Low-frequency Band Gaps Research Articles

Vibration Attenuation in a Beam Structure with a Periodic Free-Layer Damping Treatment

In order to improve the vibration reduction performance of damping treatments, a new damping structure consisting of a uniform base layer and two periodically alternating free layers was examined in this study. Closed-form solutions for both the band structure and the forced response of the periodic bi-layer beam were theoretically derived and verified via numerical solutions using the finite-element method. The results showed that the structure with periodic free-layer damping (PFLD) treatment reduced broadband vibrations, and the levels of reduction were dominated by Bragg scattering in the band gaps and damping in the passbands. The vibration experiment verified the derived theory’s accuracy and showed that the PFLD treatment could increase vibration reduction levels in low-frequency band gaps compared with traditional free-layer damping treatments. The effects of the parameters—cell lengths, sub-cell-length ratios, and thickness ratios—were also discussed, providing further understanding of the vibration reduction performance of the bi-layer beam with the PFLD treatment, and this can be used to help designers optimize the periodic bi-layer beam to achieve better performance.

Optimal design of one-dimensional elastic metamaterials through deep convolutional neural network and genetic algorithm

Deep learning (DL) has found extensive application in elastic metamaterial design. However, these methods are often limited to fixed design parameters and single structural configuration, lacking versatility. To overcome these, we propose a novel data-driven design framework combining deep convolutional neural network (DCNN) and genetic algorithm (GA) to design vibration-isolating metamaterial structures in foundations. This framework is highly adaptable, accommodating diverse design parameters by identical models. We discretize different structural configurations into a uniform tensor format, and generate multiple datasets. Two DCNN-based forward prediction models are then developed to accurately capture bandgap distributions for all body waves. Additionally, we incorporate multiple populations to enhance the parallel search capacity of GA, and integrate it with the trained DCNN models to simultaneously determine multiple optimal structures. The optimal design result for different parameters shows that the designed structures can achieve the target bandgap, and proves the effectiveness and generality of our method. Finally, through the design of two structural configurations, we find that four-layer structure exhibits wider low-frequency bandgaps and superior vibration reduction performance compared to the three-layer structure, under the same material composition and usage.

Low-frequency and wide bandgap seismic metamaterials for Rayleigh wave attenuation

This study introducesa seismic metamaterial (SM) for mitigating low-frequency seismic Rayleigh waves when embedded in the ground.. Dispersion curves and vibration modes of a unit cell incorporatingthe SM were calculated using the Bloch theorem and sound cone method in a numerical model. The lowest frequency of the bandgaps (BGs) is 1.6 Hz, with the maximum absolute bandwidth reaching 18 Hz, matching the seismic wave considered in this study. Furthermore, a comprehensive analysis of vibrational modes revealed the mechanism responsible for BG formation. Numerical simulations in both the time and frequency domains confirmed the attenuation of Rayleigh waves by finite models containing SMs, along with theconversion of Rayleigh waves into body waves. Additionally, the effects of material and geometric parameters on BG frequency range is discussed. Complex SM structures were devised by combining two distinct SMs with varying geometric parameters, achieving a complete broadband attenuation range. Finally, realistic seismic Rayleigh wave propagation through complex SMs was simulated, conclusively validating their effectiveness in providing broadband attenuation.

Tuning the acoustic characteristics of bottle plant garden

This work presents a finite element study to compute the acoustic performance of a garden that consists of periodically arranged bottle plants. The purpose of this work is to achieve low- and high-frequency noise reduction using plastic waste bottles. A harmonic excitation is given at one end, and transmission loss is calculated as a function of frequency between the two ends of the computational domain. The result shows that bottle plants produce a high-frequency wide band (1300–2100 Hz) around Bragg's frequency as well as a low-frequency sharp narrow band at the resonance frequency (∼305 Hz) of the bottle. To achieve a wider band gap at low frequencies, water level in the bottles is kept at different levels. The result showed that placing bottles with various water levels next to one another causes a bigger band gap at low frequencies (255–360 Hz). As a result, the low-frequency band gap can be tuned by changing the water level in the bottles. Plants' ability to absorb sound further dampens it at specific frequencies. Utilizing the plastic bottle to form such a garden has a major environmental impact and can function as a visually pleasing area while promoting calm and tranquilly.

