Frequency Range Of Band Gap Research Articles

Temperature-tunable topological zero-refraction acoustic metamaterials

Zero-refractive index metamaterials have a wide range of applications in directional transmission and wave-front shaping due to their unusual acoustic properties. However, for most given acoustic topological metamaterials, the operating frequency is relatively fixed and the effect of temperature on their topological properties is rarely considered. Therefore, temperature-controlled tunable topological zero-refraction acoustic metamaterials are proposed in this paper. Firstly, a metamaterial with quadruple degenerate Dirac-like points at the center of the Brillouin zone is constructed, and the influence of temperature on the Dirac-like points is analyzed. The results show that the topological bandgap frequency range is more sensitive to temperature. The existence of pseudospin-polarized edge state is demonstrated by analysing the band structure of supercells with different topological phase phonon crystal. The topological zero-refraction property of the edge states outcoupled into free space is numerically demonstrated, and the non-contact active control of their operating frequencies can be realized by temperature. This study can provide a corresponding reference for the intelligent control of near-zero refractive index acoustic topological materials in elastic wave collimation and acoustic communication.

The coupled band gap of longitudinal wave in metamaterial-based double-rod containing resonators

This study investigates the coupled band gap and vibration propagation characteristics of elastic waves in a metamaterial elastic double-rod system with attached periodic resonators. We derive the band gap structure and vibration attenuation equations of double-rod structure using the spectral element method, Bloch’s theorem, and the transfer matrix method. The validity of the coupled band gap is confirmed through forced vibration response analysis. Furthermore, we examine the effects of various parameters on the double-rod system, revealing that coupled band gaps exist with the average vibration attenuation rates of −50.23 dB for rod one and −47.87 dB for rod two, respectively. Remarkably, by adjusting the double-rod parameters, both the band gap frequency range and vibration attenuation ability of the coupled band gap can be adjusted to meet specific engineering requirements in low-frequency regions. This research contributes to developing continuous mechanical structures featuring coupled band gaps.

Geometric Parameter Effects on Bandgap Characteristics of Periodic Pile Barriers in Passive Vibration Isolation

To investigate the impact of the geometric parameters of periodic pile barriers on bandgap characteristics in passive vibration isolation, a two-dimensional, three-component unit cell was developed using the finite element method (FEM). This study analyzed the bandgap properties of periodic pile barriers and validated the effectiveness of the FEM through model testing. The FEM was then methodically applied to evaluate the effects of pipe pile thickness, periodic constant, arrangement pattern, and cross-sectional shape on the bandgap characteristics, culminating in the proposition of a novel H-shaped cross-section for the piles. The results demonstrated that the FEM-calculated bandgap frequency range, featuring steel piles arranged in a square pattern, closely aligned with the attenuation zone in the model tests. The lower band frequency (LBF) was primarily influenced by the pipe pile’s inner radius, while the upper band frequency (UBF) was predominantly affected by its outer radius. As the periodic constant increased, the LBF, UBF, and the width of band gap (WBG) all decreased. Conversely, changing the arrangement pattern from square to hexagonal led to increases in UBF and WBG, while the LBF diminished. Notably, the WBG of the H-section steel piles, possessing the same cross-sectional area, was 1.31 times greater than that of the steel pipe piles, indicating an enhanced vibration isolation performance. Additionally, the impact of transverse and vertical characteristic dimensions of the H-shaped pile on the band gap distribution was assessed, revealing that the transverse characteristic dimensions exerted a more significant influence than the vertical dimensions.

Self-aware active metamaterial cell 3D-printed in a single process

Metamaterials are capable of attenuating undesired mechanical vibrations within a narrow band-gap frequency range; however, real-world applications often require adjustments due to varying loads and frequency content. This study introduces a self-aware, thermo-active metamaterial, 3D-printed in a single process using thermoplastic material extrusion. The adjustment of the natural frequency and band-gap region is achieved through resistive heating of conductive paths, which alters the stiffness of the base cell’s resonator. Additionally, these conductive paths facilitate the detection of the resonator’s excitation frequency and temperature, thereby eliminating the need for external sensors. This dynamic adaptability, experimentally demonstrated by achieving a band-gap tuning range from 505 Hz to 445 Hz with a 17 °C temperature difference, highlights the potential of these metamaterials for applications in smart structures across the aerospace, civil, and automotive industries.

