Frequency Band Gaps Research Articles

Broadening Frequency Bandgaps in a Beam with Periodic Internal Hinges, External Supports and Attached Masses

Представлен сравнительный анализ механизма формирования запретных зон частот в однородных предварительно напряженных балках с периодическими внешними опорами, шарнирами и прикрепленными массами. На основе теории Флоке получены аналитические выражения для функции, определяющей структуру запретных зон. Рассмотрено несколько периодических топологических систем: мета балка с промежуточными внешними опорами и прикрепленными массами, мета балка с внутренними шарнирами в паре с массами. Для периодических структур выведены дисперсионные уравнения запретных зон, построены и проанализированы дисперсионные кривые. В статье новизной являются результаты, касающиеся расширения резонансной полосы фононных запрещенных зон мета балки за счет слияния раздельных множеств запретных зон, генерируемых внутренними шарнирами или внешними промежуточными опорами с прикрепленными массами. Ներկայացված է հաճախությունների արգելված գոտիների ձևավորման մեխանիզմի համեմատական վերլուծությունը նախապես լարված համասեռ, պարբերական հենարաններով, հոդակապերով և կցված զանգվածներով հեծաններում: Դիտարկված է մի քանի պարբերական տոպոլոգիական համակարգեր. մետա հեծան միջանկյալ արտաքին հենարաններով և կցված զանգվածներով և մետահեծաններ՝ ներքին հոդակապերով՝ զանգվածների հետ: Պարբերական կառուցվածքների համար դուրս են բերված արգելված գոտիների դիսպերսիոն հավասարումները, կառուցված և վերլուծված են դիսպերսիոն կորերը: Հոդվածում նորություն են այն արդյունքները, որոնք վերաբերում են մետա հեծանի ֆոնոն արգելված գոտիների ռեզոնանսային շերտի ընդլայնմանը՝ այն իրարից բաժան արգելված գոտիների միաձուլման հաշվին, որոնց առաջացումը պայմանավորված է ներքին հոդակապերով, միջանկյալ արտաքին հենարաններով և կցված զանգվածներով: A comparative analysis is presented of bandgap formation mechanism in homogeneous prestressed beams with periodic external supports, hinges and attached local masses. Based on the Floquet theory the analytical expressions are derived for deviation functions defining bandgap structure. Several periodic topological structures are considered: meta beams with intermediate external supports and attached masses, internal hinges paired with masses. For periodic structures the band gap dispersion equations are derived, dispersion curves are plotted and analyzed. The innovation in this paper is the results concerning widening of the resonant bandwidth of a meta beam phononic bandgaps by merging of multiple separated bandgaps generated by the internal hinges or external intermediate supports with attached masses.

Band Gap Engineering and Frequency Dispersive Dielectric Properties of Rare Earth (Sm3+) Modified Ba0.8Sr0.2TiO3 Ceramics for Potential Use as an Optoelectronic Materials

Lead free perovskite materials have the capability to be used in various multifunctional applications. In this regard, dielectric and light absorption properties of Sm modified Ba0.8-xSmxSr0.2TiO3 have been explored. The dielectric constant has been estimated to be 2788 for Ba0.77Sm0.03Sr0.2TiO3. The optical band gap of all prepared samples has been evaluated by employing Tauc plot method and observed that the band gap varies 3.13-2.97 eV with the increase in Sm concentration. In brief, the present study reports the physical properties of Ba0.8-xSmxSr0.2TiO3 ceramics which open window for possible use of it as lead-free optoelectronic material.

Widening the frequency bandgap and reducing thermal conductivity in phononic crystals by tuning structural parameters using a novel computational simulation method

