive model curves closely align with the actual stress−strain curves of layered sandstone under uniaxial compression.The introduced constitutive model is concise,with fewer parameters,a straightforward parameter determination process,and a clear physical interpretation.This study offers valuable insights into the theory of layered rock mechanics and holds implications for ensuring the safety of rock engineering.

Enhancing layered perovskite ferrites with ultra-high-density nanoparticles via cobalt doping for ceramic fuel cell anode

Nanoparticles anchored on the perovskite surface have gained considerable attention for their wide-ranging applications in heterogeneous catalysis and energy conversion due to their robust and integrated structural configuration.Herein,we employ controlled Co doping to effectively enhance the nanoparticle exsolution process in layered perovskite ferrites materials.CoFe alloy nanoparticles with ultra-high-density are exsolved on the(PrBa)_(0.95)(Fe_(0.8)Co_(0.1)Nb_(0.1))2O_(5+δ)(PBFCN_(0.1))surface under reducing atmosphere,providing significant amounts of reaction sites and good durability for hydrocarbon catalysis.Under a reducing atmosphere,cobalt facilitates the reduction of iron cations within PBFCN_(0.1),leading to the formation of CoFe alloy nanoparticles.This formation is accompanied by a cation exchange process,wherein,with the increase in temperature,partial cobalt ions are substituted by iron.Meanwhile,Co doping significantly enhance the electrical conductivity due to the stronger covalency of the Cosingle bondO bond compared with Fesingle bondO bond.A single cell with the configuration of PBFCN_(0.1)-Sm_(0.2)Ce_(0.8)O_(1.9)(SDC)|SDC|Ba_(0.5)Sr_(0.5)Co_(0.8)Fe_(0.2)O_(3−δ)(BSCF)-SDC achieves an extremely low polarization resistance of 0.0163Ωcm^(2)and a high peak power density of 740 mW cm^(−2)at 800℃.The cell also shows stable operation for 120 h in H_(2)with a constant current density of 285 mA cm^(−2).Furthermore,employing wet C_(2)H_(6)as fuel,the cell demonstrates remarkable performance,achieving peak power densities of 455 mW cm^(−2)at 800℃and 320 mW cm^(−2)at 750℃,marking improvements of 36%and 70%over the cell with(PrBa)_(0.95)(Fe_(0.9)Nb_(0.1))_(2)O_(5+δ)(PBFN)-SDC at these respective temperatures.This discovery emphasizes how temperature influences alloy nanoparticles exsolution within doped layered perovskite ferrites materials,paving the way for the development of high-performance ceramic fuel cell anodes.

Frequency-dependent viscoelasticity effects on the wave attenuation performance of multi-layered periodic foundations

In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6-layer unit-cells,comprising concrete/rubber,concrete/rubber/steel/rubber,and concrete/rubber/steel/rubber/lead/rubber materials,respectively,are taken into account.Also,the viscoelasticity behavior of the rubber is modeled with two factors,i.e.,a frequency-independent(FI)loss factor and a linear frequency-dependent(FD)loss factor.Following the extraction of the complex dispersion curves and the identification of the band gaps(BGs),the simulations of wave transmission in the time and frequency domains are performed using the COMSOL software.Subsequent parametric studies evaluate the effects of the rubber viscoelasticity models on the dispersion curves and the wave transmission for the longitudinal and transverse modes.The results show that considering the rubber viscoelasticity enhances the wave attenuation performance.Moreover,the transverse-mode damping is more sensitive to the viscoelasticity model than its longitudinal counterpart.The 6-layer unit-cell LPF exhibits the lowest BG,ranging from 4.8 Hz to 6.5 Hz.