Frequency Band Gaps Research Articles

Efficient dynamic topology optimization of 2D metamaterials based on a complementary energy formulation

The advent of additive manufacturing has revolutionized the design and development of hierarchical structures, with potential applications in compliant, auxetic, and band-gap structures. This paper presents an innovative approach to developing a dynamic Topology Optimization (TO) framework for designing printable lattice structures that exhibit specific dynamic properties. Utilizing parametrically defined filament-based unit cell structures for topology optimization, we achieve desired natural frequency bandgaps in the structures composed of these unit cells. To enhance computational efficiency, we employ a complementary energy-based formulation to (semi)analytically derive the flexibility and stiffness matrices of the unit cell structure, thus, eliminating extensive finite element discretization. Consequently, a wide variety of parametrically defined filament-based meso-structures can be mathematically explored. We apply this innovative framework specifically for band-gap maximization of 2D lattice structures. By tuning the geometry within each cell using TO, we maximize the band gap. Our results show the potential of this approach to create more efficient and effective hierarchical structures with desired band-gap properties.

Band gap characteristics of bionic acoustic metamaterials based on spider web

For the purpose of low-frequency vibration isolation and noise reduction, combined with the nested mode of spider web, a new concave star bionic acoustic metamaterial was proposed in this paper. Based on the finite element method (FEM) and Bloch theory, the effects of vertex connection mode, nesting level (n), and rotation angle (α) on the band gap distribution, transmission spectrum, and isofrequency line of concave star structure were discussed. The results showed that the two-dimensional (2D) concave star structure had the lowest opening frequency of the first band gap when the vertices coincide and n = 3; when α = 45°, the three-dimensional (3D) concave star structure had the widest band gap distribution and the lowest first band gap in the frequency range within 1000 Hz. The correctness of the simulation results was verified by experiments. These findings can provide a new idea for low-frequency vibration isolation and noise reduction.

Bandgap structure of tensegrity mass–spring chains equipped with internal resonators

This work studies the dispersion relation of a Maxwell type mass–spring chain formed by lumped masses and the parallel arrangement of two different types of tensegrity prisms. Use is made of the Bloch–Floquet theory of discrete systems in association with a linearized model of the response of the tensegrity units under compression loading. Such a modeling is aimed at studying the propagation of compression waves under small perturbations of the initial equilibrium state of the system. For a given value of the cable’s prestress, the tensegrity systems connecting the lumped masses react as elastic springs, which exhibit axial deformations accompanied by relative twisting rotations of the terminal bases. The twisting motion of the chain affects the expression of the kinetic energy, and is accounted for by introducing a suitable definition of equivalent masses. The bandgap structure of the analyzed system is analytically determined and numerical results are obtained for a chain formed by physical models tensegrity θ=1 prisms aligned in parallel with minimal tensegrity prisms. The given results highlight the highly tunable frequency bandgap properties of tensegrity mass–spring chains exhibiting internal resonance capabilities.

High Gain Compact Antenna-in-Package Solution Using Like Mushroom Electromagnetic Band Gap for Industrial, Scientific, and Medical Band

Abstract A single-feed circularly polarized antenna with electromagnetic band gap (EBG) has been developed for the Industrial, Scientific, and Medical (ISM) bands. The proposed antenna features a square patch with eight slits on each side and corner, along with a cross-slot in the middle. To prevent surface wave excitation caused by the patch antenna's thick substrate, new grounded like-mushroom EBG structures will surround the antenna. The frequency band gap characteristics of the EBG unit cells have been optimized at 5.8 GHz. A row of EBGs squares is 4.73 mm (0.063λo) away from the antenna square patch and surrounds it on all four sides. The proposed mushroom-like structure design improves the antenna's directivity by 43.31%, gain by 32.93%, reflection coefficient by 93%, and radiation efficiency by 35.22%. This topology enables a wide variety of wireless communications applications. Computer simulation technologies (CSTs) were used to generate simulation figures for the proposed antenna, operating at 5.8 GHz. Furthermore, the new Like-Mushroom EBG antenna simulation, experimental results, and other reported works confirm that our approach meets the studied objectives regarding polarization purity, radiation efficiency, high directivity, and gain.

