Directional Band Gap Research Articles

Investigation on enhanced band-gap properties of 2D hierarchical phononic crystals

Phononic crystals have garnered considerable attention in recent years for their unique band-gap properties, which can effectively manipulate the propagation of acoustic and elastic waves. This research focuses on exploring richer band gaps and utilizing band gap characteristics to achieve structural vibration reduction. In this study, a novel two-dimensional (2D) hierarchical phononic crystal with rich periodicities is proposed, which possesses enhanced band-gap properties. The research method used for the proposed structure is numerical simulation using the finite element method (FEM). By applying Bloch’s theorem, FEM is a more convenient tool for calculating the band gap of structures. Based on the numerical results, it can be concluded that the band gaps of the proposed 2D hierarchical phononic crystal can be classified not just into full and directional band gaps, but also into more fascinating categories based on the vibration patterns of macro and micro unit cells, which are referred to as Type I, Type II and Type III band gaps. Furthermore, the impact of structural parameter variations on the band gap is also studied, and results indicate that appropriate adjustments to the structural parameters (such as the number of unit cell n, the angle θ and the length l1) can lead to low-frequency shift and bandwidth increase in certain band gaps. A prototype of the hierarchical phononic crystal is manufactured using the 3D printing technique. Vibration tests are conducted and the simulation and experimental results are compared to verify the vibration reduction performance of the 2D hierarchical phononic crystal. The important contribution of this study is to reveal an interesting band gap generation characteristic of 2D hierarchical phononic crystals, which is beneficial for promoting understanding of the band gap mechanism in periodic structures. The enhanced band-gap properties in hierarchical periodic structures provide more potentialities and possibilities for practical vibration and noise reduction applications.

Uncovering Pattern-Transformable Soft Granular Crystals Induced by Microscopic Instability

Abstract Upon compression, some soft granular crystals undergo pattern transformation. Recent studies have unveiled that the underlying mechanism of this transformation is closely tied to microscopic instability, resulting in symmetry breaking. This intriguing phenomenon gives rise to unconventional mechanical properties in the granular crystals, paving the way for potential metamaterial application. However, no consistent approach has been reported for studying other unexplored transformable granular crystals. In this study, we present a systematic approach to identify a new set of pattern-transformable diatomic granular crystals induced by microscopic instability. After identifying the kinematic constraints for diatomic soft granular crystals, we have generated a list of feasible particle arrangements for instability-induced pattern transformation under compression. Instead of computationally intensive finite element models (FEMs) with continuum elements, we adopt a simplified mass-spring model derived from granular contact networks to efficiently evaluate these feasible particle arrangements for pattern transformation. Our numerical analysis encompasses quasi-static analysis and microscopic/macroscopic instability analyses within the framework of linear perturbation. Subsequently, the pattern transformation of the identified particle arrangements is confirmed through quasi-static analyses employing detailed finite element (FE) simulations with continuum elements. Additional numerical simulations with continuum elements reveal that the pattern transformations of particle arrangements are significantly influenced by the initial void volume and some transformed granular crystals may exhibit strong low-frequency directional phononic band-gaps, which were not observed in the initial granular crystals.

Vibration suppression of power cabin for underwater vehicle based on mechanical metamaterial flanges

The vibration of underwater vehicles affects their instrumentation and acoustic stealth capabilities. Mechanical metamaterials offer an advanced alternative to conventional vibration control methods. This study develops metamaterial flanges consisting of rectangular star-shaped cells with horizontal ligaments and localized masses. The vibration attenuation performance of metamaterial flanges within the power cabin is validated through simulations and experiments. This research examines the correlation between the bandgaps of large radial span unit cells and the frequencies of vibration attenuation, using the bandgap superposition effect. The findings reveal that the metamaterial cell exhibits exceptional load-bearing capacity and directional bandgaps in the low- to mid-frequency domain. Notably, the vibration attenuation achieved via bandgap superposition reaches 5.1 dB within 823 Hz to 1359 Hz. Specifically, within the range of 1017 Hz to 1146 Hz, the attenuation peaks at an impressive 18.6 dB. The metamaterial structure significantly reduces weight, decreasing the power cabin mass by 36.5%. This research offers new insights and serves as a valuable reference for vibration suppression in small- to medium-sized underwater vehicles.