A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting

Locally resonant metamaterials have low-frequency band gaps and the capability of converging vibratory energy in the band gaps at resonant cells. It has been demonstrated by several researchers that the dissipatioin of vibratory energy within the band gap can be improved by using viscoelastic materials. This paper designs an integrated viscoelastic metamaterial for energy harvesting and vibration isolation. The viscoelastic metamaterial is achieved by a viscoelastic beam periodically arrayed with spatial ball-pendulum nonlinear energy harvesters. The nonlinear resonator with an energy harvesting function is achieved by placing a free-rolling magnetic ball in a spherical cavity with an additional induction coil. The dynamic equations of viscoelastic metamaterials under transverse excitation are established, and the energy harvesting and vibration isolation characteristics within the dispersion relation of viscoelastic metamaterials are analyzed. The results show that the vibrations of the main body of the viscoelastic metamaterial beam are significantly suppressed in the frequency range of the local resonance band gap. At the same time, the elastic waves are limited in the nonlinear resonator with an energy harvesting function, which improves the energy output. Finally, an experimental platform of viscoelastic metamaterial vibration is established for validation purposes.

Low-Frequency Flexural Wave Acoustic Insulation Characteristics of a Double-Layer Metamaterial Plate

The effects of geometric parameters and constituent material parameters on the flexural wave bandgap of a locally resonant double-layer metamaterial plate are investigated using the finite element method. Reasonable parameters are obtained through optimization; then, a double-layer plate made of ABS material with added aluminum mass blocks is designed. The results show that it can open the low-frequency (112--124 Hz) flexural wave bandgap at a subwavelength size. The metamaterial plate is modeled as an equivalent spring-mass system, and the frequency range with negative density for the equivalent dynamic mass is consistent with the width of the flexural wave bandgap. The bandgap generation mechanism is further elucidated. Sound insulation performance of double-layer metamaterial panels verified in an acoustic chamber. The maximum amplitude of STL is achieved at the 112 Hz point in the bandgap frequency range, which indicates that the low-frequency bandgap can effectively reduce vibration and noise. These results demonstrate that this novel double-layer metamaterial plate has wide applications in engineering.

Bandgap characteristics of a hybrid multi-resonator elastic metamaterial with negative stiffness mechanism and its application to mitigate seismic response of building structures

Seismic metamaterials have attracted extensive attention due to their unique ability to attenuate the transmission of elastic waves in their frequency bandgaps. However, generating a metamaterial with a low-frequency and wide bandgap remains challenging. Previous studies have shown that negative stiffness mechanisms can lower the frequency range of bandgaps while employing a multi-resonator technique can broaden the width of bandgaps. In this study, by combining these two techniques, a negative stiffness enhanced multi-resonator elastic metamaterial (NMEM) is first proposed. The feasibility of NMEM is validated by comparing the theoretical dispersion relation and the transmission spectra of a finite cell model. The results demonstrate that low-frequency and wide bandgaps can be realized by NMEM. To further widen the bandgap, a hybrid NMEM is proposed by connecting multiple types of cells in series. The proposed hybrid NMEM consists of two types of cells, one with a single resonator and another with two resonators, which merge individual bandgaps into a continuous and wider bandgap. The proposed hybrid NMEM is then adopted as a meta-basement for a case building to demonstrate its effectiveness in mitigating seismic responses. The results show that the seismic responses of the building with the hybrid meta-basement are considerably reduced than those of the building with the conventional basement. However, the hybrid meta-basement may lead to larger structural displacement response when the dominant frequency of ground motion is outside the designed bandgap.

Locally multi-resonant meta-shells for broadband vibration suppression

This paper presents the design of a meta-shell with spring-mass resonators periodically attached onto a cylindrical shell to achieve low-frequency, broadband vibration suppression. The dispersion relations of the meta-shell are calculated using Hamilton's principle in conjunction with the plane wave expansion (PWE) method, which is verified by the finite element method (FEM). The bandgaps in different wave propagation directions are observed which is induced by the dynamic negative effective mass density. The effects of different meta-shell parameters on bandgap behavior are investigated, from which the fine-tuning of bandgaps can be achieved. The vibration propagation in finite meta-shells is then studied using FEM and the attenuation of vibration is demonstrated in the frequency range of the bandgap. To further broaden the bandgap frequency range, we propose a gradient configuration of a multi-resonant meta-shell in which the resonant frequencies of multiple sets of resonators comply with equal ratio distribution. Compared with the single-resonator meta-shell, it is shown that a 170.7 % expansion in bandwidth can be achieved while the total mass of the resonators is reduced by 41.5 %. Finally, the vibration suppression performance of the multi-resonant meta-shell is experimentally verified, demonstrating the broadband vibration attenuation in corresponding bandgap frequency ranges. This work shows promising application potentials for the multi-resonant meta-shells in vibration control engineering.