Low-frequency vibration reduction of an underwater metamaterial plate excited by a turbulent boundary layer

Flow-induced structural noise is an important component of hydrodynamic noise of underwater structures. Local resonance metamaterials are considered to have excellent performance and enormous potential in the field of low-frequency vibration and noise control. To verify its potential, the paper derived the underwater band gap of a lateral local resonance (LLR) plate through the plane wave expansion (PWE). Then, utilizing the modal superposition approach and Rayleigh integral technique, the vibro-acoustic response of a LLR plate under a turbulent boundary layer (TBL) excitation is obtained. Finite element certification is also conducted through an uncorrelated wall plane wave technique. Parametric study is conducted to analyse the factors which influence the control effects. The result shows that the plate exhibits excellent suppression performance for flow-induced vibration at band gap frequencies. The band gaps and suppression ranges generated by the underwater metamaterial plate, are dramatically narrowed due to the thick fluid load. The paper provides theoretical guidance for the control of flow-induced structural vibration and the application of acoustic metamaterials.

Nacre-like block lattice metamaterials with targeted phononic band gap and mechanical properties

The extraordinary quasi-static mechanical properties of nacre-like composite metamaterials, such as high specific strength, stiffness, and toughness, are due to the periodic arrangement of two distinct phases in a “brick and mortar” structure. It is also theorized that the hierarchical periodic structure of nacre structures can provide wider band gaps at different frequency scales. However, the function of hierarchy in the dynamic behavior of metamaterials is largely unknown, and most current investigations are focused on a single objective and specialized applications. Nature, on the other hand, appears to develop systems that represent a trade-off between multiple objectives, such as stiffness, fatigue resistance, and wave attenuation. Given the wide range of design options available to these systems, a multidisciplinary strategy combining diverse objectives may be a useful opportunity provided by bioinspired artificial systems. This paper describes a class of hierarchically-architected block lattice metamaterials with simultaneous wave filtering and enhanced mechanical properties, using deep learning based on artificial neural networks (ANN), to overcome the shortcomings of traditional design methods for forward prediction, parameter design, and topology design of block lattice metamaterial. Our approach uses ANN to efficiently describe the complicated interactions between nacre geometry and its attributes, and then use the Bayesian optimization technique to determine the optimal geometry constants that match the given fitness requirements. We numerically demonstrate that complete band gaps, that is attributed to the coupling effects of local resonances and Bragg scattering, exist. The coupling effects are naturally influenced by the topological arrangements of the continuous structures and the mechanical characteristics of the component phases. We also demonstrate how we can tune the frequency of the complete band gap by modifying the geometrical configurations and volume fraction distribution of the metamaterials. This research contributes to the development of mechanically robust block lattice metamaterials and lenses capable of controlling acoustic and elastic waves in hostile settings.

Comparative investigation of full bandgap behaviors of perforated auxetic metaconcretes with or without soft filler

The metaconcretes engineered by embedding steel balls coated by soft rubber in concrete matrix offer great potential in controlling wave propagation. However, the relatively high start frequencies of bandgaps and deadweights may limit their applications. In this work, an alternative lightweight metaconcrete design is realized by perforated auxetic materials structured by aligning orthogonally peanut-shaped holes in concrete matrix. Meanwhile, the filling case by rubber is considered as well for a comparative purpose. Then a systematic investigation is conducted for the unfilled and filled auxetic metaconcretes to reveal their full bandgap characteristics and vibration mechanism. The results indicate that the perforated auxetic metaconcretes exhibit wide potential in wave control. The combination of soft and hard materials leads to the occurrence of local resonance, instead of the classic Bragg scattering in the unfilled structure. Moreover, the unfilled structure can produce a large complete bandgap in kHz with large bandgap width, while the composite structure exhibits good wave attenuation capability in extra lower frequency below 50 Hz, although its bandgap width looks a bit narrow and needs to be optimized further. Then, the relationship between the wave isolation performance and the key structural parameters, i.e. structural porosity and stiffness-to-density ratio of material, is identified. Finally, it is worth noting that the overall mechanical properties of the present metaconcretes are insensitive to the soft filling material. This provides a promising ability in separately altering the load-bearing and bandgap properties.

Sound transmission loss of periodic Mindlin plates with non-uniformly spaced mass attachmentsa).

