Low-frequency Band Gaps Research Articles

Vibrational loss analysis of a new type of phononic crystal with a tungsten block embedded inside a rubber matrix

Vibration and noise pollution is one of the main pollution in modern society. In order to obtain good vibration damping effect, more effective phononic crystals should be designed. Based on the theory of elastic wave propagation in solids, three types of phononic crystals are designed in this paper using tungsten blocks embedded in a rubber matrix, which are cup-shaped phononic crystal, solid cylindrical phononic crystal, and hollow cylindrical phononic crystal. Firstly, the band gap characteristics and vibration losses of the three phononic crystals are analyzed by using the finite element method. Secondly, the physical mechanism of band gap formation is explored by vibration modes. Finally, the cup-shaped phononic crystal was introduced into the core layer of the sandwich plate to form the cup-shaped phononic crystal sandwich plate, and its vibration damping performance was analyzed. The results show that the three phononic crystals can form three band gaps in the range of 0–800 Hz, and the first low-frequency band gap starts at about 140 Hz and is all wider than 200 Hz. It is noteworthy that the average loss of vibration transmission of the three types of phononic crystals is more than 69 dB, which possesses stronger damping capability and wider low- and middle-frequency band gaps than the flat plate type phononic crystals. The vibration direction of the phononic crystal is at an angle of 90° to the wave vector, which prevents the propagation of elastic waves. The phononic crystal embedded in the sandwich panel plate is more in line with the actual demand of vibration damping and obtains good vibration damping effect. The research in this paper can provide more feasibility for phononic crystal damping.

A ventilation barrier for low-frequency sound insulation

This paper proposes a ventilation barrier for low-frequency sound insulation with a double-opening Helmholtz’s periodic structure. The energy band characteristics of the unit structure and the sound transmission loss of the ventilation barrier are calculated using the finite element method. The research results show that the ventilation barrier exhibits excellent sound insulation in the range of 323–803[Formula: see text]Hz, and the sound insulation band is consistent with the bandgap of the unit structure. In order to reveal the sound insulation mechanism, we have performed a modal analysis of the unit structure. Further, the effects of different dimensional parameters on the structural bandgap are analyzed by changing the structure. The results show that extending the length of the structure inlet or outlet can effectively reduce the start frequency of the low-frequency bandgap, thus achieving the regulation of the sound insulation band. The proposed low-frequency sound insulation ventilation barrier has a simple structure with great application prospects. In addition, the proposed ventilation barrier provides a new idea for noise control in low-frequency ventilation environments.

A metamaterial for low-frequency vibration damping

The local resonant phononic crystal structure is significantly smaller than the control wavelength so it is of major importance for controlling the sound field in the low-frequency band. However, lightweight and small local resonant phononic crystal structures still present a great challenge. In this paper, we propose a metamaterial for low-frequency damping. The band structures and eigenmodes are calculated using the finite element method, and the generation mechanism of the resonant band gap is analyzed. The results show high transmission losses in the band gaps of 26.8–30.8 Hz and 33.7–180.1 Hz. In addition, the effect of geometric parameters on the bandgap frequency is discussed, and the control of the low-frequency bandgap can be achieved by adjusting the geometric parameters. The results of the study provide a new design idea for obtaining phononic crystal structures with low-frequency band gaps.

Low Frequency Attenuation Characteristics of Two-Dimensional Hollow Scatterer Locally Resonant Phonon Crystals.

The finite element method (FEM) was applied to study the low frequency band gap characteristics of a designed phonon crystal plate formed by embedding a hollow lead cylinder coated with silicone rubber into four epoxy resin short connecting plates. The energy band structure, transmission loss and displacement field were analyzed. Compared to the band gap characteristics of three traditional phonon crystal plates, namely, the square connecting plate adhesive structure, embedded structure and fine short connecting plate adhesive structure, the phonon crystal plate of the short connecting plate structure with a wrapping layer was more likely to generate low frequency broadband. The vibration mode of the displacement vector field was observed, and the mechanism of band gap formation was explained based on the spring mass model. By discussing the effects of the width of the connecting plate, the inner and outer radii and height of the scatterer on the first complete band gap, it indicated that the narrower the width of the connecting plate, the smaller the thickness; the smaller the inner radius of the scatterer, the larger the outer radius; and the higher the height, the more conducive it is to the expansion of the band gap.