Band gap characteristics of new composite multiple locally resonant phononic crystal metamaterial

Locally resonant phononic crystal (LRPC) exhibit elastic wave band gap characteristics within a specific low-frequency range, but their band gap width is relatively narrow, which has certain limitations in practical engineering applications. In order to open a lower frequency band gap and broaden the band gap range, this paper proposes a new composite multiple locally resonant phononic crystal (CMLRPC). Firstly, the band structure of the CMLRPC is calculated by using the finite element method, and then the formation mechanism of the band gap of the CMLRPC is studied by analyzing its vibration mode, and the band gap width is expanded by adjusting the size of the single primitive cell in the supercell model of the CMLRPC. Secondly, an equivalent mass-spring system model for CMLRPC is established to calculate the starting frequency and cut-off frequency of the band gap, and the calculated results are in good agreement with the finite element calculation. Finally, the frequency response function of the CMLRPC is calculated and its attenuation characteristics are analyzed. Within the band gap frequency range, the attenuation values of the CMLRPC are mostly above 20 dB, indicating a good attenuation effect. Compared with traditional LRPC, this new CMLRPC opens multiple band gaps in the frequency range of 200 Hz, with a wider band gap width and better attenuation effect. In addition, considering both the contact between single primitive cell and the adjustment of their spacing in the supercell model of the CMLRPC, lower and wider band gap can be obtained. The research results of this paper provide a new design idea and method for obtaining low-frequency band gap in LRPC, and can provide reference for the design of vibration reduction and isolation structures in the field of low-frequency vibration control.

Hybrid rod-plate lattice metamaterial with broadband vibration attenuation

Based on the manufacturing advantages and design freedom of additive manufacturing, the control of elastic waves in metamaterials can be realized through the design of the unit cell. In this paper, a new design approach for 3D acoustic metamaterials consisting of rods and chiral plates (RCPM) was proposed, which displays omnidirectional low-frequency bandgaps over the irreducible Brillouin zone. The vibration modes at the boundary of the bandgaps were analyzed to illustrate the generation mechanism of the bandgaps. A spring-mass system and a clamped- clamped beam were developed to get the modes of the first bandgap boundaries. The influences of the main geometry parameters on the bandgaps were discussed systematically based on numerical simulation and theoretical formula, which demonstrates that the bandgap frequency range of the RCPM can be adjusted by altering the design. The elastic wave propagation in the metastructure was investigated by numerical and experimental approaches. The experimental results are in good agreement with the simulation, demonstrating bandgaps that occupy a much lower frequency range than what can be realized by Bragg scatter alone. The study provides a feasible approach to designing metamaterials for low-frequency vibration attenuation in engineering applications.

Band gap tunability and wave propagation of a novel fully symmetric single-phase metamaterial

In this paper, a new type of fully symmetric single-phase metamaterial structure is proposed. Based on the finite element method, the band gap characteristics of different forms of the structure and the generation principle of the band gap are discussed. The analysis of the formation mechanism of the band gap shows that the proposed structure can achieve the purpose of expanding the band gap in the low frequency range by changing the structure and adding inclusions. Then, the variation trend of the band gap frequency range in the case of small deformation of the proposed structure is discussed. In addition, the propagation characteristics of elastic waves in the proposed structure are analyzed according to the variation characteristics of frequency contours, phase velocities and group velocities. Finally, the frequency response spectrum obtained from the propagation of elastic waves in a finite lattice composed of Model No. 3 elements further confirms the role of the proposed structure in suppressing wave propagation. The results show that the proposed structure has good band gap characteristics in a certain frequency range, which can provide ideological guidance for the design of metamaterials for achieve low-frequency sound insulation and vibration reduction.

