Suppression of low-frequency ultrasound broadband vibration using star-shaped single-phase metamaterials

In order to suppress the low-frequency ultrasound vibration in the broadband range of 20 k Hz—100 k Hz,this paper proposes and discusses an acoustic metamaterial with low-frequency ultrasound vibration attenuation properties,which is configured by hybrid arc and sharp-angle convergent star-shaped lattices.The effect of the dispersion relation and the bandgap characteristic for the scatterers in star-shaped are simulated and analyzed.The target bandgap width is extended by optimizing the geometry parameters of arc and sharp-angle convergent lattices.The proposed metamaterial configured by optimized hybrid lattices exhibits remarkable broad bandgap characteristics by bandgap complementarity,and the simulation results verify a 99%vibration attenuation amplitude can be obtained in the frequency of20 k Hz—100 k Hz.After the fabrication of the proposed hybrid configurational star-shaped metamaterial by 3D printing technique,the transmission loss experiments are performed,and the experimental results indicate that the fabricated metamaterial has the characteristics of broadband vibration attenuation and an amplitude greater than 85%attenuation for the target frequency.These results demonstrate that the hybrid configurational star-shaped metamaterials can effectively widen the bandgap and realize high efficiency attenuation,which has capability for the vibration attenuation in the application of highprecise equipment.

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

The suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications.To address this concern,a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed.By combining Bloch’s theorem with the finite element method,the band structure is calculated.Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz,with a bandgap ratio exceeding 50%.The first bandgap spans from 169.57 Hz to 216.42 Hz.To reveal the formation mechanism of the bandgap,a vibrational mode analysis is performed.Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations.Additionally,detailed parametric analyses are conducted to investigate the effect ofθ,i.e.,the angle between the protruding corner of the structure and the horizontal direction,on the band structures and the total effective bandgap width.It is found that reducingθis conducive to obtaining lower frequency bandgaps.The propagation characteristics of elastic waves in the structure are explored by the group velocity,phase velocity,and wave propagation direction.Finally,the transmission characteristics of a finite periodic structure are investigated experimentally.The results indicate significant acceleration amplitude attenuation within the bandgap range,confirming the structure’s excellent low-frequency vibration suppression capability.

A bio-inspired spider-like structure isolator for low-frequency vibration

This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator.The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region.The harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental results.The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator.The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 Hz.The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.

Permeability evolution mechanism and the optimum permeability determination of uranium leaching from low-permeability sandstone treated with low-frequency vibration

Low-frequency vibrations can effectively improve natural sandstone permeability,and higher vibration frequency is associated with larger permeability.However,the optimum permeability and permeability evolution mechanism for uranium leaching and the relationship between permeability and the change of chemical reactive rate affecting uranium leaching have not been determined.To solve the above problems,in this study,identical homogeneous sandstone samples were selected to simulate lowpermeability sandstone;a permeability evolution model considering the combined action of vibration stress,pore water pressure,water flow impact force,and chemical erosion was established;and vibration leaching experiments were performed to test the model accuracy.Both the permeability and chemical reactions were found to simultaneously restrict U6þleaching,and the vibration treatment increased the permeability,causing the U6þleaching reaction to no longer be diffusion-constrained but to be primarily controlled by the reaction rate.Changes of the model calculation parameters were further analyzed to determine the permeability evolution mechanism under the influence of vibration and chemical erosion,to prove the correctness of the mechanism according to the experimental results,and to develop a new method for determining the optimum permeability in uranium leaching.The uranium leaching was found to primarily follow a process consisting of(1)a permeability control stage,(2)achieving the optimum permeability,(3)a chemical reactive rate control stage,and(4)a channel flow stage.The resolution of these problems is of great significance for facilitating the application and promotion of lowfrequency vibration in the CO_(2)+O_(2) leaching process.