The sound transmission loss (STL) of wall partitions, especially in the coincidence region, is investigated. A Mindlin plate with periodically attached masses in a periodic "supercell" pattern is analyzed theoretically and experimentally for sound attenuation. Modeling the masses as points, analytical expressions for predicting the dispersion relation and frequency bandgaps of the plate are developed. The results show that varying the distances between the masses or the masses themselves can lead to the emergence of additional lower-frequency bandgaps and slightly decrease the bandwidth of the primary complete bandgap. Additionally, a triangular periodic pattern of point masses can provide a larger complete bandgap than the conventional rectangular pattern. The results are validated by numerical analyses using the wave and finite element method. Experimental testing is conducted on large-scale plates (2.4 m × 1 m) with periodically attached masses under diffuse field conditions, demonstrating the benefits of utilizing multiple scattering to increase the STL in the coincidence region of the bare plate. The proposed approach is seen to significantly increase the STL of wall partitions in the coincidence region and provides insights into the fundamental principles of sound and vibration attenuation in complex structures based on multiple scattering.

Low frequency bandgap characteristics of a 3D chiral acoustic metamaterial structure

It has been proved that bandgaps in acoustic metamaterials can block elastic waves in certain frequencies, which offer an unprecedented solution to the low-frequency vibration control. However, there are still challenges of low bandgap frequencies and wide bandwidth. Meanwhile, chirality breaks the symmetry of the structures, which could also contribute to the formation of bandgaps in acoustic metamaterials. Based on research background mentioned above, this work proposes a type of novel 3D chiral acoustic metamaterial structures. The dispersion relations are investigated by using the Bloch's theorem. Then, the specimens are fabricated by 3D printing combined with glue processing. A series of tests is carried out to study their vibration characteristics. It is shown that the simulated results of the structures are in good agreement with experimental results, which verified the validity of the numerical models. The dispersion relations and corresponding frequency-response curves are plotted. After embedding fillers, the bandgaps of structures decrease about 62.4 % and total bandwidth decrease about 46.5 %. In addition, the regularity of bandgaps in structures with different parameters are analyzed and the structure optimized accordingly shows good vibration reduction performance in low-frequencies. This work can provide a new possibility for engineering application in the field of vibration and noise control.

Auto-adaptive metastructure for active tunable ultra-low frequency vibration suppression

Metastructures provide a new way to solve the problem of low-frequency vibration suppression because of their unique low-frequency bandgap characteristics. Traditional metastructures usually suffer from the problem of narrow bandgap at low frequencies, which cannot tolerant to uncertainties in manufacturing process of metastructures and cannot adapt to changing working conditions. One way to overcome the shortcomings is to design metastructures with tunable bandgaps. However, it is still a challenge to realize an auto-adaptive metastructure with a highly efficient tunability. In this work, we propose an active metaplate consisting of a host plate and a periodic array of local resonators that can be collectively and actively tuned using stepping motor. We demonstrate numerically and experimentally that the proposed active metaplate can realize continuous tunable ultra-low frequency bandgap. By introducing an auto-adaptive control strategy, it can realize auto-adaptive vibration attenuation at ultra-low frequencies. The proposed active metaplate has promising application prospects since it can achieve real-time active vibration suppression by using only a few active components.

A novel multi-resonator honeycomb metamaterial with enhanced impact mitigation

Local resonant metamaterials show significant promise in applications involving the attenuation of impact waves. This paper introduces a honeycomb metamaterial featuring a circular distribution of multiple mass-beam resonators designed to enhance impact mitigation by broadening low frequency bandgaps. The bandgaps of unit cells with different number of mass-beam resonators (MBR) are calculated. It is found that the unit cell with circularly distributed resonators (C-MBR) has strong low frequency local resonance in all directions, thus opening a complete wide bandgap in about 500–1200Hz. Then, a method of equivalent stiffness reduction related to the corresponding mode shapes is used to research the negative effective mass density characteristic, explaining the generation of the low frequency bandgaps. Subsequently, the impact protection capacity of local resonant metamaterial is compared with that of ordinary honeycomb metamaterial through experiment and simulation. Interestingly, the maximum acceleration values under the impact load of local resonant metamaterial are about 45% lower than that of honeycomb metamaterial, and the reaction force under the blast load is about 80% reduction. Besides, by analyzing the acceleration curve waveform and transmission spectrum, the local resonant metamaterial is found to exhibit continuous short period vibration, which blocks the wave in low frequency band. Finally, the energy dissipation performance of the local resonant metamaterial explains that it converts more impact energy into the kinetic energy of the core with resonators, thereby reducing the energy transferred to the bottom panel. These results underscore the potential application of the proposed metamaterial with multi-resonators in impact mitigation and energy dissipation.