Non-Fourier heat conduction in 2D thermal metamaterials

The challenge of achieving precise control over heat conduction has persisted for years. Recent advancements in thermal metamaterials have offered a promising avenue for addressing this challenge. Yet, predicting the behaviors of non-Fourier heat conduction within these metamaterials remains elusive. In this study, we leveraged the extended plane wave expansion method (EPWEM) to decipher the complex band structures inherent to two-dimensional (2D) thermal metamaterials. To ascertain the reliability of our approach, wave transmission in the time-domain and band structures derived from the finite element method (FEM) were juxtaposed against EPWEM results. Our findings revealed the presence of both directional and complete band-gaps in the complex band structures. Then a thermal bridge is predicted via the proposed complex band structure strategy and demonstrated numerically. By shedding light on non-Fourier heat conduction within thermal metamaterials, our analysis paves the way for groundbreaking applications in domains like laser hardening, laser cladding, metal additive manufacturing, and so on.

Smart controllable wave dispersion in acoustic metamaterials using magnetorheological elastomers

The success in the flexible design of smart acoustic metamaterials is crucially contingent upon the degree of control over the parameters that uniquely define the spectrum of band structure and morphology of dispersion surfaces. In this work, we have studied the driving physical mechanisms, the control of which makes possible operating, in real-time, on the set of band gaps formed in 3D metamaterials based on magneto elastomers. In such acoustic structures, the stiffness of the medium in which unit cells are immersed, as well as the stiffness of the shells surrounding multi-particle cores depend on the induction, B(t), of an external magnetic field. The results obtained are systematized through the qualitative analysis of diversе scenarios for the evolution of the frequency characteristics of the metamaterial and summarized in the following complete physical picture of their dynamics. Variation of the stiffness of the medium/shells changes the wavelength of the shell's surface waves at characteristic frequencies of the core vibrations and, as a result, the level of coupling between the vibration modes of the flexible shells and cores. Consequently, with an increase/decrease in the stiffnesses of the shells/medium, the dispersion surfaces of the entire acoustic system shift up/down along the frequency axis with noticeably different ‘mobilities’ that reversibly lead either to the formation of the band gaps in initially dense frequency spectrum or to the transformation of the band gaps formed into pass bands. The tuning of the set of dispersion surfaces depending on the range of changes in the magnetic field induction can be carried out in dynamic, quasi-stationary, and over-critical regimes when some of the dispersion surfaces degenerate into planes. In anisotropic metamaterials, simultaneously with creating full band gaps, it is possible to create tunable directional band gaps with adjustable frequency and angular widths. The results obtained, within the framework of the idealized discrete mass-spring model, are in good agreement with the data presented in the available experimental works and can be useful in the design of acoustic systems with desirable properties.

Bulk-local-density-of-state correspondence in topological insulators

In the quest to connect bulk topological quantum numbers to measurable parameters in real materials, current established approaches often necessitate specific conditions, limiting their applicability. Here we propose and demonstrate an approach to link the non-trivial hierarchical bulk topology to the multidimensional partition of local density of states (LDOS), denoted as the bulk-LDOS correspondence. In finite-size topologically nontrivial photonic crystals, we observe the LDOS partitioned into three distinct regions: a two-dimensional interior bulk area, a one-dimensional edge region, and zero-dimensional corner sites. Contrarily, topologically trivial cases exhibit uniform LDOS distribution across the entire two-dimensional bulk area. Our findings provide a general framework for distinguishing topological insulators and uncovering novel aspects of topological directional band-gap materials, even in the absence of in-gap states.

