Formation Mechanism Of Band Gaps Research Articles

Bandgap formation mechanism in tacticity inspired elastic mechanical metastructures

Tacticity is long known as a significant contributor in changing the chemical and mechanical properties of the polymers drastically. This study explores mechanism of bandgap formation in elastic mechanical metastructures designed with a focus on tacticity. We introduce metabeams, comprising a primary slender beam embedded with short secondary beams featuring end masses at their tips. The investigation delves into the numerically simulated vibration characteristics of metabeams using finite element analysis, with a subsequent comparison to experimental results for fabricated metabeams. Employing a unit-cell design approach that manipulates spatial and physical parameters, we explore a wide range of uniform and non-uniform metabeam configurations based on the distance between secondary beams and distribution of local resonators as per tacticity. Hence, drawing inspiration from tacticity, we extend our investigation to isotactic and syndiotactic metabeams, altering physical parameters (mass) within the unit cell for both configurations. The strategic distribution of end masses on attached secondary beams introduces unique characteristics to isotactic and syndiotactic metabeams, allowing for the modulation of bandgaps without altering the natural frequencies of the resonators in symmetric and anti-symmetric metabeam designs. Our research demonstrates, incorporating tacticity in metabeam design offers a novel and unconventional approach to modulate the bandgap formation mechanism.

Bandgap accuracy and characteristics of fluid-filled periodic pipelines utilizing precise parameters transfer matrix method

The phononic crystal theory provides a novel approach for effectively controlling the bending vibrations in fluid-filled pipelines. This paper innovatively proposes the precise parameters transfer matrix method to investigate the band calculation accuracy and bandgap characteristics of fluid-filled periodic pipelines with various beam types. Firstly, the differential equations for bending vibration of fluid-filled pipelines are established based on deformation and force analysis. The parameters of the system state are precisely represented by the structural form of multiplying the constitutive matrix with the derivative matrix. Combined with Bloch's theorem, the novel precise parameters transfer matrix method for calculating the band structure is proposed. Secondly, the validity of this method is verified through a comparison with finite element simulation results. A detailed analysis is provided regarding the mechanism of bandgap formation and the effect of fluid filling on the band structure. Then, the influence of shear deformation, moment of inertia, and their coupling on the band calculation accuracy for fluid-filled periodic pipelines is studied based on various beam theories. Finally, it delves into the bandgap characteristics of fluid-filled periodic pipelines under different material parameters, structural parameters, and excitation conditions. This research offers valuable insights for the structural design and vibration damping application in fluid-filled periodic pipelines, providing theoretical support for accurately determining their bandgaps.

Formation of photonic band gaps by direct destructive interference.

We study a photonic band gap (PBG) material consisting of multiple waveguides. The multiconnected waveguides provide different paths for direct wave interference within the material. Using coaxial cables as waveguides, we are able to tune the PBG of the material. Using direct destructive interference between different paths of the waveguides, we experimentally observe a kind of PBG which is quite different from the traditional PBG that is caused by scattering in dielectrics with inhomogeneous refractive indices. Particularly, this newly observed PBG has an extremely strong wave attenuation, making electromagnetic (EM) waves in the PBG cannot even pass through one unit cell under certain conditions. We also systematically investigate the transmission of EM waves in our PBG materials and discuss the mechanism of band gap formation. Our results provide a new insight to develop new band gap materials for photons and phonons.

Expanding the Bragg scattering bandgap of phononic crystals using acoustic black holes

In this paper, a phononic crystal with acoustic black hole (ABH) characteristics is designed based on the compression effect of ABHs on acoustic wavelengths. The simulation results show that the lower limit of the first bandgap of the phononic crystal with ABH is reduced by 127.8[Formula: see text]Hz, the upper limit is increased by 694.4[Formula: see text]Hz, and the bandgap width is increased by 822.2[Formula: see text]Hz compared with that of the phononic crystal without ABH. The mechanism of bandgap expansion is discussed based on the mechanism of bandgap formation and the acoustic modulation effect of the ABH. The influence of the geometric and material parameters of the ABH on the bandgap is analyzed. The ABHs offer a new way of optimizing phononic crystals, and this work can be used as a reference for their design.

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.

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.

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.

Sandwich Plate Structure Periodically Attached by S-Shaped Oscillators for Low Frequency Ship Vibration Isolation.