A low-frequency pure metal metamaterial absorber with continuously tunable stiffness

To address the incompatibility between high environmental adaptability and deep subwavelength characteristics in conventional local resonance metamaterials,and overcome the deficiencies in the stability of existing active control techniques for band gaps,this paper proposes a design method of pure metal vibration damping metamaterial with continuously tunable stiffness for wideband elastic wave absorption.We design a dual-helix narrow-slit pure metal metamaterial unit,which possesses the triple advantage of high spatial compactness,low stiffness characteristics,and high structural stability,enabling the opening of elastic flexural band gaps in the low-frequency range.Similar to the principle of a sliding rheostat,the introduction of continuously sliding plug-ins into the helical slits enables the continuous variation of the stiffness of the metamaterial unit,achieving a continuously tunable band gap effect.This successfully extends the effective band gap by more than ten times.The experimental results indicate that this metamaterial unit can be used as an additional vibration absorber to absorb the low-frequency vibration energy effectively.Furthermore,it advances the metamaterial absorbers from a purely passive narrowband design to a wideband tunable one.The pure metal double-helix metamaterials retain the subwavelength properties of metamaterials and are suitable for deployment in harsh environments.Simultaneously,by adjusting its stiffness,it substantially broadens the effective band gap range,presenting promising potential applications in various mechanical equipment operating under adverse conditions.

A human-sensitive frequency band vibration isolator for heavy-duty truck seats

In this study,a human-sensitive frequency band vibration isolator(HFBVI)with quasi-zero stiffness(QZS)characteristics for heavy-duty truck seats is designed to improve the comfort of heavy-duty truck drivers on uneven roads.First,the analytical expressions for the force and displacement of the HFBVI are derived with the Lagrange equation and d'Alembert's principle,and are validated through the prototype restoring force testing.Second,the harmonic balance method(HBM)is used to obtain the dynamic responses under harmonic excitation,and further the influence of pre-stretching on the dynamic characteristics and transmissibility is discussed.Finally,the experimental prototype of the HFBVI is fabricated,and vibration experiments are conducted under harmonic excitation to verify the vibration isolation performance(VIP)of the proposed vibration isolator.The experimental results indicate that the HFBVI can effectively suppress the frequency band(4-8 Hz)to which the human body is sensitive to vertical vibration.In addition,under real random road spectrum excitation,the HFBVI can achieve low-frequency vibration isolation close to 2 Hz,providing new prospects for ensuring the health of heavy-duty truck drivers.

A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms

Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations,especially in aerospace,mechanical,and architectural engineering,etc.Traditional linear vibration isolation is hard to meet the requirements of the loading capacity and isolation band simultaneously,which limits further engineering application,especially in the low-frequency range.In recent twenty years,the nonlinear vibration isolation technology has been widely investigated to broaden the vibration isolation band by exploiting beneficial nonlinearities.One of the most widely studied objects is the"three-spring"configured quasi-zero-stiffness(QZS)vibration isolator,which can realize the negative stiffness and high-static-low-dynamic stiffness(HSLDS)characteristics.The nonlinear vibration isolation with QZS can overcome the drawbacks of the linear one to achieve a better broadband vibration isolation performance.Due to the characteristics of fast response,strong stroke,nonlinearities,easy control,and low-cost,the nonlinear vibration with electromagnetic mechanisms has attracted attention.In this review,we focus on the basic theory,design methodology,nonlinear damping mechanism,and active control of electromagnetic QZS vibration isolators.Furthermore,we provide perspectives for further studies with electromagnetic devices to realize high-efficiency vibration isolation.

Improved uranium leaching efficiency from low-permeability sandstone using low-frequency vibration in the CO_(2)+O_(2) leaching process

Extraction of uranium from low-permeability sandstone is a long-standing challenge in mining.The improvement of sandstone permeability has therefore become a key research focus to improve the uranium leaching effect.To address the low-permeability problem and corresponding leaching limits,leaching experiments are performed using newly developed equipment that could apply low-frequency vibration to the sandstone samples.The test results indicate that low-frequency vibration significantly improves the uranium leaching performance and permeability of the sandstone samples.The leaching effect of low-frequency vibration treatment is approximately nine times more effective than ultrasonic vibration treatment,whereas the concentration of uranium ions generated without vibration treatment is not detectable.Mathematical model that considers the combined action of physico-mechanical vibration and chemical erosion is established to describe the effect of low-frequency vibration on the permeability.The calculated results are in good agreement with the tested permeability values.This study thus offers a new method to effectively leach more uranium from low-permeability sandstone using CO_(2)+O_(2)and provides an insight into the impact of low-frequency vibration on the uranium leaching process.