AbstractThis paper introduces and models a phononic structure based on single-crystal silicon, aiming to investigate the width of its frequency bandgap and the impact of key parameters on thermal conductivity. The modeled phononic crystal structure features a periodic arrangement of cylindrical holes in a silicon matrix. This research holds the potential to enhance thermal management performance of thermal metamaterials. Utilizing a 3D finite element method (FEM) model in COMSOL, we have computed phonon dispersion to estimate thermal conductivity. The study systematically has explored the influence of phononic crystal parameters—specifically, porosity, lattice constant, and thickness—along with their interactions on both thermal conductivity and frequency bandgap width.A comprehensive investigation of these parameters has been conducted for their optimization to achieve the maximum frequency bandgap width and minimum thermal conductivity using the response surface method model. Eigenfrequencies and wave vector parameters are extracted from the finite element model using a MATLAB script. Subsequently, thermal conductivity is calculated through the Callaway–Holland model, a simplification of the Boltzmann transport equation (BTE).Our results indicate that the frequency bandgap begins to form at approximately 43% porosity for a lattice constant and thickness of 100 nm each. Furthermore, adjusting the parameters led to a significant reduction in thermal conductivity, decreasing from 43.89 W m−1 K−1 to 0.39 W m−1 K−1. The novelty of our research lies in thermal conductivity control of phononic crystal metamaterials through their parameter variations, or a predictive method of thermal conductivity and its parameter sensitivity. This study advances the state of the art in phononic crystal metamaterial research, contributing to improved thermal management performance by enlarging frequency bandgaps.Overall, our findings deepen the understanding of how porosity, lattice constant, and thickness influence thermal conductivity and frequency bandgap width. They offer valuable insights into optimizing phononic crystal parameters, enhancing thermal management performance, and designing more efficient and effective phononic crystal structures.

Longitudinal wave propagation in a practical metamaterial lattice

A practical metamaterial lattice is constructed by integrating curved beams, four-link mechanisms, and cantilever beams with lumped masses. It can generate two complete low-frequency bandgaps due to the lateral local resonance, inertia mass, and the main chain. The effective mass density and stiffness are obtained using different effective models, which show negative within the bandgaps. The analysis of the energy distribution and the space wave attenuation reveals that the metamaterial can attenuate the elastic waves in an exponential form within the bandgaps along the lattice. The finite element model is established to show the dynamic behaviour of the elastic wave propagation in the frequency domain and transient domain. Both results show that waves can be efficiently blocked within the bandgaps, while outside the bandgaps, waves can propagate without any attenuation. Finally, the experimental model of practical metamaterial is constructed, and the test piece is excited by a force hammer. Experimental results verify that the practical metamaterial can efficiently suppress the vibration within the bandgap frequency and validate the accuracy of the theoretical prediction.

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.

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

AbstractThe suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch’s theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure’s excellent low-frequency vibration suppression capability.

Interdigitated-comb piezoelectric phononic crystals for innovative SAW devices

In this paper, piezoelectric phononic crystals made up of interdigitated combs in floating potential condition are studied. Calculation of the dispersion curves shows that, in addition to Bragg bandgaps due to the presence of periodic electrodes, supplementary bandgaps are present corresponding to electrical resonance/antiresonance of the comb pairs. Calculation of the reflection coefficient of finite-sized mirrors reveals the presence of high amplitude reflection coefficient lobes near these bandgap frequencies. The electrical response of single port resonators using these interdigitated comb mirrors fabricated with Al metallization on LiTaO3 POI substrate is contrasted with that of a resonator with classical mirrors, providing experimental verification of this mechanism for bandgap opening. Possible applications for SAW device design are finally discussed.

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.

Three-dimensional topological crystalline insulator without spin–orbit coupling in nonsymmorphic photonic metacrystal

Abstract By including certain point group symmetry in the classification of band topology, Fu proposed a class of three-dimensional topological crystalline insulators (TCIs) without spin–orbit coupling in 2011. In Fu’s model, surface states (if present) doubly degenerate at Γ ¯ and M ¯ when time-reversal and C 4 symmetries are preserved. The analogs of Fu’s model with surface states quadratically degenerate at M ¯ are widely studied, while surface states with quadratic degeneracy at Γ ¯ are rarely reported. In this study, we propose a three-dimensional TCI without spin–orbit coupling in a judiciously designed nonsymmorphic photonic metacrystal. The surface states of photonic TCIs exhibit quadratic band degeneracy in the (001) surface Brillouin zone (BZ) center ( Γ ¯ point). The gapless surface states and their quadratic dispersion are protected by C 4 and time-reversal symmetries, which correspond to the nontrivial band topology characterized by Z 2 topological invariant. Moreover, the surface states along lines from Γ ¯ to the (001) surface BZ boundary exhibit zigzag feature, which is interpreted from symmetry perspective by building composite operators constructed by the product of glide symmetries with time-reversal symmetry. The metacrystal array surrounded with air possesses high order hinge states with electric fields highly localized at the hinge that may apply to optical sensors. The gapless surface states and hinge states reside in a clean frequency bandgap. The topological surface states emerge at the boundary of the metacrystal and perfect electric conductor (PEC), which provide a pathway for topologically manipulating light propagation in photonic devices.