Experimental evidence of nonreciprocal propagation in space-time modulated piezoelectric phononic crystals

A nonreciprocal system composed of a one-dimensional piezoelectric phononic crystal whose periodic electrical conditions are modulated in time is presented. One-way longitudinal wave propagation is studied experimentally and compared to finite element temporal simulations. The modulation is performed by prescribing grounded or floating potential conditions on a periodic set of electrodes through external circuits. This approach makes it possible to consider a wide range of modulation speeds, and the large number of unit cells of the phononic crystal allows us to characterize experimentally the full dispersion curves of the system. This permits to observe the presence of directional bandgaps and to follow the shift in frequencies of these bandgaps as a function of the modulation speed. The experiments show the linear evolution of the central position of the bandgaps with the increase in the modulation speed, as well as their progressive closure, over a wide range of frequencies. Experiments are also used to estimate the evolution of bandgaps in a dispersive system, a problem discussed in several theoretical works but never observed experimentally. This work may constitute the foundation for experimental analysis of Floquet acoustic metamaterials, accelerated-modulation space-time metamaterials, or acoustic analog of the event horizon.

Impact protection enhancement by negative mass meta-honeycombs with local resonance plates

Impact and blast waves are difficult to isolate entirely because of their tremendous energy and wide-band characteristics. In this study, the meta-honeycombs are designed by adding the local resonance plates (LRP) to the honeycombs to improve the impact resistance. The negative mass property and the directional bandgap property of the LRP are investigated to form wider bandgaps to predict the impact resistance of the meta-honeycombs. For one thing, in the corresponding frequency range of the equivalent negative mass, the LRP and the impact wave vibrate towards each other, which can resist wave propagation. For another, when the frequency of impact energy is concentrated in the directional bandgap, the energy is trapped in the vibrations of the LRP plate, accelerating the attenuation of the impact wave. It is verified that the three meta-honeycombs, whose cores are re-entrant, hexagonal, and semi-re-entrant honeycombs, can effectively protect the stability of the structure against impact and blast waves through experiments and simulations. Further, the mechanical properties of the meta-honeycombs are optimized by coupling the bandgap generated by the LRP containing different resonators. The universality of the design method lays the foundation for engineering application.

Gradient-index surface acoustic metamaterial for steering omnidirectional ultra-broadband seismic waves

Elastic phononic crystals (PnCs) and metamaterials show promising prospects in seismic wave protection. Hitherto, most existing solutions for this purpose use PnCs’ bandgaps against seismic waves (mainly Rayleigh waves). However, due to the lack of available large-bandgap PnCs at low frequencies so far, their operating bandwidths are relatively small. The bandwidth will be even smaller for omnidirectional protection since the full bandgaps are always smaller than the directional bandgaps. Here, to realize ideal protection against seismic Rayleigh waves, we propose a gradient-index seismic metamaterial based on a surface acoustic PnC. Constructed using common building materials (e.g, steel and concrete), this seismic metamaterial is robust, convenient to implement, and can protect buildings from ultra-broadband seismic Rayleigh waves omnidirectionally. For example, such a metamaterial with a lattice constant of 6 meters can suppress 15–30 dB Rayleigh waves in a frequency range from 4 Hz to 20 Hz.

Effects of Cu, Ag and Au on electronic and optical properties of α-Ga2O3 oxide according to first-principles calculations

Ga2O3 is a promising semiconductor material, but, improving its electronic and optical properties is important for the development of semiconductor materials. To improve the electronic and optical properties, we used the first-principles calculations to study the effects of alloying elements on the electronic and optical properties of α-Ga2O3. Three alloying elements comprising Cu, Ag and Au were considered. The results showed that the Cu-doped α-Ga2O3 has greatly stability compared with Ag and Au doped α-Ga2O3. These alloying elements can expand the volume and lattice of α-Ga2O3 because of the discrepancy in the valence electronic density. Importantly, we calculated the directional band gap of α-Ga2O3 as 2.970 eV. It should be noted that the band gap calculated for the transition metal-doped α-Ga2O3 is smaller than that for the parent α-Ga2O3 because adding the alloying element changes the electronic balance between the Ga atom and O atom near the Fermi level. This result demonstrates the ultraviolet properties of α-Ga2O3. However, adding alloying elements (Cu, Ag and Au) leads to migration from the ultraviolet region to the visible light region. In particular, these alloying elements can improve the storage optical properties of the parent Ga2O3.