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.

Multimode auxetic piezoelectric energy harvester for low-frequency vibration

Herein, we propose a piezoelectric energy harvester (PEH) capable of vibrating in multi-degrees-of-freedom. The resonant frequency, working bandwidth, and output power of the PEH were improved by introducing an auxetic structure (AS). The proposed PEH exhibited a symmetric serpentine structure with a doubly clamped configuration comprising several proof masses at the junctions. Finite element method (FEM) simulation was conducted to investigate the characteristics of an AS PEH and a plain-structure PEH. Prototypes of the PEHs were manufactured by three-dimensional (3D) printing technology, and their performance was evaluated through vibrational energy-harvesting experimental tests. The results showed that introducing the AS reduced the first and second resonant frequencies by 49% and 44%, respectively, considerably improved the output power in the first mode (up to 2548%) and narrowed the frequency bandgap between the first two resonance modes by 29%. The proposed multimode AS PEH can operate in a low-frequency environment of less than 20 Hz. Finally, we discussed several ways of optimizing the AS. It has been found that the PEH performance could be further improved by selecting a reasonable thickness for the AS, increasing the number of periodic unit cells, and using an AS with a variable cross-section unit cell.

Tunable Ultralow-Frequency Bandgaps Based on Locally Resonant Plate with Quasi-Zero-Stiffness Resonators

In order to suppress the transverse vibration of a plate, a quasi-zero-stiffness (QZS) resonator with tunable ultralow frequency bandgaps was introduced and analyzed. The resonator was designed by introducing the quasi-zero-stiffness systems into mass-in-mass resonators. The plane wave expansion method was employed to derive the bandgap characteristics of the locally resonant (LR) plate with QZS resonators, and corresponding simulations were carried out by finite element method (FEM). The results show that an LR plate with a QZS resonator can provide two bandgaps, and the ranges of the bandgaps agree well with the vibration attenuation bands calculated by FEM. Owing to the introduction of the QZS system, the bandgaps can be easily transferred to a lower frequency or even an ultralow frequency. The damping of the QZS resonators can effectively broaden the vibration attenuation bands. In addition, the differentiated design of the bandgap frequencies can be realized to obtain broadband low-frequency transverse wave suppression performance. Finally, a mechanical structure design scheme was proposed in order to achieve flexible adjustment of the bandgap frequency, which significantly increases the engineering applicability of QZS resonators.

Band gap of shear horizontal waves for one-dimensional phononic crystals with chiral materials.

Extensive applications of chiral lattice structures in the field of acoustic wave manipulation and vibration modulation show the effectiveness of chirality route to the design of phononic crystals. However, how and to what extent the material chirality affects the band gap properties of phononic crystals remains unclear. In this study, one-dimensional phononic crystals made of chiral materials is proposed, and a theoretical model of shear horizontal (SH) wave propagation in the chiral phononic crystals is developed based on the noncentrosymmetric micropolar elasticity theory. Through the transfer matrix method, the dispersion relationship of SH wave propagation is obtained and the effects of material chirality on the band-gap properties are investigated. Our work demonstrates that the change of material chirality can significantly affect the dispersion relationship of phononic crystals, leading to the wide band gap and low frequency. In a unit cell, when the chiral coefficients of the two parts have opposite signs but the same magnitude and the chiral directions are consistent with the vibrational direction, it is the most favorable for the phononic crystals to achieve the lowest frequency and widest band gap. This study suggests that the material chirality can be harnessed to effectively tune the band-gap properties of phononic crystals. The present study provides insight for the chirality route to the design of phononic crystals.

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

In this paper, a new defective phononic crystal (PC) microbeam model in a thermal environment is developed with the application of modified couple stress theory (MCST). By using Hamilton’s principle, the wave equation and complete boundary conditions of a heated Bernoulli–Euler microbeam are obtained. The band structures of the perfect and defective heated PC microbeams are solved by employing the transfer matrix method and supercell technology. The accuracy of the new model is validated using the finite element model, and the parametric analysis is conducted to examine the influences of size and temperature effects, as well as defect segment length, on the band structures of current microbeams. The results indicate that the size effect induces microstructure hardening, while the increase in temperature has a softening impact, decreasing the band gap frequencies. The inclusion of defect cells leads to the localization of elastic waves. These findings have significant implications for the design of microdevices, including applications in micro-energy harvesters, energy absorbers, and micro-electro-mechanical systems (MEMS).