Analysis of Low-Frequency Vibrational Modes and Particle Rearrangements in Marginally Jammed Amorphous Solid under Quasi-Static Shear

We present the numerical simulation results of a model granular assembly formed by spherical particles with tIertzian interaction subjected to a simple shear in the athermal quasi-static limit. The stress-strain curve is shown to separate into smooth, elastic branches followed by a subsequent plastic event. Mode analysis shows that the lowest-frequency vibrational mode is more localized, and eigenvalues and participation ratios of low- frequency modes exhibit similar power-law behavior as the system approaches plastic instability, indicating that the nature of plastic events in the granular system is also a saddle node bifurcation. The analysis of projection and spatial structure shows that over 75% contributions to the non-affine displacement field at a plastic instability come from the lowest-frequency mode, and the lowest-frequency mode is strongly spatially correlated with local plastic rearrangements, inferring that the lowest-frequency mode could be used as a predictor for future plastic rearrangements in the disordered system jammed marginally.

Dimensionless Variation of Seepage in Porous Media with Cracks Stimulated by Low-Frequency Vibration

Pulse excitation or vibration stimulation was imposed on the low permeable formation with cracks to enhance the production or injection capacity.During that process,a coupling of wave-induced flow and initial flow in dual-porous media was involved.Researchers had done much work on the rule of wave propagation in fractured porous media,whereas attentions on the variation law of flow in developing low permeable formation with cracks under vibration stimulation were not paid.In this study,the effect of low-frequency vibration on the seepage in dual-porous media was examined for the application of wave stimulation technology in developing reservoirs with natural cracks.A model for seepage of single-phase liquid in porous media with cracks under low-frequency vibration excitation was built by combining wave propagating theory for porous media with cracks and dual-porous media seepage mechanics.A governing equation group for the model,which was expressed by dimensionless fluid and solid displacements,was derived and solved with a numerical method.Variable physical properties were simulated to check the applicability of external low-frequency vibration load on dual-porous media and a parametric study for various vibration parameters.Stimulation of low-frequency vibration affected flow velocities of crack and rock matrix fluids.Compared with that in single-porous media,the stimulation effect on the fluid inner matrix of dual-porous media was relatively weakened.Different optimal vibration parameters were needed to increase the channeling flow between the crack and rock matrix or to only promote the flow velocity in the rock matrix.The theoretical study examines wave-coupled seepage field in fractured porous media with results that are applicable for low-frequency stimulation technology.

Low-Frequency Vibrations of Indole Derivatives by Terahertz Time-Domain Spectroscopy

Several indole derivatives with different ＇3-＇ substituents have been investigated by terahertz （THz） time-domain spectroscopy. The low-frequency absorption spectra and refractive indices were obtained in the range of 0.2 THz to 2.5 THz （7 cm-1 to 83 cm-1）. These derivatives with different substituents present distinct features, which suggests that THz spectroscopy is sensitive to different structures and components of these chemicals. The density functional theory was employed to calculate the low-frequency vibrational properties of indole-3-carboxylic acid and indole-3-propionic acid based on their crystal structures, and the intermolecular interactions were involved. Meanwhile, the temperature dependence of the spectra agreed with the calculated results. The quantitative analysis of a ternary mixture was studied by taking the THz fingerprints into account, and the results demonstrate THz spectroscopy has great potential for the practical applications in biochemistry and pharmaceutics.

Piezoelectric nanofoams with the interlaced ultrathin graphene confining Zn–N–C dipoles for efficient piezocatalytic H_(2) evolution under low-frequency vibration

Unique nanofoams consisting of interweaved ultrathin graphene confining Zn–N–C dipoles (ZnNG) are constructed via calcination of Zn-coordinated precursor.Due to the introduction of local polar Zn–N–C configurations,with hypersensitivity for mechanical stress,the piezoelectricity is created on the nonpiezoelectric graphene,and the hierarchical ZnNG exhibits obvious piezocatalytic activity of water splitting for H_(2) production even under mild agitation.The corresponding rate of H_(2) production is about 14.65 μmol g^(-1)h^(-1).It triggers a breakthrough in piezocatalytic H_(2) evolution under low-frequency vibration,and takes a significant step forward for piezocatalysis towards practical applications.Furthermore,the presented concept of confining atomic polar configuration for engineering piezoelectricity would open up new horizon for constructing new-type piezoelectrics based on both piezoelectric and nonpiezoelectric materials.