Locally resonant phononic crystals are a kind of artificial periodic composite material/structure with an elastic wave band gap that show attractive application potential in low-frequency vibration control. For low-frequency vibration control problems of ship power systems, this paper proposes a phononic crystal board structure, and based on the Bloch theorem of periodic structure, it uses a finite element method to calculate the band structure and the displacement fields corresponding to the characteristic mode and vibration transmission curve of the corresponding finite periodic sandwich plate structure, and the band gap characteristics are studied. The mechanism of band gap formation is mainly attributed to the mode coupling of the phononic crystal plate structure. Numerical results show that the sandwich plate structure has a double periodicity, so it has a multi-stage elastic wave band gap, which can fully inhibit the transmission of flexural waves and isolate the low-frequency flexural vibration. The experimental measurements of flexural vibration transmission spectra were conducted to validate the accuracy and reliability of the numerical calculation method. On this basis, the potential application of the proposed vibration isolation method in a marine power system is discussed. A vibration isolation platform mounted on a steel plate is studied by numerical simulation, which can isolate low-frequency vibration to protect electronic equipment and precision instruments.

Flexural Wave Propagation in a Double-Beam System Interconnected by Local Resonators with Two Degrees of Freedom

The flexural band gaps in a double-beam system on elastic foundations periodically interconnected by local resonators with two degrees of freedom were investigated using the plane wave expansion method. The transmission property of the finite periodic system was examined by the finite-element method to verify the existence of the band gaps. The mechanism of band gap formation was further studied according to the eigenmodes at the edges of band gaps and the transverse deformation patterns. The technique of broadening the band gaps was also proposed. The results indicated that significant attenuation still appears outside the band gaps for the heterolateral transmission due to the counteraction of the approximate symmetric and antisymmetric flexural bands. The band gaps can be effectively broadened, and the propagating waves are even completely eliminated in the last pass band by only adding a spring. It was also observed that increasing the distance between the left and right attached points and the gravity of the resonator gradually from the asymmetric distribution to the symmetric distribution makes two band gaps coupled to form a superwide gap. The presented results emphasize the promising potential of the double-beam system in controlling the propagation of the flexural wave.

Nonlinear Ultrasonic Detection Enhanced by 3-D Printed Phononic Crystals

Nonlinear ultrasonic methods are a novel non-destructive testing and evaluation technology due to their high sensitivity to micro-defects. However, the inherent nonlinearity of ultrasonic equipment hinders the feature extraction with micro-defects information and limits the full-scale use of nonlinear ultrasonic NDT techniques. In this work, we propose a material-enabled filter using phononic crystals (PCs) as functional units to eliminate the unapplicable inherent nonlinearity component. The PCs composed of mass blocks and connective layers symmetrical about the host plate, are simultaneously processed by melting deposition of PLA. The finite element method with Bloch–Floquet boundary condition is implemented to obtain the bandgap at 100 kHz. Based on the mass-spring model, the mechanism of bandgap formation is proved to be attributed to the negative effective mass density band induced by the local resonance of mass block. The PCs successfully opens a propagation wave transmission gap and eliminates the inherent nonlinearity to improve the nonlinear detection of micro-defects in the aluminum plate. This work provides a useful methodology for the wide application of PC-based nonlinear detection methods in the non-destructive testing field.

Meta-Kagome lattice structures for broadband vibration isolation

One-dimensional (1D) phononic crystal (PC) beams have been extensively studied due to their bandgap properties, but the idea of using this functional beam components to form three-dimensional (3D) periodic structures has rarely been mentioned. In this paper, the PC beam element is used to replace the ordinary member of the conventional Kagome lattice structures, thus, a meta-Kagome lattice (MKL) structure is innovatively constructed with broadband vibration isolation performance. The dispersion analysis is performed to reveal the mechanism of bandgap formation and the reason of getting broad bandgaps. Three kinds of MKL structures, namely, with triangular, rectangular and hexagonal pyramids are designed. The vibration transmission properties of the MKL columns with or without interfaces are studied to illustrate the isolation effect. Moreover, the vibration isolation performance of the sandwich structures composed of MKL cores is also studied, and the influence of the skin characteristics on the properties is discussed. Vibration transmission tests were conducted to verify the results. This work provides a new method to develop 3D multi-functional lattice structures, especially for load-bearing and vibration reduction.

