Bragg Band Gaps Research Articles

Composite trampoline metamaterial with enlarged local resonance bandgap

The engineered resonance phenomena by artificial structures have opened a new frontier in modern science and technology. Artificial structures such as pillared phononic crystals and metamaterials are emerging domain due to their surface resonance features that are governed by periodic array of pillars embedded on a host plate. The dual aspects of pillared structure exhibiting both Bragg and local resonance bandgaps make it a prominent choice for wave manipulation in general and vibration isolation in particular. The present study proposes pillared-plate structure based composite trampoline metamaterial that can exhibit ultrawide local resonance bandgap with relative bandwidth around 100%, confirmed by numerical and experimental approaches. The study establishes that composite nature of the pillar together with trampoline effect caused by drilling periodic array of holes in the host plate can enhances the effective mass density and reduce the plate stiffness, respectively that eventually lead to enlarged local resonance bandgap. The evolution of composite design with trampoline effect from parent pillar-plate structure is also fully discussed through wave dispersion and frequency response studies, and the widening of local resonance bandgap is demonstrated. By a parametric study, the effect of geometric parameters on the reported bandgaps is elaborated. Both numerical and experimental results validate the effectiveness of composite trampoline pillar-plate structure in attenuating bulk waves over broadband frequency spectrum. The new findings reported here provide another perspective on the dynamical characteristics and usefulness of pillared metamaterials for wave manipulation and subwavelength vibration attenuation.

Purified nonlinear guided waves through a metamaterial filter for inspection of material microstructural changes

Nonlinear guided waves (NGWs) exhibit extraordinary sensitivity to microstructural changes in materials which are often considered as damage precursors in many structural health monitoring (SHM) applications. However, these changes are usually very small at the microstructural level, thus generating weak nonlinear wave components which are prone to or even overwhelmed by other deceptive and non-damage-related nonlinear sources present in a monitoring system. This may jeopardize the practical implementation of the NGW-based SHM methodology. To tackle this problem, this paper proposes a metamaterial filter (meta-filter (MF)), in the form of a patch to be surface-mounted over the structure under inspection. The MF is designed to purify the probing waves during propagation before reaching the inspection area through tactical elimination of non-damage-related nonlinear components from the actuation. Considering different bonding conditions and the lattice symmetry of the MF, two types of bandgaps, corresponding to Bragg scattering and local resonances, alongside their respective band properties are analyzed. Time-domain finite element simulations are carried out to assess the efficacy of the MF in terms of wave purification in the context of SHM, supported by experimental validations. The designed MF is deployed in an aluminum strip to detect the material microstructural changes induced by a thermal ageing treatment. Results demonstrate the designed MF significantly enhances the detection ability of NGW-based SHM system. Both locally resonant and Bragg bandgaps can, in principle, be used for wave purification. While the former requires precise control of the bonding quality of the MF, the latter relies on symmetrical installation of the MF to ensure a reasonably wide wave filtering range. Considering variability factors in the implementation of the MF and better immunity to the nonlinearity of the bonding layers, preference is given to Bragg bandgap for NGW-based SHM applications.

Phononic crystal sandwich for broadband and low frequency acoustic insulation under diffuse field

Light and thin structures exhibiting high sound insulation over a wide frequency range are a major industrial concern, especially in the transport and building sectors. Phononic crystals constitute promising solutions to solve this issue due to their particular dispersion properties. In this work, we build a system consisting of a well-known sandwich panel comprising a soft elastic core layer hosting periodically arranged rigid inclusions. Diffuse field measurements show a huge improvement of the Transmission Loss compared to the system without inclusions. In fact, for this kind of panel, the structured core enables Bragg band-gap opening for guided slow propagating waves leading to low frequency and broadband enhancement of the Transmission Loss. Using a 3cm-thick material we are able to improve the response from 300 Hz on (λ/38 in air). We then develop a finite elements model to achieve a precise description and understanding of the problem. We also propose a numerical tool to analyze the system's band-structures from a vibroacoustic point of view. It proves very useful for the further development of practical solutions.