Эффекты отрицательного преломления волн в металлических фотонных кристаллах

The paper considers the interaction of optical radiation with the boundaries of media formed by two-dimensionally periodic systems of well-conducting cylindrical elements of small cross-section – metal photonic crystals. It is shown that at band gap frequencies in the spectrum of the crystal's own electromagnetic states when waves propagate obliquely relative to the elements, such structures can be characterized by hyperbolic isofrequency diagrams in the space of wave vectors. A consequence of this is the possibility of negative refraction effects occurring when waves are incident on the boundary of such an anisotropic hyperbolic medium formed by a two-dimensional crystal with elements of limited length. The problem of incidence of a plane-wave Gaussian optical beam on the surface of a metal photonic crystal is solved using the finite-difference method in the time domain. It has been proven that negative refraction of waves occurs under certain conditions at the boundary of the medium formed by such a crystal.

Periodic strings: A mechanical analogy to photonic and phononic crystals

We present a theoretical study of a periodic vibrating string composed of a finite sequence of string segments connected periodically, with each segment characterized by a constant linear mass density. The main purpose is to provide a model that can mimic the properties of photonic or phononic crystals. This system displays frequency intervals for which wave propagation is not allowed (frequency bandgaps), in close analogy to photonic and phononic crystals. We discuss the behavior of these bandgaps when varying physical parameters, such as the values of the linear mass densities, the oscillation frequency, and the number of string segments constituting the entire system.

Non-contact electromagnetic controlled metamaterial beams for low-frequency vibration suppression

To address the challenge of suppressing extremely-low frequency vibration and noise in precision instruments and equipment, a novel non-contact metamaterial beams is proposed in this paper. The resonators of the metamaterial beams integrate negative stiffness mechanism and electromagnetic damping tuning system. Based on the magnetic dipole theory and the electromagnetic induction law, the mechanical model of magnetic resonator is established. The band structure and transmission spectrum of the metamaterial beams are obtained by transfer matrix method. Besides, the results of numerical simulations are used to verify the accuracy of theoretical results. The result shows that the negative stiffness can be controlled by nonlinear magnetic force among the magnets. Based on this mechanism, the bandgap frequency can be reduced to a minimum of 50Hz. Then, the method of combining electromagnetic damping and negative impedance circuit is proposed to form a tuning system which can reduce the initial frequency of the bandgap to 4Hz. Interestingly, the proposed bandgap control mechanism achieves the extremely-low bandgap while broadens the bandwidth relatively, which overcomes the deficiency of traditional quasi-zero-stiffness metamaterials that reduce the bandgap frequency while causing the bandwidth to narrow. This study is expected to provide valuable ideas for the application of metamaterials in the field of low-frequency vibration and noise reduction.

Low-frequency band gap design of acoustic metamaterial based on cochlear structure

In this paper, a new chiral spiral structure based on the cochlear structure is proposed. The chiral spiral structure consists of four orthogonally oriented cochlear structures with the same geometric parameters connected at the inner endpoints of the four cochlear structures. Based on the Bloch’s theory and finite element method, the band gap characteristics of the proposed chiral spiral structure are studied. The effects of ligament bending angle (θ), the ratio of arc radius of cochlear contour (α), the ligament thickness (tc ), and the level of the chiral spiral structure (n) on the chiral spiral structure are discussed. The results show that the two-level chiral spiral structure (n= 2) has the best band gap characteristics when θ = 180° and α = 0.45. With the decrease of tc and the increase of n, the opening frequency of the first band gap gradually decreases. When n = 22, the chiral spiral structure has the lowest opening frequency, 1.91 Hz. The existence of the band gap is verified through the low amplitude elastic wave transmission tests. The distribution of the iso-frequency lines indicates that with the increase n, the propagation of elastic waves of the chiral spiral structure shows more distinct directivity, which provides a basis for the propagation control of elastic waves. These findings can provide new design ideas and directions for low-frequency vibration and noise control.