Band Gap Properties in Metamaterial Beam with Spatially Varying Interval Uncertainties

First, this study proposed a metamaterial beam model with spatially varying interval density. The interval dynamic equation of this model could be established by incorporating the decomposition results of the interval field based on Karhunen–Loeve expansion into the finite element method. An interval perturbation finite element method was developed to evaluate the bounds of the dynamic response interval vector. Then, an interval vibration transmission analysis could be performed, and the frequency range of the safe band gap could be determined. Meanwhile, Monte Carlo simulations and the vertex method are also presented to provide reference solutions. By comparison, it was found that the calculation accuracy of the interval perturbation finite element method was acceptable. The numerical results also showed that the safe band gap range was significantly smaller than that of the deterministic band gap.

Broadband vibration attenuation study and wave propagation analysis of extended arrow tetragonal lattice structure

In order to reduce vibration and noise with wide frequency, a new extended arrow tetragonal lattice topology is proposed. The band gap characteristics are discussed by combining the finite element method and Bloch’s theorem. The generation principle of band gap is explained by vibration mode analysis. By topological optimization of the structure, band gap has obvious optimization effect. The propagation characteristics of elastic waves with a specific frequency in the structure are studied from the point of view of energy. Finally, the band gap frequency range is compared with the transmission function, and the stress cloud diagram is analyzed. The research shows that the structure has good band gaps and can play a good role in vibration and noise reduction. Through the topological design of the structure, the band gap frequency range of the structure is optimized, which provides a new design idea for wide frequency vibration attenuation.

Innovative structural design of chiral lattices with low frequency wide multiple band gaps and vibration suppression

In order to achieve low-frequency vibration and noise reduction, this paper proposes an innovative structure based on the four-ligament chiral structure. The band gap characteristics and the principle of band gap generation are numerically analyzed by using the finite element method. By optimizing the proposed structure, the band gap is obviously transferred to the low frequency. The propagation characteristics of elastic waves with a specific frequency on the passband in the proposed structure are studied. Finally, the calculated band gap frequency range is compared with the finite element simulation results, and the two correspond perfectly. The research shows that the proposed structure has a good bandgap frequency range, which can play a good role in suppressing vibration transmission, and by improving the chiral structure of the basic four ligaments, the bandgap frequency range of the structure can be transferred from a high frequency to low frequency, which provides ideological guidance and scheme for the structural design of metamaterial that suppress low-frequency waves.

Evaluation of the seismic response of frames implemented with metamaterials

This research aims at introducing a new idea in the design of frames to eliminate or suppress the transmission of waves through the structure in a certain designated range of frequencies that is called hereinafter as frequency band gap. To achieve this goal, we apply a concept from the mechanics of metamaterials to the investigated structural system by proposing a new beam-column connection in a multistory 2D frame. Modal and harmonic analysis are carried out for both the new proposed frame and the ordinary one in order to investigate the response of both systems. A thorough time history analysis is applied, also we demonstrate the response of the new proposed model under the loading of 9 different earthquake loads and a comparison between the resulted displacement and base shear is performed. Furthermore, a realization of the new connection is demonstrated. Results, comparison, and discussion are presented. The results show that the new proposed frame exhibits the calculated frequency band gap and the effect of seismic waves with frequencies within the bandgap frequency range was significantly mitigated. The novelty of this research is the ability of the new proposed idea to generate and tailor a frequency band gap in order to prevent the transmission of waves in this range of frequencies through the structural system itself. Consequently, the bandgap range of frequencies for each structure can be tuned depending on the seismic risk of its region on the global scale. This new feature could have a great impact and significant application to mitigate the effects of seismic waves on a structure.

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.

Optimization of vibration characteristics and directional propagation of plane waves in branching ligament structures of wind models

To achieve multi-frequency vibration suppression and wave propagation modulation, eight branching ligament structures for wind models are proposed. Using lattice theory, dynamical model and finite element release method, the structures are verified to have multi-frequency bandgaps. By attaching a solid disc at the center of the model, the bandgap coverage of the structure is improved and the bandgap frequency is reduced. The modal analysis shows that the vibration of branch ligaments and border ligaments has a suppression effect on elastic waves. The phase constant surface, phase velocity and wave propagation direction plots at specific frequencies are calculated to verify the directional and regional nature of wave propagation. And the good correspondence of group velocity and wave propagation finite element simulation results at specific frequencies. Finally, the calculated bandgap frequency range is compared with the vibration transfer function, and the two agree well. And the stress cloud diagram also shows that the optimized structure has an excellent vibration suppression capability. The innovatively designed structure has the combined advantages of light weight, ease of fabrication, wide frequency and low frequency vibration control, while the integrated in-plane wave analysis provides the theoretical basis for structural optimization.