Piezoelectric metastructures for simultaneous broadband energy harvesting and vibration suppression of traveling waves

In this paper, we explore an electromechanical metastructure consisting of a periodic array of piezoelectric bimorphs with resistive-inductive loads for simultaneous harvesting and attenuation of traveling wave energy. We develop fully coupled analytical models, i.e. an electroelastic transfer matrix method, and exploit both locally-resonant and Bragg band gaps to achieve a multifunctional metastructure which is capable for maximum energy conversion and vibration mitigation in a broadband fashion. Our analytical and numerical results show that the proposed metastructure can achieve energy harvesting efficiency up to 95% at the local resonance frequency of 3.18 kHz, while reaching about 51% at 5.8 kHz near the upper limit of the Bragg band gap. The broadband vibration mitigation performance based on 50% power attenuation is predicted as 1.8 and 1.1 kHz in the vicinity of the band gaps. The theoretical frameworks and the applicability of the proposed metastructure are validated using a full-scale experimental setup.

Study on band gap properties of asymmetric locally resonant complex phononic crystals

In this paper, the band structure and transmission characteristics of asymmetric locally resonant complex phononic crystals are studied. Based on the Bragg band gap mechanism, an asymmetric local resonance element was designed and the structural parameters were optimized to obtain a wide band gap. The results show that the range of the first complete band gap is obviously affected by the size of the scatterer, the radius and height of the locally resonant cylinder and the position of the cylinder. At the same time, the transmission characteristics of the 10*10 periodic arrangement structure are calculated to verify the accuracy of the energy band structure.

An ultrawide-zero-frequency bandgap metamaterial with negative moment of inertia and stiffness

Metamaterials have demonstrated great potential for controlling wave propagation since they are flexibly adjustable. A new one-dimensional metamaterial model with both a negative effective moment of inertia and negative effective stiffness is proposed. A negative effective moment of inertia and negative effective stiffness can be achieved by adjusting the structural parameters in certain frequency ranges. Bandgaps in the low-frequency range with exponential wave attenuation can be generated in the metamaterial. A flat band is obtained that couples two Bragg bandgaps to achieve a wide bandgap in the low-frequency range, where the effective moment of inertia and effective stiffness are both infinite. A zero-frequency bandgap can be achieved by adjusting the structural parameters. Quick attenuation of wave is observed in the zero-frequency ranges with single-negative parameters. Furthermore, an ultrawide-zero-frequency bandgap is obtained by optimizing the structural parameters of the system. In addition, it is easy to switch between the Bragg and locally resonant bandgaps. This new metamaterial can be applied to ultralow-frequency-vibration isolation.

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.

Topological phononic crystal plates with locally resonant elastic wave systems

In this paper, we study the topological properties of subwavelength bands in elastic phononic crystal (PC) plate hybridized with extra local resonances and analyze the band-structure evolution of a topological PC plate with local resonator using finite element method (FEM). Our structure can produce two bandgaps in the subwavelength region: one originates from the local resonator of unit cell and the other one stem from breaking the C6v symmetry of an original plate PnC in a honeycomb lattice to introduce valley pseudospins. It is found that the edge states only existed in the Bragg bandgaps and the directional spread of elastic waves can be realized in both straight and bent waveguides, and the numerical simulation in a waveguide plate perfectly agrees with the theoretical results. In addition, experimental test is used to validate theoretical and numerical approach to the design of topological waveguides. This study provides an effective approach of producing robust elastic wave topological edge modes in the subwavelength region for plate-like structure.