Description of bandgaps opening in chiral phononic crystals by analogy with Thomson scattering

Chiral phononic crystals (PnCs) provide unique properties not offered by conventional metamaterial based on classic Bragg scattering and local resonance. However, it is insufficient to only consider the inertial amplification effect to describe its bandgap mechanism due to the absence of the bandgap caused by the chirality in some specific chiral structures. Here, we theoretically and experimentally introduce an analogy with Thomson scattering in electromagnetic waves to characterize the bandgap phenomena in chiral PnCs with translation–rotation coupling. Another phononic structures with translation–translation coupling are proposed to illustrate the universality of the analogy. We evidence that the coupling motion in chiral unit cells is similar to the result of Thomson scattering, which quantitatively formulizing as inertial amplification in theory and, twice elastic Thomson scattering allows the waves in the same polarization mode to superpose in antiphase, which is essence of the bandgap formation. This finding sheds a new light on the physics of the elastodynamic wave manipulation in chiral PnCs, thus opening a definite route for the pragmatic exploitation of chiral PnCs as well as other structures with motion coupling in achieving low-frequency and broad bandgaps.

Study on bandgap characteristics and vibration attenuation mechanism of double-oscillator power-exponent prism phononic crystal plate

This study introduces a local resonance mechanism to a periodic acoustic black hole (ABH) structure to achieve vibration control of plate structures and proposes a double-oscillator power-exponent prism phononic crystal. Results show that the periodic power-exponent prism can generate a high-frequency bandgap, the interior oscillator can generate a low-frequency bandgap, and the top oscillator can separate the frequency dispersion curve at around 700 Hz to form a bandgap with a width of 189 Hz. The double-oscillator power-exponent prism phononic crystal, composed of two types of oscillators and a power-exponent prism, can simultaneously have high-, middle-, and low-frequency bandgaps. Simulations and experiments show that it has a good attenuation effect on flexural vibration in the bandgap frequency band. The present results can provide a useful reference for bandgap design based on the combination of multiple mechanisms.

Roton-Enabled Mechanical Diode at Extremely Low Frequency

Abstract This paper presents a refined model for a mechanical diode based on a mass-spring system. The proposed model utilizes a bilinear spring to construct a frequency converter, which effectively disrupts the reciprocal transmission of acoustic waves. By employing a mass-spring-mass system as a filter, a nonlocal connection is introduced to generate an extremely low-frequency band gap (2–4 Hz), thereby achieving a mechanical diode with a lower operating frequency. The feasibility of these low-frequency mechanical diodes is demonstrated through comprehensive numerical simulations and experimental analyses. In addition, we evaluated the effect of bilinear springs and nonlocal connection parameters on the diode performance.

Ultra-broad low-frequency forbidden bands in 1D solid–fluid acoustic superlattices with multiple solid constituents

In this paper, a theoretical model of underwater acoustic wave propagation, based on the transfer matrix method, is employed to calculate acoustic wave transmission through a 1D solid–fluid superlattice (SFSL) with multiple solid constituents. The band structure of infinite multi-element SFSL and the transmission coefficient of finite one are obtained, both of which reveal the existence of multiple separated ultra-broad low-frequency forbidden bands, even in the case of solid constituents with very close acoustic parameters. Simulations about the finite multi-element SFSL are carried out to verify the correctness of these findings. In addition, the influence of the acoustic parameters and the structural parameters on the low-frequency forbidden bands (LFBs) of SFSL with two solid constituents (m = 2) is also investigated. It is found that the required two separated LFBs can be achieved by choosing appropriate material parameters. For the situation of m ≥ 2, it is expected to provide more possibilities to engineer low-frequency bandgaps. Our results infer that multiple separated LFBs in multi-element SFSL can be quite useful for making highly performing low-frequency acoustic filters in selective angle ranges, which are useful for the elimination of the side lobes of low-frequency acoustic transducers.

Topological Design of Two-Dimensional Phononic Crystals Based on Genetic Algorithm.

