Band Gap Formation Research Articles

Broadband vibration attenuation characteristic of 2D phononic crystals with cross-like pores

The emergence and development of phononic crystals provide a feasible way to manipulate the propagation of elastic waves in structures. In this study, a class of single-phase 2D phononic crystals with tetragonal topology and cross-like pores is proposed. Both numerical simulation and theoretical analysis are performed to reveal the formation and regulation mechanism of bandgap and to obtain broadband vibration attenuation capability. The results show that the X-shaped pores can lead to the multiband and broadband characteristics of the structure, which are closely related to the coupling mechanisms of Bragg scattering and local resonance. In contrast, cross-shaped pores can open wide bandgaps at low frequencies. Notably, by means of identifying the bandgap edge modes to establish simplified vibrating systems, the analytical formulations derived from structural mechanics can accurately predict the bandgap edge frequencies, which provide effective guidance for bandgap tuning and structural design. Moreover, the vibration mitigation capability can be further enhanced by combining structures with different mass distributions. Compared with the multiphase structure, the structure proposed in this study is lighter and easier to fabricate, which provides significant guidance for the design of tunable phononic devices.

Aniline dimers serving as stable and efficient transfer units for intermolecular charge-carrier transmission

Because any perturbation in the number of oxidation sites associated with the polymeric backbone can cause changes in the electrical properties, the stability of electrical properties has strongly prevented the wide adoption of most conducting polymers for commercialization, e.g., polyanilines (PANI). Herein, we showed that aniline dimers (AD) had more stable conductivity during redox due to their determinately separate oxidization or reduction units. Instead of intramolecular charge transfer as PANI, AD could serve as effective transfer units to facilitate intermolecular charge-carrier transmission due to low band-gap formation induced by the J-aggregation of AD, ensuring efficient conductivity. Typically, the electrical properties of AD-derived materials will still be stable after 10,000 redox cycles under a high operating voltage, far surpassing PANI under equivalent conditions. Meanwhile, the AD-derived materials could act as effective conducting and sensing layers with good stability. This approach opened an avenue for improving the stability of conductive polymers.

Intercalation of Sr in AA stacked bilayer graphene : DFT study of the electronic structure and optical properties

We report the structure, electronic band structures, and total and partial electron density of states of strontium intercalation in the A A bilayer of graphene (Sr-intercalated AA stacked BG) from first-principles calculations. Our results show that the Sr intercalation influences the electronic properties. Indeed, we observed the contribution of the Sr atom to the band gap formation. The p and d orbitals of the Sr atom have a remarkable contribution to the formation of the DOS of the Sr-intercalated AA stacked BG. The Dirac point where the gap is non-zero in the AA stacked BG is located at about 1 . 38 e V below the Fermi level. Thus, the electron density is maximal around the C atoms, which leads to an efficient transfer of electric charges from the Sr atom to the C atoms. In addition, we have exploited the complex dielectric function to calculate the absorption coefficient, refractive index, and extinction index. The static refractive index increases in vertical polarization and diverges in parallel mode, confirming the pure metallic behavior of the Sr-intercalated AA stacked BG material. Moreover, the value of the absorption coefficient in the visible region increases in the vertical mode while it decreases in the parallel direction. These results indicate that AA stacked BG intercalated by Sr has relevant properties for optoelectronic and ultrafast devices.

Experimental Evidence of the Band Gap Formation in Rotors With Longitudinal Periodicity

Abstract The longitudinal periodicity of the rotating elements in a rotating machine can impose band gaps (modal spacing) on the frequency spectrum of the system. These band gaps are characterized by a large distance between two adjacent modes with a low vibrating response of the system. Here, the rotating elements of the machine (e.g., the stages or the impellers) are considered to be the periodic elements of the rotor. In this disk-like configuration of the rotor, the system can present band gaps due to two different reasons: the matching between the number of disks and the eigenmode wavenumber (usually in slender rotors); the presence of local-mode shapes (usually in large rotors). This work presents experimental evidence of the band gap formation in a slender periodic rotor. The obtained results validate the theoretical predictions of previous works.