3D printing of fiber composite sandwich metamaterial with spiral resonators for attenuation of low-frequency structural vibration

This paper proposes a fiber composite sandwich metamaterial as a stiff structure with a low-frequency band gap. The proposed structure is a locally resonant metamaterial that inhibits the propagation of elastic waves with spiral resonators. The dispersion curves and stiffness of the metamaterial were obtained using the finite element method. The numerical analysis results indicated that the proposed sandwich structure contributes not only to the improvement of the specific stiffness but also to the widening of the band gap. From observations of the band gap boundary modes, an analytical model was developed to derive the lower and upper bound frequencies of the band gap. A metamaterial sample manufactured by 3D printing exhibited a frequency range with low vibration transmissibility, which agreed with the results of the frequency response analysis. The specific bending stiffness and band gap center frequency of the proposed metamaterial were compared with those of existing plate-type metamaterials.

Ultra-low-frequency multi-broadband and vibration suppression mechanism of innovative star-shaped hybrid metamaterials

Metamaterials with low-frequency band gap have always been the focus of research. For this reason, many researchers have proposed many structural design schemes. In this paper, an innovative star-shaped hybrid metamaterial structure is proposed. Based on Bloch's theorem and finite element method, a dynamic model of the proposed structure is established, the band gap characteristics of the proposed structure are analyzed, and the generation mechanism of band gap is discussed with the mode shape of specific frequency. Then, the propagation characteristics of elastic wave in the proposed structure are analyzed by using the dispersion surface and group velocity images, and the attenuation region of vibration transmission in the finite periodic structure is consistent with the frequency range of band gap. Finally, the relationship between band gap and structure parameters is explored. The results show that the proposed structure has good band gap characteristics in the frequency range of 1000 Hz, the lowest frequency of band gap reaches 60.207 Hz, and the total band gap width accounts for 54.463%. This research opens up an ideological route for the design of low frequency metamaterial structures.

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.

Low frequency band gap and vibration suppression mechanism of innovative multiphase metamaterials

In order to achieve low frequency vibration and noise reduction, researchers have found and explored many types of metamaterial structures. Based on this, an innovative multiphase metamaterial structure composed of hard materials and soft materials is proposed in this paper. According to Bloch’s theorem, the band gap characteristics of the proposed structure are calculated using the finite element method, and the formation mechanism of the band gap is analyzed. In addition, the effects of the stiffness and density of the two materials on the band gap are studied in detail. Then, the phase velocity, group velocity and wave propagation direction are calculated according to a certain frequency of the specific dispersion curve, and the important information of wave propagation in the structure is obtained. Finally, according to the transmission characteristics of vibration in a finite periodic structure, it is verified that the existence of band gap can inhibit the vibration transmission, and it is further clarified that the proposed structure has a good performance in the design of low-frequency band gaps with large amplitude.

Elastic wave propagation and bandgaps mechanism of two-dimensional windmill-like elastic metamaterials

Inspired by the advantages of the grille structures, an innovative two-dimensional (2D) windmill-like elastic metamaterials (EMs) based on multiple resonators is presented for obtaining ultrawide bandgaps at a relatively low frequency. The dispersion relations and the mechanism of bandgap formation are investigated using an analytical model of windmill-like EMs. Moreover, the low-frequency bandgap between the optical and acoustic dispersion curves of windmill-like EMs with a single local resonator has been independently determined analytically. Afterward, the band structures of windmill-like EMs with different numbers of local resonators and symmetry and the same total mass are compared. By applying the finite element method, continuous symmetrical and chiral windmill-like EMs are established and analyzed based on the analytical results. The introduction of the antisymmetric chiral structure results in a 23.08% reduction in the frequency of the first bandgap compared to symmetric windmill-like EM.A further study is conducted on the formation of bandgaps as well as the propagation of waves based on eigenmodes and transmission spectra. Both the numerical analysis and experimental validation of finite periodic lattices demonstrate the effect of vibration attenuation on longitudinal elastic waves. This research provides important clues and theoretical guidance for the design of vibration isolators, beams, plates, and other renewed devices.

A metamaterial cylindrical shell with multiple graded resonators for broadband longitudinal wave attenuation

This paper investigates a metamaterial cylindrical shell with local resonators for broadband longitudinal wave attenuation. A three-component phononic crystal metamaterial cylindrical shell that opens local resonant bandgaps at low frequencies is formed by periodically inserting a lead column coated with soft rubber into an ordinary cylindrical shell. First, the governing equations of elastic wave propagation in cylindrical shell structures are derived through coordinate transformation. Subsequently, numerical models of the metamaterial cylindrical shell are established, and the dispersion relation and vibration transmission characteristics of this structure are calculated using the Finite Element Method (FEM). Finally, in order to further broaden the bandgaps and the strong suppression range of the structure, a multiple-graded-resonator metamaterial cylindrical shell with three different local resonators is also proposed. These local resonators have different start frequencies and locations of their longitudinal wave bandgaps, so they can be combined to produce a wider overall bandgap. Numerical results show that this kind of multiple-graded-resonator metamaterial cylindrical shell has a good vibration suppression effect on longitudinal waves in the range of approximately 180–710 Hz and the vibration suppression effect can reach −40 dB at best. In addition, experimental results on vibration transmission characteristics show good agreement with the numerical results. This work provides a new idea and method for the development of acoustic metamaterials to obtain broadband and low-frequency bandgaps for cylindrical shell structures.