Bandgaps and topological interfaces of metabeams with periodic acoustic black holes

Acoustic black hole (ABH) with extraordinary properties of wave manipulation and energy focalization has been drawing growing attention in mechanical metamaterial, and the development of topological phenomena provides a novel way for investigation of ABH characteristics. This paper explores the physical mechanism of dispersion curves of three metabeams with embedded periodic ABHs and studies the topological phenomena of the compound metabeam for energy localization. First, the mass-spring models are employed according to lattice dynamics method to clarify the formation mechanism of bandgaps and the effect of the parameters on dispersion relation. Meanwhile, the diatomic mass-spring model provides an analytical framework to investigate the band inversion and the displacement distribution of topological states. Furthermore, numerical analyses are carried out to investigate the band structures, eigenmodes, transmission, and the achievement of topological interface state by proposed compound metabeam. The adjustment of structural parameters, changing the mass and stiffness of the mass-spring model, can broaden the bandgap in low frequency for better vibration attenuation performance. Besides, the modal formation in low frequency is explained by masses vibration distribution. The correctness of the method is verified by comparing the transmission numerically with previous experiments. This work enriches the existing knowledge of ABH on wave manipulating and energy harvesting.

A novel locally resonant metastructure with soft-material rings for broadband and low frequency vibration attenuation

Metastructure has been discovered as a new and effective means of vibration suppression in recent studies. Based on the basic principle of the locally resonant (LR) metastructure, a novel two-dimensional LR metastruture is proposed in this paper. The host plate is punched out several concentric holes and filled with soft materials, with the resonator installed in the center. The band structure of an infinite structure is calculated by using Gaussian expansion method as well as the finite element method. To further evaluate the vibration attenuation performance, the vibration transmission of a finite plate is obtained by both numerical and experimental methods. Formation mechanism of band gaps (BGs) is revealed by analyzing eigenmodes at boundary frequencies. The significance of the novel design is clarified from the mechanism level, about the characteristics of generating broad band gaps in low frequencies. The influence of both geometric parameters and material damping properties on BGs are discussed, including examples of a non-periodic plate and a periodic damped plate. Because of its features and simple design, it can be expected to be widely applied in engineering.

A snowman-like seismic metamaterial

A snowman-like seismic metamaterial is proposed in this study. The proposed model gives a lower and wider complete bandgap compared with the seismic metamaterials of the same volume in previous research. The vibration modes are investigated to clarify the mechanism of bandgap formation. Past studies used large amounts of steel to attenuate waves at low frequencies. On the contrary, to reduce the cost, this work only uses concrete. In addition, a set of geometric parameters is suggested through parametric studies. The shielding performance of the proposed seismic metamaterials against surface waves is also demonstrated using time domain finite element simulations. The results from the transient analysis are in good agreement with the dispersion curves, validating the accuracy of the numerical simulations.

Double-beam metastructure with inertially amplified resonators for flexural wave attenuation

A new type of double-beam metastructure with periodically attached inertially amplified (IA) resonators is designed to attenuate the flexural wave propagation in the low-frequency range. An analytical approach based on the spectral element method (SEM) and the Wittrick-Williams algorithm is developed. The results of SEM show superior accuracy and an order of magnitude higher computational efficiency compared to the finite element method (FEM). Employing the developed approach, the wave attenuation behavior is presented as a function of the parameters including truss angle, beam thickness, IA mass, spring, and damper location to exhibit the perfect adjustability of bandgaps realized by the proposed structure. The local resonance bandgap frequencies are effectively lowered under the effect of inertial amplification. In addition, the damping amplification is also achieved by the IA structure, which is advantageous for extending the wave attenuation range. Finally, multibody dynamics numerical simulations are carried out to validate the reliability of the theoretical method and the rationality of simplifications used in the theoretical derivation. Furthermore, the formation mechanism of bandgaps is revealed by exploring the eigenmode shape on dispersion curves to obtain a thorough understanding of the structure.

Mechanism of Band Gap Formation in the Spin-Wave Spectrum of Coupled Magnon Crystals

Mechanism of Band Gap Formation in the Spin-Wave Spectrum of Coupled Magnon Crystals

Design of vibration isolators by using the Bragg scattering and local resonance band gaps in a layered honeycomb meta-structure

In this study, a vibration isolator is designed using the Bragg scattering and local resonance band gaps in a layered honeycomb meta-structure. Various studies have been conducted on the noise and vibration problems of engineering structures by utilizing the band gaps in phononic crystal meta-materials. However, no study on the application of phononic crystal meta-materials to the design of vibration isolators has been published due to the large lattice constant and narrow band gap. To overcome the difficulties of realization in vibration isolators, a layered honeycomb meta-structure is proposed in this study. The proposed meta-structure consists of a layered square honeycomb structure and a local resonator placed inside the honeycomb core. A transfer matrix model based on the effective mass is developed to comprehend the mechanism of band gap formation. Furthermore, a strategy for designing an ultra-wide low-frequency coupled band gap is established analytically. Then, a four-layer honeycomb meta-structure is designed and fabricated based on the proposed design strategy. Experimental results demonstrate the successful realization of an ultra-wide coupled band gap with the introduction of the resonators with meticulously selected parameters. Finally, the designed meta-structure is applied to a vibration isolator, and the vibration isolation performance is verified experimentally. This work has broad engineering application prospects and is of high significance for promoting the implementation of elastic wave meta-materials in the engineering field.