Broadband bandgap and shock vibration properties of acoustic metamaterial fluid-filled pipes

This paper describes the design of an acoustic metamaterial fluid-filled pipe with periodically variable materials. The aim of this design is to improve the broadband vibration attenuation frequency range of fluid-filled pipes by combining the mechanism of local resonance (LR) and Bragg scattering bandgaps (BGs). The vibration bandgap (BG) of the pipe is investigated using the transfer matrix method. It is demonstrated that the coupling of LR and Bragg scattering BGs produces a remarkable improvement in effective bandwidth. Additionally, the external shock excitation effect on pipe vibration is calculated using the finite element method. This indicates that the strongest interaction between the LR and Bragg BG is achieved when the LR is located in the center of the softer material. However, this strong coupling effect may cause some degeneration in the Bragg BG. Moreover, in practical applications, the position of the LR BG should be determined according to the vibration BG requirements. Experimental samples are prepared, and an experimental test and verification procedure is conducted. The positions and widths of the BG and the shock vibration properties measured during the experiment agree well with the theoretical results. This research provides a technical and theoretical basis for the attenuation design of vibration reduction systems for fluid-filled pipes that may be subjected to explosive loads.

An Inertant Elastic Metamaterial Plate With Extra Wide Low-Frequency Flexural Band Gaps

Abstract Arranging inerter arrays in designing metamaterials can achieve low-frequency vibration suppression even with a small configuration mass. In this work, we investigate flexural wave bandgap properties of an elastic metamaterial plate with periodic arrays of inerter-based dynamic vibration absorbers (IDVAs). By extending the plane wave expansion (PWE) method, the inertant elastic metamaterial plate is explicitly formulated in which the interactions of the attached IDVAs and the host plate are considered. Due to the additional degree-of-freedom induced by each IDVA, multiple band gaps are obtained. Along the ΓX direction, the inertant elastic metamaterial plate exhibits two locally resonant (LR) band gaps and one Bragg (BG) band gap. In contrast, along the ΓM direction, two adjacent LR band gaps are obtained. Detailed parametric analyses are conducted to investigate the relationships between the flexural wave bandgap properties and the structural inertant parameters. With a dissipative mechanism added to the IDVAs, extremely wide band gaps in different directions can be further generated. Finally, by adopting an effective added mass technique in the finite element method, displacement transmission and vibration modes of a finite inertant elastic metamaterial plate are obtained. Our investigation indicates that the proposed inertant elastic metamaterial plate has extra-wide low-frequency flexural band gaps and therefore has potential applications in engineering vibration prohibition.

Bandgap properties in metamaterial sandwich plate with periodically embedded plate-type resonators

In this study, a novel plate-type resonator is proposed, and the bandgap properties of a metamaterial sandwich plate containing a two-dimensional periodic array of these plate-type resonators are numerically and experimentally investigated. The finite element method is applied to calculate the band structure and the transmission spectra. The formation mechanisms of the bandgaps are investigated via the analysis of the mode shapes of the plate-type resonator and face plate in a unit cell. The results demonstrate that both locally resonant and Bragg bandgaps exist in the proposed structure. The selective coupling between the resonant modes of the plate-type resonator and the face plate is a necessary condition for the generation of locally resonant bandgaps that the resonant modes of the plate-type resonator can produce a reaction force on the support. The effect of the geometric parameters and surface mass ratio on the bandgaps is investigated, and the effect of the introduction of the plate-type resonator on the Bragg bandgap is studied. The improvements of the plate-type resonator by changing its structure or moving its attachment point are also discussed. Moreover, a metamaterial sandwich plate specimen is fabricated and vibration experiments are conducted, and it is observed that there is good agreement between the numerical predictions and the experimental results. The proposed strategy contributes to the possibility of fabricating a simpler structure to promote the exploitation of metamaterial sandwich plates in engineering.

Elastic Wave Properties of an Adaptive Electromechanical Metamaterial Beam

An adaptive metamaterial beam with a couple of electromechanical resonators in each unit cell is proposed in this study to open Bragg bandgap or locally resonant bandgap for flexural wave attenuation in Euler–Bernoulli beams. The electromechanical resonator is composed of a piezoelectric layer with segmented electrodes and shunt circuits, which affect the dynamic equivalent stiffness. It is illustrated that there is only a Bragg bandgap when the circuits of the two adjacent resonators are approximate to a short circuit or open circuit, and the locally resonant bandgap will be generated in the pure inductance circuits when the resonant frequencies are different in general. The locally resonant bandgap can be broadened by adding more resonators into the unit cell with the resonant frequencies of the shunting circuits satisfying a proper ratio.