Study of Non-Periodical Mechanical Metamaterials: Design and Application

We studied a typical mechanical metamaterial with different geometry patterns to demonstrate its effect in wave transmission. An inclusion geometry described by the trigonometric function is employed to generate local resonance under wave propagation. It has been found that the inclusion geometry plays an important role in the bandgap formation and attenuation of sound wave. More importantly, for a hybrid unitcell, the existing of flat and negative-slope bands indicates the translational mode of the dense core, which is critical to understand the wave reflection through non-periodical metamaterials. Furthermore, we propose a concept of velocity tuning of its individual components, which gives rise to local high strain energy, to explain why the absorptivity of sound wave is high. With help of embedded electronic units and dielectric materials, we can realize the active control of the deformation and reconfiguration of the unitcell, thus, to alter its band structure properties. The fabrication of such metamaterials can be realized by plasma etching, laser printing and nanofabrication from centimeter scale to nanometer scale. Therefore, the applications of mechanical metamaterials can be extended from sound filtering in centimeter scale to thermal management in nanometer scale.

A wave and Rayleigh–Ritz method to compute complex dispersion curves in periodic lossy acoustic black holes

In this work we first propose a wave and Rayleigh–Ritz method (WRRM) to analyze the vibrations of periodic systems. It is well-known that one of the main difficulties of the Rayleigh–Ritz method (RRM) is to find suitable basis functions that satisfy the problem boundary conditions. In the WRRM, this is done by expanding the system response as a superposition of the basis of the nullspace of the matrix defining the system periodic conditions. Therefore, the WRRM widens the potential of the RRM and constitutes a computationally efficient alternative to the wave and finite element method (WFEM) for structures requiring very fine meshes. Although the method is of general application, in this paper it is presented for an infinite periodic beam consisting of acoustic black holes (ABHs) cells with damping layers. Periodic ABHs exhibit broadband vibration reduction thanks to bandgap formation at low frequencies and to the ABH effect in the mid-high frequency range. The WRRM allows one to obtain the equations of motion of the periodic ABH beam and to define linear and quadratic eigenvalue problems to respectively obtain the system’s real and complex dispersion curves. While the former have been studied at extent, the latter have been barely analyzed for periodic ABH beams or plates. And they are of critical importance given that ABHs are strongly damped systems and that damping layer properties may be frequency-dependent. Therefore, the second contribution of this work is to carefully inspect the role played by the imaginary part of the complex dispersion curves on the functioning of the ABH periodic beam. Its value below and above the ABH cut-on frequency is inspected and a parametric analysis considering variations on the ABH profile and damping layer geometry is carried out. The underlying physics is explained and, finally, a transmissibility analysis on a finite ABH periodic beam with five cells is provided to confirm the mechanisms found for infinite periodic damped ABH beams.

Band gap mechanism and vibration attenuation of a quasi-zero stiffness metastructure

PurposeThe main purpose of this paper is to investigate the vibration isolation performance of a quasi-zero stiffness (QZS) metastructure by employing the band gap (BG) mechanism.Design/methodology/approachThe metastructure QZS characteristic was investigated through static analysis by numerical simulation. Based on that, the BG mechanism is primarily used in this article to investigate the wave propagation characteristics of this structure. The model's dispersion relation is then examined using theoretical (perturbation method) and finite element techniques. The dynamic response of the finite-size systems and experimental analysis is used to confirm the vibration mitigation property under investigation. Finally, the model's ability to absorb energy was examined and contrasted with a traditional model.FindingsThe analytical analysis reveals the dispersion curve and the effect of the nonlinear parameter on the curve shifting. The dispersion curve in the finite element method (FEM) result depicts five complete BGs within the range of 0–1,000 Hz, and the BG width accounted for 67.4% of the frequency concerned (0–1,000 Hz). Eigenmodes of the dispersion curves were analyzed to investigate the BG formation mechanisms. The dependence of BG opening and closure on structure parameters was also studied. Finally, the energy absorption property of the QZS metastructure was evaluated by comparing it with a classical model. The QZS structure absorbs 4.08 J/Kg compared to the 3.69 J/Kg absorbed by the classical model, which reveals that the QZS demonstrates better energy absorption performance. Based on the BG mechanism, it is clear that this model is an excellent vibration isolator, and the study reveals the frequencies at which complete vibration mitigation is achieved. As a result, this model could be a promising candidate for vibration mitigation engineering structures and energy absorption.Originality/valueThe tough vibration issue, which is primarily experienced in mechanical equipment, will be resolved in this study. This study provides a precise understanding of the QZS metastructure's isolation of vibration, including the frequencies at which this isolation occurs.