Hybrid intelligent framework for designing band gap-rich 2D metamaterials

An artificial intelligence machine learning-based design framework is proposed to design lattice-based metamaterials with hexagonal symmetry that deliver wide band gaps at user-desired frequency ranges between 0 and 1000 kHz. The design approach starts by selecting a traditional, easy-to-manufacture parent lattice-based material that does not necessarily exhibit wide or functional band gaps. Subsequently, the parent lattice is transformed into a band-gap-rich lattice by superposing periodic triangular-shaped perturbations (i.e., zigzag-sine-based curvatures) with controllable frequencies and magnitudes on its ligaments. Finally, the frequency and magnitude parameters needed to deliver a specific band gap between 0 and 1000 kHz are determined using a hybrid intelligent framework, developed based on an Adaptive Neuro-Fuzzy Inference Systems (ANFIS). The ANFIS network integrates fuzzy logic expert models and artificial neural networks’ machine learning capabilities. Such a hybrid network is known for its ability to model strongly nonlinear and complex data. The data used in training the ANFIS models is generated using parametric finite element-based simulations where band gaps corresponding to a wide range of perturbation frequencies and magnitudes are computationally determined. The parametric study showed a nonlinear and complex topology-band gap characteristic relation; however, the Adaptive Neuro-Fuzzy Inference System (ANFIS) proved capable of modeling the observed complex topology-band gap behavior efficiently. The accuracy of the ANFIS models exceeded 99 % in several design ranges (i.e., perturbation parameters ranges). These were designated as high-accuracy design regions and were highlighted in the proposed design approach. Using multiple case studies with different band gap requirements, the ANFIS-based design framework proved effective in delivering customized lattice-based metamaterials with user-defined band gap frequencies.

Nonlinear pendulum metamaterial to realize an ultra-low-frequency field effect bandgap

A field effect transistor (FET) is an extensively employed component in large-scale integrated circuits to regulate circuit on or off by modulating its gate voltage. The mechanical counterpart of a FET is of great significance for advanced regulations of acoustic or elastic waves. Recently proposed active metamaterials are promising scenarios of FET based on the opening and closing of frequency bandgaps through active elements, but hindered by the structural complexity in practice. In this study, we propose and experimentally realize a nonlinear pendulum metamaterial (NPMM) as a mechanical ultra-low-frequency FET. By employing the perturbation method to investigate its dispersion relationship, we show that the NPMM possess a field effect bandgap. Namely, the bandgap can be opened or closed by controlling the excitation amplitude of the impinging wave, which is largely affected by the relative mass of the inner pendulum unit. As a verification, the transmission behavior of the NPMM is numerically studied and experimentally tested. It shows that, once the amplitude of the impinging wave exceeds a certain threshold, the disappearance of a bandgap will be observed with a sudden amplification of the output wave. The central frequency of the field effect bandgap is as low as 4 Hz, whereas the characteristic size of the unit cell is only 4 cm. We expect that the present work opens a new avenue for low-frequency wave regulation.

Origin and tuning of bandgap in chiral phononic crystals

The wave equation revealing the wave propagation in chiral phononic crystals, established through force equilibrium law, conceals the underlying physical information, such as the essence of the motion coupling and the inertial amplification effect. This has led to a controversy over the bandgap mechanism. In this article, we theoretically unveil the reason for this controversy, and put forward an alternative approach from wave behavior to formulate the wave equation, offering an alternative pathway to articulate the bandgap physics directly. Based on the physics revealed by our theory method, we identify the obstacles in coupled acoustic and optic branches to widen and lower the bandgap. Then we introduce an approach based on spherical hinges to decrease the barriers, for customizing the bandgap frequency and width. Finally, we validate our proposal through numerical simulation and experimental demonstration.

Tunable bandgaps of guided waves by periodic shunting circuits in multilayered piezoelectric plates

The multi-mode and dispersion characteristics of guided waves in plate bring great challenges to the manipulation of guided waves and controlling vibration and noise. In this study, the Stroh formalism is developed to establish a theoretical model for deriving the dispersion relations of guided waves in a multilayered piezoelectric plate. The dispersion characteristics under different electrical boundary conditions introduced by periodic shunting circuits are discussed to reveal the influences of external circuits on guided wave propagation. The proper shunting circuit is not only the key point to obtain the specific frequency of bandgap, but also the effective method to control the bandwidth. Furthermore, for the separation of symmetric and anti-symmetric modes of guided waves, the multilayered piezoelectric plate with a mirror plane is studied by using an equivalent model. Results indicate that the propagation behaviors of guided waves in multilayered piezoelectric plates can be interpreted by developed Stroh formalism, and their bandgaps can be effectively manipulated by periodically external circuits. The tunable bandgaps in this work could be helpful for designing smart devices of wave isolation based on multilayered piezoelectric plate.