Phononic crystals are a kind of artificial acoustic metamaterial whose mass density and elastic modulus are periodically arranged. The precise and efficient design of phononic crystals with specific bandgap characteristics has attracted increasing attention in past decades. In this paper, an improved adaptive genetic algorithm is proposed for the reverse customization of two-dimensional phononic crystals designed to maximize the relative bandwidth at low frequencies. The energy band dispersion relation and transmission loss of the optimal structure are calculated by the finite-element method, and the effective wave-attenuation effect in the bandgap range is verified. This provides a solution for the custom-made design of acoustic metamaterials with excellent low-frequency bandgap sound insulation or other engineering applications.

Isotacticity in chiral phononic crystals for low-frequency bandgap

Realizing a low-frequency and broad bandgap is extremely challenging because the lattice constant, equivalent stiffness, and equivalent density must be taken into account in practice. Despite the advances of inertial amplification which is one of the ideal strategies to address this issue, the design ideas are mainly limited to the classic geometries featured by mirror symmetry (syndiotacticity), confining then progress in this topic. Here, we report numerical and experimental investigation of a chiral phononic crystal without mirror symmetry (isotacticity) according to the analogous Thomson scattering. Numerical analysis shows that due to the lack of one degree of freedom in isotactic lattice (ISL) compared to syndiotactic lattice (SYL), the bandgap starting-frequency of the ISL is significantly lower than that the one of the SYL by up to 66%. The bandgap properties are further demonstrated by simulation and experimental measurements. This research reveals that the condition of having alternating arrangement orientations between neighboring atoms is not indispensable for this kind of bandgap, and a rational geometry satisfying the Thomson scattering-based bandgap conditions can further reduce the bandgap frequency without affecting the stiffness and lightweight of the structure.

Metamaterials of Auxetic Geometry for Seismic Energy Absorption.

The propagation of earthquake energy occurs primarily through elastic waves. If the seismic force input to a structure can be directly reduced from the source, then the structure can be protected from seismic wave energy. Seismic metamaterials, regarded as periodic structures with properties different from conventional materials, use wave propagation characteristics and bandgaps to dissipate seismic wave energy. When the seismic wave is located in the bandgap, the transmission of seismic wave energy is effectively reduced, which protects the structure from the damage caused by seismic disturbance. In practical application, locating seismic frequencies below ten Hz is a challenge for seismic metamaterials. In the commonly used method, high-mass materials are employed to induce the effect of local resonance, which is not economically feasible. In this study, a lightweight design using auxetic geometry is proposed to facilitate the practical feasibility of seismic metamaterials. The benefits of this design are proven by comparing conventional seismic metamaterials with metamaterials of auxetic geometry. Different geometric parameters are defined using auxetic geometry to determine the structure with the best bandgap performance. Finite element simulations are conducted to evaluate the vibration reduction benefits of auxetic seismic metamaterials in time and frequency domains. Additionally, the relationship between the mass and stiffness of the unit structure is derived from the analytical solution of one-dimensional periodic structures, and modal analysis results of auxetic metamaterials are verified. This study provides seismic metamaterials that are lightweight, small in volume, and possess low-frequency bandgaps for practical applications.

Design and compression-induced bandgap evolution of novel polygonal negative stiffness metamaterials

The paper proposes a novel polygonal negative stiffness (NS) metamaterial composed of folded beams and stiffening walls, which exhibits excellent performance in attenuating waves over a broad frequency range and shows compression-induced bandgap evolution characteristics. Dispersion relation and bandgaps for the propagation of elastic waves in NS metamaterials are calculated utilizing a semi-analytical periodic spectral method (PS-SAFE). The results demonstrate that broadband bandgaps can be achieved in the proposed polygonal NS metamaterials. Mode analysis and transmission spectrum are utilized to explain the underlying mechanisms of wave attenuation. Furthermore, appropriate deformation conditions are applied to the NS metamaterials to realize compression-induced bandgap evolution, which shows that compression-induced configuration variations significantly impact the frequency range and bandwidth of the bandgaps. As the deformation increases, folded beams enter the elastic instability stage, and the internal stress change strongly influence the vibration displacement modes, leading to various symmetric and antisymmetric displacement vibration modes within a similar frequency range, forming low-frequency broadband bandgaps. This work provides valuable insights into the design of advanced materials for low-frequency broadband wave attenuation.