Broadband omnidirectional near-infrared reflector based on an angle-insensitive photonic band gap.

Owing to the Bragg interference mechanism, band gap in all-dielectric one-dimensional photonic crystal (1DPC) is strongly sensitive to the incident angle, which limits the width of omnidirectional band gap. Based on the angle-insensitive Bragg band gap in 1DPC composed of alternating dielectric and hyperbolic metamaterial layers, we design a broadband omnidirectional near-infrared mirror with the bandwidth of 943 nm (52.3% relative bandwidth) without using the conventional cascade method. In addition, we show that the angle-insensitive property of the band gap is robust against the layer thickness disturbance. This multilayer-based broadband omnidirectional reflector will possess potential applications for omnidirectional filters within broad stopbands and photonic crystal fibers with broad operating bandwidths.

Lightweight architected lattice phononic crystals with broadband and multiband vibration mitigation characteristics

A novel architected lattice metamaterial with broadband and multiband bandgap characteristics is studied here. A slight structural modification in a regular lattice structure has succeeded to significantly magnify the vibration attenuation capability of these lightweight periodic lattices. The vibration control properties of these lattices are investigated both theoretically and experimentally. The sinusoidal-shaped ligament is found useful in generating a broadband Bragg bandgap with robust wave attenuation characteristics. The embedment of circular masses at the center of these lattices help induce multiband low frequency bandgaps. The properties of sinusoidal-shaped ligament such as the number of sine wave undulations/ligament wavelength and the effect of central mass radius on bandgaps are investigated. Introducing material damping flattens the transmission peaks and it results in a broadband bandgap distributed throughout the frequency spectrum. The experimental results are in good agreement with numerical solutions. The proposed lightweight lattice metamaterial can be effectively applied at any length scale for controlling acoustic/elastic waves propagation.

Artificial resonant crystals for hydroelastic waves

Engineering the propagation of water waves is a crucial challenge for potential applications at oceanic scale. Despite their apparent complexity, they do not fundamentally differ from any other kind of physical wave. Similar to recent approaches in optics or acoustics, we propose to artificially manufacture materials at the sub-wavelength scale to modify the propagation characteristics at will. We demonstrate that hydroelastic waves allow for the straightforward control of the medium properties, as well as the quantitative measurement of the full wave field. We investigate propagation in hydroelastic metamaterials made from periodic arrays of tunable resonators. We fully characterize the band structures of such materials, revealing the coexistence of Bragg and hybridization bandgaps. We also introduce a theoretical approach to model this complex system and predict its band structure. These unprecedented experimental and theoretical results reveal the possibility to efficiently control water waves at the laboratory scale.

Bandgap and Vibration Reduction of Laminated Galfenol Phononic Crystal With Shunt Circuit

It is of great significance to adjust bandgaps (BGs) of laminated Galfenol phononic crystal (PC) by using nonlinearity of Villari effect and shunt elements for effectively reducing vibration. Based on the modified constitutive equations, the effective elastic modulus, and transfer matrix method (TMM), a dynamic nonlinear model with tunable elastic modulus for the PC is established. Comparisons between the calculated and measured results show that the model can describe the changing laws of the Galfenol rod's effective elastic modulus with frequency and shunt capacitance, and can predict nonlinearity of the rod. The effects of stress and bias field on the attenuation constant peak and cutoff frequency of Bragg BGs (BBGs) are analyzed, and the optimal and suboptimal operating points of BBGs are determined. The effects of shunt capacitance and stress on BBGs, resonant BGs (RBGs), and common BGs (CBGs) are analyzed, and it is found that larger magnetomechanical coupled factor and smaller shunt capacitance can effectively reduce vibration.