Investigations on the Complex Band Diagram of Flexural Wave through the Fluid-Loaded Phononic Plate

This paper investigates the complex band diagram of flexural waves in the phononic plate with semi-infinite heavy fluid loading. The system under examination is a square plate lattice with two-dimensional periodicity immersed in a fluid domain with infinite height. The numerical models based on the wave field transformation and the Galerkin method combined with the finite element discretization technique are developed to investigate the real and imaginary parts of the dispersion relation of flexural waves propagating through the phononic plate incorporating the fluid-loading effects. A perfect agreement is found between the location and width of stop bands from the real band diagram and the attenuation diagram, which supports the validity of the numerical models. Moreover, the complex band diagram is verified by the transverse vibration transmittance of the finite phononic plate. The results demonstrate that the external fluid loading is able to adjust the location, bandwidth, and decaying level as well as affect the degree of attenuation anisotropy of the complete and directional band gaps.

Wave propagation in two-dimensional elastic metastructures with triangular configuration

A triangular configuration spring–mass model is proposed in this paper to investigate the dependence on structural parameters of elastic wave propagation in two-dimensional (2D) elastic metamaterials/metastructures (EMs). Based on the lattice dynamics, the dispersion relations of the multiple degrees of freedom (DOF) unit cell and the vibration propagation of elastic waves are derived. Moreover, the effects of the configuration angle, spring stiffness, and mass distribution on the frequency and width of bandgaps are explored. The bandgap can be widened by 31.5% or as low as 32 Hz by reasonably adjusting the stiffness and mass distribution. Finally, the asymmetric structure (Model II-1) with the most pronounced full-bandgap difference produced by scanning along two irreducible Brillouin zones (IBZs) of Γ-X-M-Γ and Γ-Y-M-Γ was selected to explore the directional bandgap properties of EM. The dispersion curves obtained by the eigenmode division method are more consistent with the attenuation ranges of the vibration transmittance and can be used to easily and comprehensively identify the bandgap properties. This research provides important clues and theoretical guidance for the design of vibration isolators, beams, plates and other renewed devices.

Active nonreciprocal metamaterial using a spatiotemporal modulation control strategy

A class of active nonreciprocal metamaterial (ANMM) is presented which consists of an acoustic duct with periodically placed active diaphragms that are controlled by a spatiotemporal modulation strategy. The acoustic nonreciprocities can be realized by modulating a system's properties spatiotemporally. Such an approach has been extensively employed by many investigators to break the reciprocity in acoustic and elastic metamaterials. However, our proposed ANMM distinguishes itself from the above-mentioned methods by introducing actively tunable space-time modulated feedback gain of the controllers. The controller is implemented in an analog manner to enable fast response at high modulation frequencies. By discretizing a 1D acoustic duct into multiple acoustic unit cavities, we introduced a time-varying gain with a phase difference between adjacent acoustic cavities. Directional band gaps of the modulated system are numerically analyzed as the asymmetric acoustic wave propagation can be realized by converting the acoustical energy from the fundamental mode to higher order modes. In addition, nonreciprocal behavior of the proposed ANMM was experimentally demonstrated using a waveguide with periodically placed condenser microphones (sensors) and speakers (actuators).

Flexural Wave Band Gaps in Periodic Bi-Directionally Orthogonal Stiffened Plates with Holes

Plate frame structure with holes is a novel candidate to reduce the weight and strengthen the architectural structures to fulfill the requirements of practical engineering applications. The designed periodic hole structure can generate a band gap from the perspective of the frequency spectrum. In this study, a new band gap calculation method was proposed under the basic energy method framework for the analysis of hole periodic structures. Gaussian wavelet function with a good localization characteristic was adopted to overcome the inaccurately assumed displacement filed function due to the introduced hole issue. The entire plate structure was divided into cell elements and an artificial spring model was introduced to satisfy the cell coupling conditions. The coupling constraints were converted into elastic potential energy to be added to the energy functional for the entire system. The dispersion curves obtained by this method are in excellent agreement with the results of the finite element method. It was observed that periodic hole plates lead to the generation of complete and directional flexural wave band gaps. By introducing bi-directionally orthogonal stiffeners, the band gap of periodic hole plates could be significantly lengthened and complete band gaps could be successfully generated. Furthermore, geometrical parametric studies on flexural wave band gaps were analyzed. A wide and complete band gap could be realized by increasing the width of the stiffener to a certain extent, but not fully proportional.