Development of locally resonant meta-basement for seismic induced vibration control of high-rise buildings

High-rise buildings may suffer severe damage or even collapse when subjected to excessive vibrations during earthquake excitations. Suppressing seismic induced vibrations is of great significance to ensure the safety of these high-rise structures. Many vibration control techniques have been proposed in the past decades, but certain inherent limitations exist in these methods. Recent investigations in the field of solid-state physics have revealed that periodic structures, termed elastic metamaterials, can be used to manipulate the propagation patterns of acoustic/elastic waves. Waves are not able to propagate through the periodic structure when the frequencies of input waves fall within the bandgaps of the structure. This special characteristic has motivated researchers to develop meta-based techniques for structural vibration control. On the other hand, floating floor structure (FFS), in which the floor is isolated from the supporting beam, has been used to control the vibrations of buildings. Inspired by the periodic theory and FFS, in the present study, the conventional underground basement of high-rise building is modified to form a locally resonant meta-basement to block the propagation of seismic waves for mitigation of building vibrations during earthquake excitations. Firstly, the formation of bandgap of the proposed method is demonstrated through analytical study on the infinite number of unit cells and finite element modelling on the finite number of meta-basement. The influences of three key parameters of the meta-basement, i.e., the connecting spring stiffness, the number of meta-basement levels, and the parking ratio on the bandgap characteristics are then examined. Two design strategies of the meta-basement with the capability of reducing the seismic wave energy at frequencies corresponding to the vibration frequencies of the super-structure or reducing the seismic wave energy at its dominant frequency contents are proposed. Numerical simulations are carried out in both the frequency and time domains to evaluate the control effectiveness of the two design strategies on an example building structure. Results show that the proposed meta-basement can reduce the seismic responses of high-rise buildings and designing the meta-basement to mitigate the transmission of seismic wave energy at vibration frequencies of the super-structure is more effective to reduce building vibrations.

Transmission characteristics of DNA templated 1D photonic crystal system for 3D printing applications: Simulation

This paper discusses the novel features of DNA-templated one dimensional photonic crystals (1D PC) for additive manufacturing (AM) or 3D printing applications. AM applications utilize a variety of materials with tailored thermal, physical, chemical, and mechanical properties. However, the integration of optical properties into AM materials is less explored. AM parts produced from the materials having specific optical properties opens up many opportunities to develop novel integrated optoelectronic and photonic systems and provide sustainable structural color to the produced parts. This work proposes micro level periodic structures which can be used to replace existing color dyes for durable, non-toxic, cost-effective 3D printing applications. Based on ink jet printing technology, we designed DNA templated one dimensional (1D) photonic crystal (PC) of three-layer unit cell. The light transfer properties of the proposed 1D PC were examined theoretically in the range of 400 nm–800 nm of visible region of light using transfer matrix method (TMM). The photonic bandgap for DNA templated 1D PC is obtained around 450 nm and 650 nm of visible spectra region. The theoretical simulation shows that the presence of DNA template decreases the band gap width in the visible region and the three-layered periodic system helped to control the formation of multiple color bands in the visible region. The dispersion relation also confirmed that the electromagnetic fields in the stratified structure have been undergone multiple scattering and that results the formation of bandgap within the visible region. We also presented the standard deviation of the transmission coefficients in the range of 450 nm–650nm of visible spectra. Based on these observation and analysis, DNA templated PCs can be effective for tuning desired color spectra. Besides, this system can be used to replace the existing health hazardous synthetic dyes by incorporating with inkjet printing processes to create durable and colored 3D objects for aesthetic as well as technical purposes.