Realization of a novel multimode waveguide with photonic band gap hopping based on coupled-resonator optical waveguide theory

Traditionally, in the application of photonic crystals, defect modes are mostly introduced in the photonic band gap to realize high-performance waveguides, and electromagnetic waves beyond the photonic band gap cannot be controlled in photonic crystals. Here we demonstrated a kind of deep subwavelength quasi-photonic crystal waveguide, named 2D closed surface-wave photonic crystal, by combining a photonic crystal with a spoof surface plasmon polaritons-based metal–insulator–metal structure. The closed surface-wave photonic crystal waveguide can realize the introduction of the defect mode in the frequency band where the first-order dispersion curve of the surface-wave photonic crystals is located, instead of being limited to the frequency range of the photonic band gap of surface-wave photonic crystals. At the same time, we confirmed the correctness of the coupled-resonator optical waveguide theory under the conditions of the first-order mode and the multi-order mode based on the closed surface-wave photonic crystal guided-wave mechanism. We have verified our work in 80–130 GHz through experiments, theory, and simulation, which are consistent. The closed surface-wave photonic crystals can be used as a kind of highly integrated waveguide and multi-bandpass/band-elimination filter in integrated optical circuits, and can adjust the working frequency band at very low cost.

A Direct Near-Field Observation of Conversion Between Waveguide Modes and Leaky Modes in Periodic Metal Structures

In order to directly observe the conversion between guided-wave modes and leaky-wave modes in a periodic structure, quadrilateral periodic metal diaphragms arranged in two ways on metal surfaces were analyzed. In the first scheme, each unit cell in the periodic structure contains a metal diaphragm, of which the dispersion characteristics of periodic structures were analyzed by the finite element method. The results of the numerical show that by adjusting lattice constants of periodic structures and geometrical parameters of metal diaphragms, the transmission bandwidth of the present 1-D periodic metal diaphragm structures could be limited to X-band, where the transmission characteristics are easy to be measured. In the second scheme, a pair of mirror-symmetric and staggered quadrilateral metal diaphragms is introduced into a unit cell. It can be found in the theoretical calculation that a new dispersion curve, which passes through the light line in a high frequency range, can be exhibited. The propagation constants of dispersion curves become complex numbers and provide highly directional electromagnetic radiation that scans as the frequency changes. After the relative positions of the two metal diaphragms were properly adjusted, the frequency range of the forbidden band gap between two dispersion curves can be minimized, so as to increase the transmission bandwidth of the 1-D periodic metal structures. The experimentally measured show that the dispersion curves of the two periodic structures were highly consistent with the theoretical results. The narrowing of the band gap could be verified by measuring the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters. The near-field measurement of the periodic metal structures can demonstrate the conversion between the guided-wave modes and the leaky-wave modes, and the far-field measurement can show the frequency dependence of beam elevation. We expect that these artificial material structures could be widely used for designing new microwave and terahertz band devices.

Study on bandgap and vibration attenuation mechanism of novel chiral lattices

The chiral metamaterials have been well applied in engineering applications, but the chiral structure of a single material is difficult to achieve low-frequency sound insulation or vibration reduction. Therefore, a new chiral lattice structure is proposed in this paper. Based on the Bloch's theorem, finite element analysis is carried out, and the energy band structures of different types of structures are calculated. The principle of band gap generation of Model No.1 is emphatically analyzed. The effect of geometric parameters on the band gap is discussed. In addition, the propagation characteristics of elastic waves with a specific frequency in the structure are explored. Finally, according to the corresponding relationship between the finite element simulation of vibration transmission in finite period structures and the band gap frequency range, it is verified that the structure can effectively restrain the vibration transmission. The research results show that the structure has excellent broadband gap performance in the frequency range of 3000 Hz, and has a certain filtering effect on vibration transmission.