Three-magnet-ring quasi-zero stiffness isolator for low-frequency vibration isolation

A three-magnet-ring quasi-zero stiffness(QZS-TMR)isolator is designed to solve the problem of low-frequency vibration isolation in the vertical direction of precision equipment.QZS-TMR has both positive and negative stiffness structures.The positive stiffness structure consists of two mutually repelling magnetic rings and the negative stiffness structure consists of two magnetic rings nested within each other.By modulating the relative distance between positive and negative stiffness structures,the isolator can have QZS characteristics.Compared with other QZS isolators,the QZS-TMR is compact and easy to manufacture.In addition,the working load of QZS-TMR can be flexibly adjusted by varying the radial widths of the inner magnetic ring.In this paper,the static analysis of QZS-TMR is carried out to guide the design,and the low-frequency vibration isolation performance is studied.In addition,the experimental prototype of QZS-TMR is designed and manufactured.The static and vibration isolation experiments are carried out on the prototype.The results show that the initial vibration isolation frequency of the experimental prototype is about 4 Hz.The results show an excellent low-frequency vibration isolation effect,which is consistent with the theoretical research.This paper introduces a new approach to the design of the QZS isolator.

Low-frequency ride comfort of vibratory rollers equipped with cab hydro-pneumatic mounts

Based on the advantages of hydraulic and pneumatic mounts,a new hydro-pneumatic mount(HPM)is proposed to improve the low-frequency ride comfort of vibration rollers.Through the experiment of the vibratory roller,a nonlinear vehicle dynamic model working on off-road soil grounds is then established to assess the HPM's ride comfort in the low-frequency region.Two indices,the power spectral density(PSD)acceleration and root mean square(RMS)acceleration of the operator vibration and cab shaking,are chosen as objective functions in both the frequency and time regions.The research results show that when the cab isolations are equipped with the HPM,the RMS values of the operator's seat,cab's pitch and roll angles are reduced by 35%,42%and 53%;and the maximum PSD of the operator's seat,cab's pitch and roll angles are decreased by 39%,59%and 65%,respectively.Consequently,the characteristics of the nonlinear damper and high-static stiffness of HPM can greatly reduce the operator vibration and cab shaking in the low-frequency region when compared to the vibratory roller's cab using the rubber mounts.

A brief review of metamaterials for opening low-frequency band gaps

Metamaterials are an emerging type of man-made material capable of obtaining some extraordinary properties that cannot be realized by naturally occurring materials.Due to tremendous application foregrounds in wave manipulations,metamaterials have gained more and more attraction.Especially,developing research interest of low-frequency vibration attenuation using metamaterials has emerged in the past decades.To better understand the fundamental principle of opening low-frequency(below 100 Hz)band gaps,a general view on the existing literature related to low-frequency band gaps is presented.In this review,some methods for fulfilling low-frequency band gaps are firstly categorized and detailed,and then several strategies for tuning the low-frequency band gaps are summarized.Finally,the potential applications of this type of metamaterial are briefly listed.This review is expected to provide some inspirations for realizing and tuning the low-frequency band gaps by means of summarizing the related literature.

Tracking coherent low frequency vibrational information of Rh101 in ground and excited electronic states by broadband transient grating spectroscopy

Time-and frequency-resolved broadband transient grating(BB-TG) spectroscopy is used to distinguish between ground-and excite-electronic state vibrational coherence at different wavelengths. Qualitative theoretical analysis using double-sided Feynman diagrams indicates that a superposition of ground and excited state vibrational coherence are contained in the ground state absorption(GSA) and stimulated emission(SE) overlap band, while only the excited state is contained in the excited state absorption(ESA) band. The TG experiment, in which a white light continuum(WLC) is adopted as a probe, is conducted with rhodamine101(Rh101~+) as the target molecule. Fourier analysis of TG dynamics in a positive delay time range at specific wavelengths enables us to distinguish the low-frequency vibrational modes of Rh101 in ground-and excite-electronic states.

Coupling of quasi-localized and phonon modes in glasses at low frequency

Boson peak of glasses,a THz vibrational excess compared to Debye squared-frequency law,remains mysterious in condensed-matter physics and material science.It appears in many different kinds of glassy matters and is also argued to exist in damped crystals.A consensus is that boson peak originates from the coupling of the(quasi)-localized non-phonon modes and the plane-wave-like phonon modes,but the coupling behavior is still not fully understood.In this paper,by modulating the content of localized modes and the frequencies of phonon modes,the coupling is clearly reflected in the localization and anharmonicity of low-frequency vibrational modes.The coupling enhances with increasing cooling rate and sample size.For finite sample size,phonon modes do not fully intrude into the low frequency to form a dense spectrum and they are not sufficiently coupled to the localized modes,thus there is no Debye level and boson peak is ill-defined.This suggestion remains valid in the presence of thermal motions induced by temperature,even though the anharmonicity comes into play.Our results point to the coupling of quasi-localized and phonon modes and its relation to the boson peak.