Bandgap and Vibration Suppression Mechanisms of Novel Star‐Shaped Hybrid Metamaterials

Herein, a novel star‐shaped hybrid acoustic metamaterial structure is proposed. Based on Bloch's theorem and the finite element method, the bandgap characteristics and the bandgap formation mechanism of different combinations of structures are first analyzed. Then, the propagation characteristics of elastic waves in Model C2 are studied with focus on equal frequency contours, phase velocity, and group velocity. And the attenuation of elastic waves in the finite size structure of Model C2 illustrates that the elastic waves are effectively suppressed in the bandgap frequency range, which further confirms the perfect correspondence between the bandgap and the vibration attenuation region. Finally, the influence of structural parameters on the bandgap is analyzed, as well as the change of the bandgap when the structure undergoes large deformation, which can realize the tunability and flexibility of the bandgap. This study provides important clues for the design of vibration isolators and metamaterials, and shows the good engineering application potential of the structure for vibration isolation.

Thomson scattering-induced bandgap in planar chiral phononic crystals

Releasing the dependence of the low-frequency and broad bandgaps on low stiffness and bulky masses has been an intractable bottleneck. Although inertial amplification is a terrific candidate for addressing the barrier, numerous extended ideas are limited to the classical models, thus, slowing or stalling the advances in this demand. To break this limit, we report a kind of planar chiral phononic crystal based on Thomson scattering. Different from the optimization effect produced in the locally resonant phononic crystals, the mirrored chirality can open a Thomson scattering-induced broad bandgap when the local resonant sub-structure is discarded. In addition, while simplifying the material components, we lower the starting frequency of the bandgap with a virtually unchanged width for the same lattice constant, stiffness and mass. Consequently, the starting frequency of the attenuation can be in the same order of magnitude as the local resonance bandgap, while the width is significantly better than the latter. Our proposal may open a new way to manipulate broadband elastic waves and validate that Thomson scattering is a promising alternative approach and mechanism for bandgap formation.

Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals.

Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong interactions between photonic modes of the same energy, where the level repulsion and the hybridization between modes causes the emergence of photonic bandgaps. However, most often this phenomenon does not lead to a complete and inverted bandgap formation over the entire Brillouin zone. Here, by systematically breaking the symmetry of a two-dimensional square photonic crystal, we investigate the formation of Dirac points, line node singularities, and inverted bandgaps. The formation of this complete bandgap is due to the level repulsion between degenerate modes along the line nodes of a semimetal-like photonic crystal, over the entire Brillouin zone. Our numerical experiments are performed by a home-build numerical framework based on a multigrid finite element method. The developed numerical toolbox and our observations pave the way towards designing complete bandgap photonic crystals and exploring the role of symmetry on the optical behaviour of even more complicated orders in photonic crystal systems.

Variable Dual Auxeticity of the Hierarchical Mechanical Metamaterial Composed of Re‐Entrant Structural Motifs

Herein, a novel hierarchical mechanical metamaterial is proposed that is composed of re‐entrant truss‐lattice elements. It is shown that this system can deform very differently and can exhibit a versatile extent of the auxetic behavior depending on a small change in the thickness of its hinges. In addition, depending on which hierarchical level is deforming, the whole structure can exhibit a different type of auxetic behavior that corresponds to a unique deformation mechanism. This results in a dual auxetic structure where the interplay between the two auxetic mechanisms determines the evolution of the system. It is also shown that depending on the specific deformation pattern, it is possible to observe a very different behavior of the structure in terms of frequencies of waves that can be transmitted through the system. In fact, it is demonstrated that even a very small change in the parametric design of the system may result in a significantly different bandgap formation that can be useful in the design of tunable vibration dampers or sensors. The possibility of controlling the extent of the auxeticity also makes the proposed metamaterial to be very appealing from the point of view of protective and biomedical devices.