Vibration characteristics of innovative reentrant-chiral elastic metamaterials

In this work, an innovative two-dimensional (2D) hybrid auxetic elastic metamaterial (MODEL I) with reentrant triangular and chiral structures is proposed to open the broaden bandgap for vibration attenuation. Furthermore, the hybrid reentrant-chiral lattice with embedded resonators (MODEL II) shows multiple bandgaps at ultra-low frequency. Based on theoretical lumped mass-in-mass method and finite element method, the bandgap and longitudinal elastic wave attenuation are characterized. There is no complete bandgap in classical reentrant triangular lattice (MODEL 0), while the complete bandgaps width for MODEL I and II account for one forth of the concerned frequency range (0–4500 Hz). What more, the lower boundary of the first bandgap for MODEL II is 56% lower than that of MODEL I. The bandgap formation mechanisms are investigated by analyzing the mode shapes on the dispersion curves, and the frequency-dependent energy flow are studied through the iso-frequency contours, phase and group velocities. Finally, the longitudinal elastic wave attenuation of finite-size lattice of MODEL II illustrates ultra-wide vibration attenuation frequency range in the directional bandgaps. This research provides important clues and theoretical guidance for the design of vibration isolators, beam, plates and other renewed devices.

Merging Bragg and Local Resonance Bandgaps in Perforated Elastic Metamaterials with Embedded Spiral Holes

Perforated elastic metamaterials (EMMs) comprising periodic distribution of holes have recently attracted growing attention due to relatively simple fabrication process and unusual physical properties. Rational design of perforation configuration for practical applications in low-frequency vibration mitigation is challenging and important. In this study, a novel type of perforated EMMs with two bandgap formation mechanisms (i.e., Bragg scattering and local resonance) is proposed for low-frequency and broadband wave attenuation. Four concentric spiral holes are introduced into each matrix material of the conventional EMMs plate with mutually orthogonal rectangular holes. The analysis of bandgap formation mechanism indicates that the coiled waveguide introduced by the spiral holes enhances the wave scattering in the matrix material, and that the wave scattering in the divided matrix material by the orthogonal rectangular holes couples the local resonance modes formed by the spiral holes, where the coupling modes lead to the generation of the coupling bandgap and the improvement of wave attenuation. Both experiments and numerical analyses demonstrate that the proposed metamaterials can create multiple bandgaps in the sub-wavelength frequency domain compared to the metamaterials with single-type holes, which include two Bragg bandgaps with a reduced frequency of 76%, two overlapping bandgaps with local resonance dominating, and two deaf bands.

Characteristics of Band Gap and Low-Frequency Wave Propagation of Mechanically Tunable Phononic Crystals With Scatterers in Periodic Porous Elastomeric Matrices

Abstract The characteristics of passive responses and fixed band gaps of phononic crystals (PnCs) limit their possible applications. For overcoming this shortcoming, a class of tunable PnCs comprised multiple scatterers and soft periodic porous elastomeric matrices are designed to manipulate the band structures and directionality of wave propagation through the applied deformation. During deformation, some tunable factors such as the coupling effect of scatterer and hole in the matrix, geometric and material nonlinearities, and the rearrangement of scatterer are activated by deformation to tune the dynamic responses of PnCs. The roles of these tunable factors in the manipulation of dynamic responses of PnCs are investigated in detail. The numerical results indicate that the tunability of the dynamic characteristic of PnCs is the result of the comprehensive function of these tunable factors mentioned earlier. The strong coupling effect between the hole in the matrix and the scatterer contributes to the formation of band gaps. The geometric nonlinearity of matrix and rearrangement of scatterer induced by deformation can simultaneously tune the band gaps and the directionality of wave propagation. However, the matrix’s material nonlinearity only adjusts the band gaps of PnCs and does not affect the directionality of wave propagation in them. The research extends our understanding of the formation mechanism of band gaps of PnCs and provides an excellent opportunity for the design of the optimized tunable PnCs and acoustic metamaterials (AMMs).