Design of distributed dynamic absorbers for vibration suppression of panel structures

Distributed dynamic absorbers have many advantages such as wide frequency bandwidth for vibration suppression,strong detuning adaptability,and high system stability,making them very suitable for the vibration and noise control of continuous structures.Therefore,they have broad application prospects in various fields such as transportation,aviation,and aerospace.However,there are still many challenges in the engineering applications of distributed dynamic absorbers for vibration suppression,including the engineering realization of the optimal damping of traditional optimal coherence dynamic absorbers,and the engineering applicability of the finite periodic array dynamic absorbers.Based on the damping material properties obtained by the dynamic mechanical analyzer tests,this paper establishes the finite element model of the cantilever-beam-type dynamic absorber with constrained damping layers,aiming to realize the accurate determination of the optimal damping.Experiments are conducted by attaching the traditional dynamic absorbers with the optimal damping to a thin-walled panel with four clamped edges.Results show that the vibration of the panel is well suppressed,with the reduction of the frequency response peak larger than 14 dB and the reduction ratio of RMS larger than 58%within 500 Hz.Afterwards,the periodically arrayed dynamic absorbers are designed according to the bandgap regulation method.The tuning behavior of the arrayed dynamic absorbers by changing designing parameters is investigated.The vibration reduction effect of arrayed dynamic absorbers is compared with that of the traditional dynamic absorbers under the same mass ratio through experiments.Results indicate that the arrayed dynamic absorbers are easier to design,and have a similar reduction effect on the modal vibration of the thin panel as the traditional dynamic absorbers within a narrow frequency range near the natural frequency,while they perform unsatisfactory in a broad band.Significantly,if the appropriate frequency and damping of the arrayed absorbers are chosen,a relatively wide bandgap can also be generated,which shows high engineering applicability.The research work in this paper provides beneficial reference for the design of distributed dynamic absorbers suitable for vibration suppression of thinwalled panel structures.

Vibration response analysis of floating slab track supported by nonlinear quasi-zero-stiffness vibration isolators

To improve the low-frequency vibration reduction effect of a steel spring floating slab track(FST),nonlinear quasizero-stiffness(QZS)vibration isolators composed of positive stiffness elements(PSEs)and negative stiffness elements(NSEs)were used to support the FST.First,considering the mechanical characteristics of the nonlinear QZS vibration isolators and the dynamic displacement limit(3 mm)of the FST,the feasible parameter groups were studied with the nonlinear stiffness variation range and bearing capacity as evaluation indices.A vertical vehicle quasi-zero-stiffness floating slab track(QZS-FST)coupled dynamic model was then established.To obtain a reasonable nonlinear stiffness within a few millimeters,the original length of the NSEs must be analyzed first,because it chiefly determines the stiffness nonlinearity level.The compression length of the NSEs at the equilibrium position must be determined to obtain the low stiffness of the floating slab without vehicle load.Meanwhile,to meet the dynamic displacement limit of the FST,the PSE stiffness must be increased to obtain a higher stiffness at the critical dynamic displacement.Various stiffness groups for the PSEs and NSEs can provide the same dynamic bearing capacity and yet have a significantly different vibration reduction effect.Excessive stiffness nonlinearity levels cannot effectively improve the vibration reduction effect at the natural frequency.Furthermore,they also significantly amplify the vibrations above the natural frequency.In this paper,the vertical vibration acceleration level(VAL)of the floating slab and the supporting force of the FST can be decreased by 6.9 dB and 55%,respectively,at the resonance frequency.

Parametric Modeling of Electromagnetically Induced Vibration Processes Occurring Within Induction Systems

A continuum based model is presented which identifies a favorable set of operational conditions whereby an effective and efficient electromagnetically induced vibratory motion can proceed within an induction system.Specifically, an analytical assessment is presented for the electromagnetic field and the electromagnetically induced acoustic field, with parametric factors incorporated into the model to permit a normal modes solution for the acoustic field which here is sensitive to the compliance of both the molten metal and the wall,as well as electromagnetic properties of the metal.A parametric analysis is presented which identifies the importance of matching the mechanical impedances of the melt-wall configuration so that the generation of acoustic energy within the melt system can be more effectively utilized.Relatively straight-forward calculations,presented for the acoustic field,may provide a more computationally efficient means for implementing process simulation studies for these systems.