Dispersion engineering of two-dimensional photonic crystals composed of graphene-covered tellurium rods

We investigate theoretically the frequency spectrum of two-dimensional photonic crystals using the well-known Dirichlet-to-Neumann (D-to-N) map method. The PhCs with square and triangular arrangements are built by graphene-covered tellurium rods which are surrounded by ion gel. The resulting frequency spectrum represents two forbidden frequency band, termed Bragg and graphene photonic band gaps. It is demonstrated that these forbidden band gaps can be controlled actively by altering the graphene chemical potential through applying external voltage. A tuning range of 4.81 THz and 5.31 THz was achieved for Bragg photonic band gap in square and triangular lattices, respectively, and a wide tuning range of 13.85 THz and 14.69 THz was achieved for graphene photonic band gap, when the chemical potential varies from μc = 0 to μc = 1.2 eV. These achievements may have future applications in some optical devices such as filters, sensors, nano-composites and energy storage devices in THz spectrum.

Ultra-thin Piezoelectric Lattice for Vibration Suppression in Pipe Conveying Fluid

In this paper, an electrically active, ultra-thin, easy-to-implement, and tunable phononic crystal (PC)-based device is proposed to suppress excessive vibration in pipes conveying fluids. We demonstrate that this device can be realized by periodic implementation of piezoelectric patches with shunt circuits on the pipe acting as PCs for vibration suppression. The mathematical model of the pipe structure is simplified to the form of the Euler–Bernoulli beam, and the transfer matrix method and the finite element method are used to predict the effective bandgap. Conversion between mechanical vibration energy and electrical energy via the piezoelectric effect is observed. As a result, the pipe vibration is suppressed by combined Bragg and electroelastic bandgaps. The comparison with previous literature shows that this ultra-compact device provides a new solution for vibration and noise control in long-distance fluid-conveying pipe systems.

Tunable Bragg reflector with parallel bulk Dirac semimetals at terahertz frequencies

We propose numerically a terahertz Bragg reflector with two parallel bulk Dirac semimetals (BDSs) sheets separated by alternated dielectric gratings using the finite-difference time-domain (FDTD) method. The transmission of the proposed reflector can be tuned via not only varying the permittivity of the dielectric grating but also changing the period number of the unit cells. By adjusting the separation distance of the parallel BDS sheets, we can derive another degree of freedom to tune the Bragg band gap. In addition, the transmission spectra can also be freely tuned by means of alkaline metal doping. At last, the defect resonant mode is realized in the Bragg reflector. Our proposed Bragg reflector will have potential prospects in designing integrated photonic circuits at terahertz frequencies.

Ultrawide coupled bandgap in hybrid periodic system with multiple resonators

Mechanical metamaterials can be used to control elastic waves, but it is challenging to obtain multiple or ultrawide bandgaps. A one-dimensional simple periodic system with multi-resonator unit cells can achieve multiple locally resonant bandgaps. A unit cell that comprises multiple cells is called a hybrid unit cell. Two different metamaterials with hybrid unit cells are proposed to achieve a wider coupled bandgap. The first type of metamaterial with a hybrid unit cell comprises two simple cells that have different bandgaps connected by a spring. A new Bragg bandgap appears near the locally resonant bandgaps. By adjusting the spring stiffness, these two types of bandgaps can be coupled to achieve an ultrawide coupled bandgap in a lower frequency range. The second type of metamaterial with a hybrid unit cell comprises two different sub-periodic systems. The bandgaps can be combined to achieve a wider bandgap. With this hybrid periodic system, a wider bandgap can be achieved by designing sub-periodic systems with different bandgaps. In addition, the transmission of a finite periodic system is calculated by the transfer-coefficient method, and the results show that elastic waves can be suppressed in wider frequency range in hybrid periodic systems. This paper provides new ways to design metamaterials with wider and lower bandgaps, which can be used for wide and low-frequency vibration isolation in engineering applications.