Comprehensive analysis of band gap of phononic crystal structure and objective optimization based on genetic algorithm

In this paper, a type of acoustic metamaterial structure is proposed, which provides a new idea for the structural design of metamaterials with specific wave propagation direction. The structure is named snowflake-like square phonon crystal structure (SLS). Firstly, based on Bloch theorem and finite element method, the energy band curve of the structure is obtained, and the low frequency band gap in the range of 300–600Hz is obtained, and the band gap is analyzed comprehensively with the main band gap. It includes the vibration modal analysis at the corresponding point of the boundary of Brillouin zone and the establishment of a corresponding simplified model to explain the mechanism of band gap opening and closing more deeply. At the same time, the band gap characteristic of SLS structure is verified by the transmission curve, and the difference of elastic wave transmission results between inside and outside the band gap is given. Not only that, the real propagation direction of the band gap is described by group velocity and equal frequency diagram. The results show that in the range of relatively low frequency elastic waves, the propagation of elastic waves in the structure has a certain direction and region, that is, the structure can play a good effect of vibration and noise reduction. In addition, after the comprehensive analysis, this paper analyzes the influence trend of various factors on the band gap of the structure, and establishes the optimization model of the target band gap based on genetic algorithm, and finally obtains the optimized SLS structure. The results show that the band gap width is more than 2.5 times larger than the initial band gap width. It shows that even under the specific structure, the optimization space of the band gap still has a high lifting upper limit.

Study on vibration damping performance of a petal-shaped seismic metamaterial

Seismic metamaterial (SM) is a new vibration damping technology, but the bandgap is difficult to concentrate in the low frequency range due to the limitation of the lattice size and there is a lack of experiments for validation. Based on this, we propose a petal-shaped seismic metamaterial by numerical simulation combined with experiments to change the internal scatterer into a petal-shaped consisting of four sectors. This structure can form an ultra-low frequency bandgap to cover the frequency band where the seismic energy is concentrated and provide effective attenuation of seismic waves. Firstly, the energy band structure and vibration modes are calculated by numerical simulation. The effects of geometric and material factors on the bandgap are analyzed with the vibration modes. Then the frequency response curves of lamb waves on SM are calculated. And the scaled-down model is fabricated and vibration tests are conducted. The results show that the new two-dimensional SM has excellent vibration damping performance compared with conventional structures and can generate low-frequency bandgap. It has potential applications in the field of seismic isolation and attenuation of buildings.

A petal–cylindrical seismic metamaterial occupying low-frequency wide bandgaps in horizontally stratified soils

Earthquake prevention is of fundamental interest in seismic research area. Seismic metamaterials proved very useful for this purpose, but because they are mainly based on resonant structures, the working frequency bandwidth of these metamaterials is narrow. This work aims to increase the bandwidth by improving cylindrical resonant structure. Two types of cylindrical structures with four petals attached to the four sides of hollow and solid cylinders are proposed. Their bandgap properties have been investigated by using the finite element method. Particularly, considering more realistic site conditions for seismic surface wave propagation, we explored the properties of the proposed structures for horizontally stratified soils, besides homogeneous soil. The results show that a low-frequency wide bandgap is provided in case of homogeneous soil. Excitedly, in case of a stratified substrate, an additional bandgap is obtained in lower frequency region. Moreover, to confirm the feasibility of the proposed structures, the transmission coefficients for the finite unit cells are calculated for both homogeneous and horizontally stratified soils along with the different directions. The finding substantiates that the finite system for stratified soils can effectively attenuate seismic surface waves within the two low-frequency bandgaps occupying the relative bandwidths of 154% and 81%.

Low-Frequency Ultrawide Band Gap Study of Symmetric Conical Scatterer Phononic Crystal