Analytical dispersion curves and bandgap boundaries for quadrilateral lattices

The two-dimensional quadrilateral lattice structures are the most common periodic structures in industrial engineering application. This paper investigates the Bragg bandgap mechanism of classical quadrilateral periodic lattice structures. The explicit expressions of dispersion relations are obtained analytically and those with the eigenmodes corresponding to the same dispersion relation solution are connected to form the band structure. Unlike the existing works, it is the first to connect dispersion curves with the same eigenmodes, which explains the bandgap formation and transmission loss more reasonably. Four kinds of two-dimensional quadrilateral lattice structures are investigated to discuss the effects of shear force and mid-masses. The analytic expressions of bandgap boundaries are obtained and the influence of parameters including the mass ratio, tensile stiffness ratio and shear stiffness ratio on the bandgap boundaries is discussed.

Understanding the role of resonances and anti-resonances in shaping surface-wave bandgaps for metasurfaces

An array of surface-mounted prismatic resonators in the path of Rayleigh wave propagation generates two distinct types of surface-wave bandgaps: longitudinal and flexural-resonance bandgaps, resulting from the hybridization of the Rayleigh wave with the longitudinal and flexural resonances of the resonators, respectively. Longitudinal-resonance bandgaps are broad with asymmetric transmission drops, whereas flexural-resonance bandgaps are narrow with nearly symmetric transmission drops. In this paper, we illuminate these observations by investigating the resonances and anti-resonances of the resonator. With an understanding of how the Rayleigh wave interacts with different boundary conditions, we investigate the clamping conditions imposed by prismatic resonators due to the resonator’s resonances and anti-resonances and interpret the resulting transmission spectra. We demonstrate that, in the case of a single resonator, only the resonator’s longitudinal and flexural resonances are responsible for suppressing Rayleigh waves. In contrast, for a resonator array, both the resonances and the anti-resonances of the resonators contribute to the formation of the longitudinal-resonance bandgaps, unlike the flexural-resonance bandgaps where only the flexural resonances play a role. We also provide an explanation for the observed asymmetry in the transmission drop within the longitudinal-resonance bandgaps by assessing the clamping conditions imposed by the resonators. Finally, we evaluate the transmission characteristics of resonator arrays at the anti-resonance frequencies by varying a few key geometric parameters of the unit cell. These findings provide the conceptual understanding required to design optimized resonators based on matching anti-resonance frequencies with the incident Rayleigh wave frequency in order to achieve enhanced Rayleigh wave suppression.

Optimization of Band Gaps in Rotors With Longitudinal Periodicity and Quasi-Periodicity

Abstract Structures with inertia periodicity present the phenomenon of band gap formation, i.e., the appearance of regions in the frequency spectrum with a higher modal spacing and lower vibration response. Rotating machines can also present such phenomenon when their working elements are mounted periodically along the shaft (longitudinal periodicity). In the present work, this phenomenon in rotating machines is reviewed, and it is shown that band gaps can be moved toward desired locations in the frequency spectrum by mounting the working elements at optimized positions along the shaft. For that, a mathematical model of the rotating machine is correlated to experimental results, and the model is used to optimize the position of the working elements (disks) in the rotor. The optimized rotor is then experimentally tested, and the resultant band gap is measured. The obtained experimental results show that one can indeed tailor the band gaps and move them toward higher or lower frequencies as desired without changing the inertia of the working elements.