Bloch wave propagation in finitely stretched soft lattice

In this study, the in-plane Bloch wave propagation in a finitely stretched square lattice is investigated numerically and theoretically. Precisely, the elastic band diagram is calculated for an infinite periodic structure with a cruciform hyperelastic unit cell under uniaxial or biaxial tension. Meanwhile, an elastodynamic tight-binding model is proposed to investigate the formation and evolution of the band structure. In said lattice, the finite stretch was found to not only tune the symmetry of the band structure but also purify the elastic waves into easy modes. The uniaxial stretch exhibits the opposite impacts on the evolution of two easy modes, while the effect of the biaxial stretch is equated with the superposition of the uniaxial stretches in the two tessellation directions. The mentioned effects on the band structure could be attributed to the competition between the effective shear moduli and lengths for different beam components. As a result, the finite stretch could tune the directional elastic wave bandgap of the soft lattice, and the broadest bandgap could be anticipated in an equi-biaxial stretch. This study may shed some light on the design and implementation of elastic wave control devices with weight efficiency and tunability. It also reveals that the theoretically predicted flat bands did not exist in the numerical calculations, a difference between the physical system and the corresponding simplified theoretical model.

Directional Bandgap Analysis in Phononic Crystal with Rectangular Super Cell Structure

Phononic crystals have promising applications in the field of elastic waves and to attenuate the vibrations with their extraordinary feature of stop bands also known as bandgaps. Due to periodicity in structure, the wave in certain band of frequencies is not allowed to propagate. In this paper, we have proposed a phononic crystal whose unit cell is composed of super cell structure consisting of air voids and scatterer distributed in nice rectangular units. The new design is found to have a wider directional band gap in the low-frequency zone. The dispersion relationship of the model is obtained by the computational method using finite element analysis. Numerical results show that the improved phononic crystal with super cell structure enhances the directional bandgap by around 180% when compared with the conventional phononic crystal having one scatterer with same filling factor. The proposed model with super cell structure opens the directional bandgap of 84 Hz with the lower bound frequency of 125Hz and upper bound frequency of 209 Hz in the horizontal (Γ→X) direction.

Nonreciprocal acoustic scattering from an elastic plate with spatiotemporally modulated material properties

Acoustic and elastic metamaterials with space- and time-dependent material properties have received great attention recently as a means to realize nonreciprocal wave propagation. The nonreciprocal behavior of propagating waves in a spatiotemporally modulated infinite medium is usually characterized by directional bandgaps present in the frequency-wavenumber spectrum. However, less attention has been given to acoustic scattering from spatiotemporally modulated media. In this work, we consider nonreciprocal reflection and transmission from a spatiotemporally modulated, infinite elastic plate excited by a plane wave at oblique incidence. A semi-analytical approach is developed that considers the coupling between the acoustic waves and the displacement of the plate. The reflection and transmission response of the plate for each generated frequency harmonic as a function of the incident angle are reported. Finally, we find conditions on the modulation parameters that yield a large degree of nonreciprocity. The present analysis leads to potential applications in acoustic communications, such as directional wave sensing.

Parametrically excited unidirectional wave propagation in thin beam phononics

Wave attenuation, filtering and guiding is an ongoing topic of scientific research, as there are many opportunities for improvement of existing solutions in modern industry. One of the recent advancements has been made with the use of non-reciprocal metamaterials.Certain properties of metamaterials have made them suitable for use in various engineering fields. In this study, we investigate non-reciprocal wave propagation behavior in coupled thin beams phononics, due to time-modulation of material properties and axial loads. We compare the results for the beams which are interconnected with Winkler?s type of elastic layers and elastic or viscoelastic Pasternak layers. An analytic approach is used to discover directional band gaps and investigate wave propagation through these systems of beams, at relevant excitation frequencies. The proposed framework can be exploited in further analysis of phononic systems based on multiple beams coupled through different mediums and structural elements modeled with higher-order beam theories.