PurposeOne of the key challenges in the research of phononic crystals is achieving small-size control of large wavelengths, which means obtaining low-frequency band gaps with relatively small lattice dimensions. Previous studies have mostly been unsatisfactory in this regard. To obtain lower starting frequencies and more satisfactory band gap widths, this work presents a novel design for a phononic crystal structure.Design ApproachThe proposed phononic crystal consists of a silicon rubber connecting plate, an epoxy resin substrate, and tungsten metal cone scatterers. Through finite element method (FEM) calculations and analysis, we have successfully achieved an ultrawide band gap. To delve further into the origin of the ultra-wideband gap in a newly conceived phononic crystal, the vibrational modes of this crystal were carefully studied.FindingsThis work has successfully achieved an ultrawide band gap with a width ranging from 122.47 to 4360.2 in the case of a lattice constant of a = 8.5 mm. It was found that the low-frequency ultra-wideband gap cannot be obtained without the presence of silicone rubber. Furthermore, an equivalent spring model was developed, and the accuracy of this model was successfully validated through meticulous calculations. At last, It is found that d1, d4, h1, and h3 have the most pronounced effect on the ultrawide bandgap, and the intrinsic reason is the fact that they determine the geometric structure of the silicone rubber connection plate.Research Limitations/implicationsDue to the chosen research method of finite element analysis, the study results may vary depending on the different mesh discretizations, but this type of error is small and can be ignored.Practical ImplicationsThis work provides a new design solution for phononic crystal miniaturization.Originality/valueCompared with previous reports, the new phonon crystals designed in this paper have smaller size, lower starting frequency, and wider band gap.

Synergistic effect of flexural wave broadband attenuation in beam with periodic-parallel constrained layer damping (P-PCLD)

The efficient suppression of broadband flexural waves is an important area of research. Owing to the multi-bandgap behaviors of parallel beams and the broadband wave attenuation characteristics of the constrained layer damping (CLD) treatment, their interaction mechanism might improve the flexural wave attenuation efficiency. Hence, in this study, a beam with a periodic parallel constrained layer damping (P-PCLD) was formed using Euler and sandwich beam parallel coupling. The wave propagation constant of the P-PCLD was derived based on the infinite periodic structure theory and evaluated using the finite element method. The practical benefit of the P-PCLD was first evaluated by studying the enhancement of the flexural wave suppression in sandwich beams (SBs) by adding parallel Euler beams. Further, the performance difference between the P-PCLD and constrained layer damping (CLD) treatments with a similar material weight was compared. The results showed that a reasonably designed P-PCLD could achieve better flexural wave attenuation performances than SBs or an equivalent weight CLD in both the low-frequency bandgap and passband range.

Temperature controlled quasi-zero-stiffness metamaterial beam for broad-range low-frequency band tuning

Despite their engineering significance, locally resonant metamaterials are facing the challenge to cope with the need for broad-range band gap adjustment at low-frequencies. To tackle this problem, this study proposes using shape memory alloys (SMAs) to achieve temperature-controlled quasi-zero-stiffness (TC-QZS) metamaterial beam, which entails tunable and low-frequency band gap through ambient temperature changes. The basic configuration of the proposed TC-QZS resonator embraces a negative mechanism, steming from an SMA and a nonlinear geometrical structure. The stiffness of the positive stiffness mechanism can be effectively neutralised by the negative one, and the neutralisation can be adjusted based on temperature change applied to the SMA. The resultant stiffness variation yields broad-range tunability of the resonant frequency of the TC-QZS resonator. The band gap structure of the metamaterial beam is obtained using the transfer matrix method and verified by numerical simulation. Effects of dominant parameters on band gaps are scrutinized. Results show that the frequency range of the band gap can be continuously tuned from 26 to 69 Hz. This study provides guidance for the realisation of band gap tunibility over a wide frequnecy range and lays the groundwork for the development of elastic wave manipulation and vibration isolation.

Vibration attenuation performance of isolator based on locally resonant phononic crystal via train load

A locally resonant phononic crystal isolator (LRPCI) that the external ring vibrators attached to the central connectors through the rubber is designed, and it is installed to attenuate vibration under the track of rail transit. The energy band structure of the isolator is calculated by the finite element method, and its bandgap range is from 49.7 Hz to 104.9 Hz. The transmission loss and the equivalent mass density are further calculated to verify the accuracy of the bandgap, and they are perfectly corresponding to the bandgap. Then, the vehicle-rail-floating slab track-tunnel multibody dynamic model is built to analyse the vibration attenuation performance of the floating slab track installed the LRPCI and steel spring isolator under the train load. The results show that the LRPCI has a low frequency bandgap and can reduce the low frequency vibration, and the vibration isolation performance of the LRPCI is better than that of the steel spring isolator. The LRPCI has a low frequency bandgap, which can isolate the vibrations caused by wheel-rail interaction, and further reduce the impact of vibrations on surrounding buildings and the environment.

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.