Hybrid Bragg-locally resonant bandgap behaviors of a new class of motional two-dimensional meta-structure

Bragg scattering and local resonance are two fundamental mechanisms for bandgap (BG) formation of phononic crystals (PCs) and acoustic metamaterials (AMs). In this paper, a new class of motional two-dimensional (2D) hybrid Bragg-locally resonant (LR) meta-pipe model is developed, and the BG interaction behaviors of such a meta-structure are explored. The pipe is axially composed of alternate materials, and is periodically encircled with dual-layer rings, which are used to simultaneously trigger Bragg scattering and local resonance. Meanwhile, the pipe conducts an axially spinning motion, and a steady fluid flows inside the pipe. Compared to static periodic structures, the orthogonal traveling waves due to spin bring about a 2D meta-structure, and the spinning local resonators yield an additional centrifugal effect on the pipe. The results reveal the formation of hybrid Bragg-LR BGs in such a motional meta-structure, and further demonstrate their complicated evolutions with the location, number and geometry of the local resonators as well as the pipe material. The impacts of motional properties on the hybrid BGs are discussed, and they are compared with the behavior of Euler-Bernoulli model. This study provides a more in-depth interpretation for the interaction of Bragg and LR BGs, which is especially beneficial to the vibration and noise reduction of rotors and fluid-transporting devices.

Electronic and Spin Structure of Topological Surface States in MnBi4Te7 and MnBi6Te10 and Their Modification by an Applied Electric Field

The electronic and spin structure of topological surface states in antiferromagnetic topological insulators MnBi4Te7 and MnBi6Te10 consisting of a sequence of magnetic MnBi2Te4 septuple layers separated by nonmagnetic Bi2Te3 quintuple layers has been calculated within the density functional theory. Features characteristic of systems with different terminations of the surface (both septuple and quintuple layers) have been analyzed and theoretical calculations have been compared with the measured dispersions of electronic states. It has been shown that a band gap of about 35–45 meV, as in MnBi2Te4, opens at the Dirac point in the structure of topological surface states in the case of the surface terminated by a magnetic septuple layer. In the case of the surface terminated by a nonmagnetic quintuple layer, the structure of topological surface states is closer to the form characteristic of Bi2Te3 with different energy shifts of the Dirac point and the formation of hybridized band gaps caused by the interaction with the lower-lying septuple layer. The performed calculations demonstrate that the band gap at the Dirac point can be changed by varying the distance between layers on the surface without a noticeable change in the electronic structure. The application of an electric field perpendicular to the surface changes the electronic and spin structure of topological surface states and can modulate the band gap at the Dirac point depending on the magnitude and direction of the applied field, which can be used in applications.

Investigation on Atomic Bonding Structure of Solution-Processed Indium-Zinc-Oxide Semiconductors According to Doped Indium Content and Its Effects on the Transistor Performance.

The atomic composition ratio of solution-processed oxide semiconductors is crucial in controlling the electrical performance of thin-film transistors (TFTs) because the crystallinity and defects of the random network structure of oxide semiconductors change critically with respect to the atomic composition ratio. Herein, the relationship between the film properties of nitrate precursor-based indium-zinc-oxide (IZO) semiconductors and electrical performance of solution-processed IZO TFTs with respect to the In molar ratio was investigated. The thickness, morphological characteristics, crystallinity, and depth profile of the IZO semiconductor film were measured to analyze the correlation between the structural properties of IZO film and electrical performances of the IZO TFT. In addition, the stoichiometric and electrical properties of the IZO semiconductor films were analyzed using film density, atomic composition profile, and Hall effect measurements. Based on the structural and stoichiometric results for the IZO semiconductor, the doping effect of the IZO film with respect to the In molar ratio was theoretically explained. The atomic bonding structure by the In doping in solution-processed IZO semiconductor and resulting increase in free carriers are discussed through a simple bonding model and band gap formation energy.

Attenuation bands for flexural–torsional vibrations of locally resonant Vlasov beams

In this paper, a study on flexural–torsional vibrations of finite beams with a large number of resonators periodically attached along the length is presented. Emphasis is given in determining bandgaps, defined as frequency ranges free of resonances. The structural model is based on a modified Vlasov theory that incorporates the resonators effect by means of sectional inertial properties depending on the excitation frequency. Analyzing these last properties, the mechanism of weak and strong bandgap formation is enlightened. Analytical formulas for the edge frequencies of bandgaps are obtained. Also, an exact analytical solution for the free and forced vibration of simply supported beams is presented. This approach allows exploring, from another point of view, the location of attenuation bands.