Unidirectional transmission of funnel-shaped waveguide with complete bandgap

It will be a future trend to apply quantum photonic technology to communication technology and information processing. One of major developing directions of quantum photonic technology is the miniaturization and on-chip integration. Like the diodes in integrated electric circuitry, optical unidirectional transmitter devices (UTDs) play an important role in processing the quantum information and also represent the main components of integrated optical devices. Thus, the design of UTDs has become one of the research hotspots. With photonic bandgap and localization characteristics, as well as easy micro-nano scaled integration, the photonic crystals (PCs) are often preferred when used to develop micro-nano integrated optical devices. At present, the common methods of achieving UTD with photonic crystals include directional bandgap mismatch, asymmetrical coupling by a micro-cavity, odd-even mode conversion, total reflection of photonic crystals with grating and photonic crystal heterostructure, etc. However, these optical unidirectional transmitters gained through the above methods generally have a low forward transmission, narrow working band, complex structure, etc. In the paper a novel method of UTD is put forward based on photonic crystal and a UTD of funnel-shaped waveguide is designed. The design of the device is divided into two parts: optimal funnel waveguide design and optimal point defect design. The band structure of TE polarized photonic crystal is calculated by R-soft. A triangular lattice circular air hole photonic crystal with complete photonic band gap is used as the initial structure and line defects are introduced to form a funnel-shaped waveguide structure (FSWS). The FSWS consists of the first waveguide W1, the second waveguide W2 and a funnel cavity. The funnel cavity is shaped like a funnel and located at the coupling between W1 and W2. Owing to the unique characteristics of the waveguide, the light wave transmission will be localized in the waveguide, which is conducive to improving the forward transmission. The influence of width variation of W2 with forward and backward incident light are analyzed by the finite difference time domain (FDTD) method, and W2 is selected as a waveguide formed by removing 11 rows of air holes. The FSWS achieves the initial asymmetric transmission, while the backward transmission remains high. Further studies are conducted to introduce four types of point defects to suppress the backward transmittance. The point defects refer to moving one or two air holes. In the work the FDTD is also used to calculate four kinds of point defect backward transmittance spectra and optimize the positions of point defects. Finally, it is found that when the optimal point defect mode is type I and <i>d</i> = 5<i>a</i>, the forward transmission (<i>T</i><sub>f</sub>) and transmission contrast (<i>C </i>) at 1550 nm are 0.716 and 0.929, respectively. Working bandwidth (<i>B</i>) can be increased up to 111 nm (1501–1612 nm). By mode analysis, it is found that the point defect introduces mode mismatch between W1 and W2, by converting the fundamental mode in W2 into high-order modes. Thus, the back-propagating light waves in W2 cannot effectively couple into W1, resulting in complete blockage of backward propagation. In addition, the structure is made of silicon based air hole photonic crystal. The 2D air-hole PC slab is mature and even compatible with conventional complementary metal oxide semiconductor (CMOS) processing. The designed UTD is easy to implement, and has the advantages of simplicity and high unidirectional transmission characteristics. Therefore, it can provide a new solution for UTDs with higher requirements for integrated optical path at present.

Acoustic Tunneling Study for Hexachiral Phononic Crystals Based on Dirac-Cone Dispersion Properties

Acoustic tunneling is an essential property for phononic crystals in a Dirac-cone state. By analyzing the linear dispersion relations for the accidental degeneracy of Bloch eigenstates, the influence of geometric parameters on opening the Dirac-cone state and the directional band gaps’ widths are investigated. For two-dimensional hexachiral phononic crystals, for example, the four-fold accidental degenerate Dirac point emerges at the center of the irreducible Brillouin zone (IBZ). The Dirac cone properties and the band structure inversion problem are discussed. Finally, to verify acoustic transmission properties near the double-Dirac-cone frequency region, the numerical calculation of the finite-width phononic crystal structure is carried out, and the acoustic transmission tunneling effect is proved. The results enrich and expand the manipulating method in the topological insulator problem for hexachiral phononic crystals.