Low-frequency noise mitigation and bandgap engineering using seismic metamaterials for terrestrial gravitational wave observatories

AbstractGravitational waves have become one of the most important observational methods for studying the Universe since their first detection. However, ground-based observatories have an inherent barrier to their detection frequency band due to the seismic and gravity gradient noises near the perturbation of the surroundings. A recent intriguing development of artificial structures for media called metamaterial is opening a new branch of wave mechanics and its application in various fields, in particular suggesting a novel way of mitigating noises by controlling the media structure for propagating waves. In this paper, we propose a novel framework for handling noises in ground-based gravitational wave detectors by using wave mechanics under metamaterial media. Specifically, we suggest an application of the bandgap engineering technique for mitigating the underground effects of acoustic noises resulting from seismic vibration in the KAGRA gravitational wave observatory.

Vibration Analysis of Locally Resonant Beams with L-Joint Using an Exact Wave-Based Vibration Approach

This paper employed and developed the wave-based vibration approach to analyze the band-gap characteristics of a locally resonant (LR) beam with L-joint, which is common in engineering practices. Based on the proposed modular approach, where the discontinuities on the beam are created as modules, the design and modeling work for such an LR beam can be simplified considerably. Then, three kinds of LR beams with an L-joint suspended with transverse-force type resonators and two cells of longitudinal-force-moment type resonators are analyzed, respectively, to show their suppression ability on the axial wave's propagation and widened effect on the low-frequency band-gaps, where the longitudinal-force-moment type resonators at the 3rd-4th cells can better suppress the propagation of the axial waves. Meanwhile, the proposed analysis results are compared with the ones obtained with the finite element method and further verified the accuracy and efficiency of the wave-based vibration approach. The aim of this paper is to provide an efficient method for the analysis and design of the LR beam with L-joint for low-frequency vibration attenuation in engineering practices.

Investigation on band gap mechanism and vibration attenuation characteristics of cantilever-beam-type power-exponent prismatic phononic crystal plates

This study proposes a novel phononic crystal (NPC) configuration composed of power-exponent prismatic phononic crystal (EPC) and cantilever beams to address the vibration problem of the ship plate structure. Through the dispersion curve, it is found that NPC has complete flexural band gaps of low-, medium-, and high-frequency. The medium-frequency and high-frequency band gaps are the coupled band gaps induced by local resonance under the superimposition between the resonance of cantilever beams and the energy concentration effect in the primary structure. It is found that the addition of cantilever beam can make EPC produce low-frequency, and medium-frequency band gaps and broaden high-frequency band gap. Changing the parameters of the cantilever beam can adjust the low-, medium-, and high-frequency band gaps at the same time. Changing the parameters of the power index prism can adjust the medium-frequency and high-frequency band gap without changing the low-frequency band gap. The present simulation and model tests validated the above conclusions. Compared with the traditional embedded ABH model, NPC cannot weaken the structural strength with greater flexibility in application, suggesting broad application prospects in ship structure engineering. The present research results can support the vibration control of ship structures.

3D printed circular nodal plate stacks for broadband vibration isolation

This paper introduces additively manufactured plate stack isolators capable of broadband vibration isolation over multiple frequency ranges. The isolator consists of axisymmetric stepped plates stacked in series and connected using compliant hinges. The monolithic design eliminates friction, leading to deeper stop bands and a potentially larger cycle life. A Kirchhoff–Love plate model predicts the frequency response. Additively manufactured polymer plate network isolators show that multiple band gaps can be achieved by model based tuning of plate geometries. A sensitivity study shows that additive manufacturing tolerance errors affect the width and center frequency of the band gap. Finally, the experimentally validated model predicts that metal isolators manufactured with Laser Powder-Bed fusion are capable of achieving low frequency band gaps and other design metrics of commercially available vibration isolators.