Novel small-size seismic metamaterial with ultra-low frequency bandgap for Lamb waves

Seismic metamaterials (SMs) possess bandgap characteristics, enabling effective attenuation of seismic waves within a specific frequency range. However, small-sized SMs typically struggle to achieve a wide low-frequency bandgap. This paper proposes four types of SMs. The dispersion curves of these models were analyzed, and their vibration modes were studied to elucidate the bandgap mechanism. To investigate the influence of structural parameters on the bandgap, geometric variables are analyzed. Subsequently, the spectrum and acceleration time history curves of Lamb waves in a finite SM system are analyzed to verify the bandgap's authenticity. The designed structure exhibits a bandgap ranging from 1.24 Hz to 16.86 Hz, with a relative bandwidth as high as 172.6% and over 96% maximum vibration displacement attenuation of the El Centro seismic wave. The designed SMs effectively cover the 2 Hz seismic peak spectrum that leads to structural damage. They possess ideal relative bandwidth and excellent isolation performance, further advancing the engineering application of SMs.

Novel Frame-Type Seismic Surface Wave Barrier with Ultra-Low-Frequency Bandgaps for Rayleigh Waves

Seismic surface waves carry significant energy that poses a major threat to structures and may trigger damage to buildings. To address this issue, the implementation of periodic barriers around structures has proven effective in attenuating seismic waves and minimizing structural dynamic response. This paper introduces a framework for seismic surface wave barriers designed to generate multiple ultra-low-frequency band gaps. The framework employs the finite-element method to compute the frequency band gap of the barrier, enabling a deeper understanding of the generation mechanism of the frequency band gap based on vibrational modes. Subsequently, the transmission rates of elastic waves through a ten-period barrier were evaluated through frequency–domain analysis. The attentional effects of the barriers were investigated by the time history analysis using site seismic waves. Moreover, the influence of the soil damping and material damping are separately discussed, further enhancing the assessment. The results demonstrate the present barrier can generate low-frequency band gaps and effectively attenuate seismic surface waves. These band gaps cover the primary frequencies of seismic surface waves, showing notable attenuation capabilities. In addition, the soil damping significantly contributes to the attenuation of seismic surface waves, resulting in an attenuation rate of 50%. There is promising potential for the application of this novel isolation technology in seismic engineering practice.

Square-root topological insulator for a dual-band photonic waveguide

We show that square-root topological insulators can be utilized as a platform for dual-band topological waveguides in 2-dimensional photonic crystals. Valley states for each of two frequency band gaps in differently perturbed decorated honeycomb lattices have opposite directions of the phase rotations, revealing opportunities for dual-band unidirectional topological valley transport. The topological valley edge states exist at the boundary between differently perturbed photonic crystals in the two frequency bands. In addition, unidirectional, and robust propagation of electromagnetic waves along the boundary in the two frequency bands are numerically performed. Our work provides extensions of square-root topological insulators to robust, unidirectional, and dual-band photonic waveguides.

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.

Multi-frequency and low frequency bandgap characteristics of concentric ring cement-based locally resonant phononic crystal

Multi-frequency and low frequency bandgap characteristics of concentric ring cement-based locally resonant phononic crystal

Existence of edge modes in periodic microstrip transmission line

The microstrip of modulated width is a realization of a one-dimensional photonic crystal operating in the microwave regime. Like any photonic crystal, the periodic microstrip is characterised by the presence of frequency bands and band gaps that enable and prohibit wave propagation, respectively. The frequency bands for microstrip of the symmetric unit cell can be distinguished by 0 or π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document} Zak phase. The sum of these topological parameters for all bands below a given frequency gap determines the value of the surface impedance at the end of the microstrip. We demonstrate that edge modes are absent in a finite microstrip terminated at both ends in the centres of unit cells, but they can be induced by adding the defected cells. Edge modes present at both ends of the microstrip enable microwave tunneling with high transitivity in the frequency gap with or without a change in phase. This has been demonstrated experimentally and developed in detail using numerical simulations and model calculations. The investigated system, with a doublet of edge modes in the frequency gap, can be considered as a narrow passband filter of high selectivity and characterised by a significant group delay.