Uncertainty quantification in inerter-based quasiperiodic lattices

Inerter-based periodic structures have attracted significant interest among the research community due to their wide range of applications. However, existing studies on quasiperiodic structures, especially with inerters, are limited. Therefore, this timely work investigates the dynamics of novel one-dimensional inerter-based quasiperiodic lattices with and without local resonators. The quasiperiodicity is introduced through the modulation of both spring and inerter properties resulting in the well-known Hofstadter-like butterfly spectrum having a fractal structure. Moreover, by considering the appropriate boundary conditions and many mass–spring-inerter subsystems, the bulk spectrum of the system is investigated demonstrating the existence of multiple edge states in lower and higher frequency ranges. The deterministic study showed that the effect of inertia amplification is to reduce the frequencies of the Hofstadter-like butterfly and to widen the low frequency band gaps. The second contribution of this work involves investigating the effect of parametric uncertainty for the acoustic-metamaterial-like chain based on Monte Carlo simulations. Moreover, to address the computational aspect of the problem, grey-box modeling using machine learning was performed. A Gaussian process model was trained on a limited dataset and was found to capture the stochastic responses of the lattices adequately. The statistical variation of parameters with different levels of uncertainty demonstrated significant effects on the Hofstadter-like butterfly, band gaps, corresponding edge states and frequency responses. The sensitivity of the dynamic behavior in quasiperiodic lattices to variabilities reveal the need to account for system uncertainties for their targeted performance as future vibration absorbers and energy harvesters. The study also paves the way to utilize the results as useful prior information for robust design optimization of real inerter-based quasiperiodic lattice devices.

Low frequency attenuation of acoustic waves in a perforated pipe.

This paper presents new experimental and numerical evidence that perforations in a pipe wall result in a low-frequency bandgap within which sound waves rapidly attenuate. These perforations are modelled as an acoustically soft boundary condition on the pipe wall and show that a low frequency bandgap is created from 0 Hz. The upper bound of this bandgap is determined by the dimensions and separation of the perforations. An analytical model based on the transfer matrix method is proposed. This model is validated against numerical predictions for the pipe with varying perforation geometries. A numerical study is undertaken to model the effect of perforations with ideal acoustically soft boundary conditions and surrounded with an air gap. Close agreement is found between the numerical and analytical models. Experimental evidence shows that the width of the bandgap is accurately predicted with the numerical and analytical models.

Three-dimensional quasi-zero-stiffness metamaterial for low-frequency and wide complete band gap

Three-dimensional quasi-zero-stiffness metamaterial for low-frequency and wide complete band gap

Multiple band gaps of two-dimensional elastic metamaterials with self-similar hierarchy

Elastic metamaterials with band gaps can block the transmission of elastodynamic waves and have wide applications in life and industry. Wide band gaps and low-frequency band gaps are the two goals of research on elastic metamaterials with band gaps. In this study, two models of two-dimensional elastic metamaterials with self-similar hierarchies were designed. The models were obtained by replacing the arms in the unit cell with composite structures. There is a wide band gap and low-frequency band gap for each unit cell with second-order replacement. The influence of the geometric dimensions of the arms on the properties of the band gaps was also studied. The properties of the band gaps can be altered by changing the arm dimensions. Vibration analyses based on the finite element method (FEM) were conducted for materials with improved unit cells to verify the existence of band gaps. Metamaterials can be applied in many cases to reduce or isolate noise and vibrations.

Metamaterial beams with negative stiffness absorbers and rotation: band-gap behavior and band-gap merging

Two novel configurations of metamaterial beams, i.e., a monatomic and a diatomic one, are proposed in this paper through a proper combination of negative stiffness absorbers (NSAs) and rotation of flexural beams amplified by outriggers. The advantage of using the rotation rather than transversal deformation of the host beam in achieving low-frequency band gap is recognized. Then, the behavior of the rotational unit cell with NSAs are systematically investigated by concerning the influences of parameters including the negative stiffness ratio, the outrigger length, and the damping ratio. Moreover, the damping magnification effect of NSAs provides substantial damping ratios for the passband. In this way, a wider band gap can be achieved through the band-gap merging effect for the proposed diatomic configuration, where the passband between the two band gaps is capable of mitigating the waves owing to the damping magnification effect of NSAs.

Low frequency attenuation of acoustic waves using sound-soft scatterers

The attenuation of acoustic waves by silencers is typically achieved through the employment of rigidly backed cavities, connected to a main waveguide by a perforated panel. This invokes a resonant response at frequencies determined by the dimensions of the perforation and the rigidly backed cavity. A limiting factor in this approach is that to achieve low frequency attenuation, either large cavity depths are required, which is often impractical, or narrow neck regions need to be used, where performance is limited due to the viscothermal losses. Within this paper, a non-rigidly backed perforated pipe is presented where the pressure release condition at each perforation creates an acoustic sound-soft boundary condition. By the introduction of sound-soft boundary conditions, a low frequency band gap is created as the first order mode is shifted to a non-zero value, the frequency of which is determined by the dimensions and separation of the perforations. Experimental results displaying this band gap are presented along with numerical models verifying the phenomenon and an ideal analytical model based upon the transfer matrix method.