Wave Band Gaps Research Articles

Structural designs, principles, and applications of thin-walled membrane and plate-type acoustic/elastic metamaterials

Many advanced physical properties can be realized by using well-designed acoustic metamaterial (AM) structures, which have significant application value in engineering. In particular, thin-walled membrane, plate, and shell-type structures with deep subwavelength thicknesses that can meet light weight requirements have attracted the attention of many researchers and engineers from various specialized fields. This Tutorial systematically introduced the structural design methods, acoustic/elastic wave attenuation and regulation principles, and engineering applications of thin-walled AMs for low-frequency sound insulation, sound absorption, and vibration reduction. In particular, the design methods and sound insulation/absorption properties of thin-walled AMs for realizing narrow-band and broadband sound attenuation were explored. Furthermore, the local resonance bandgap characteristics, quantitative extraction method for the bending wave bandgap, vibration suppression properties, and the design method for local resonance vibration dampers for elastic wave regulation by thin-walled elastic metamaterials were summarized successively. Moreover, other thin-walled AM applications, such as the wavefront steering performance of thin-walled acoustic/elastic metasurfaces, and the active thin-walled AMs, were introduced as well.

Vibration and acoustic insulation properties of generalized phononic crystals

Based on the previous studies, the concept of generalized phononic crystals (GPCs) is further introduced into the cylindrical shell structures, and a type of cylindrical shells of generalized phononic crystals (CS-GPCs) is constructed. Subsequently, the structure field and acoustic-structural coupled field of that composite cylindrical shells are examined respectively in this paper. Considering the Bloch theorem is not capable of explaining the generalized periodic situation existing in this structure field, a new analysis method involving transferring matrix eigenvalue based on the mechanical state vector is proposed to calculate the energy band structure. Through observing the energy band structure, an obvious wave band gap is obtained when the elastic wave propagates in the CS-GPCs for modes with different order, whose forming mechanism includes two aspects, i.e., the wave front expansion effect and the Bragg scattering effect. In addition, we further explore the related influences of the longitudinal wave mode and shear wave mode in structure on these band gaps, and some conclusions are illustrated. For acoustic-structural coupled field, the expressions of the acoustic transmission coefficients for different modes are built, and the frequency responses are numerically calculated to verify the band gap characteristics of the CS-GPCs. Furthermore, the acoustic pressure distribution of the internal and external acoustic fields is also analyzed in detail, and the influence laws of the parameters (offset distance and frequency) of the line source on acoustical pressure distribution and its directivity are explored.

Effect of Hydrostatic Pressure and Temperature on Quantum Confinement of AlGaN/GaN HEMTs

In this paper, an analytical model for quantum confinement electron density in two-dimensional quantum well, has been investigated. In order to obtain the exact AlGaN/GaN HEMTs parameters such as electron density, the wave function, band gap, polarization charge, effective mass and dielectric constant, the hydrostatic pressure and temperature effects are taken into account. It has been found that the electron density decreases with increasing temperature and increases with increasing hydrostatic pressure. With increasing hydrostatic pressure, the effective mass decreases and the quantum confinement electrons are increased in the quantum well. Also with increasing hydrostatic pressure, the height of wave functions increase and decreases electron wave functions to penetrate the quantum barrier but increasing the temperature behaves the opposite of increasing the pressure. However, with increasing temperature, the effective mass is increased and the quantum confinement electrons are reduced. The calculated results for electron density are in good agreement with existing experimental data.

Spectral variational multiscale enrichment method—A new computational approach to transient dynamics of phononic crystals and acoustic metamaterials

Phononic crystals and acoustic metamaterials hold tremendous potential in controlling mechanical and acoustic waves, thereby enabling remarkable and novel engineering applications such as seismic wave mitigation, impact wave mitigation, elastic cloaking, and acoustic superlens. Given the potential complexity associated with the microstructure of these materials, direct numerical simulation of irregularly shaped and/or large engineering components could be computationally very costly and in many cases prohibitive. Multiscale computational modeling, coupled with model order reduction methodologies present a feasible strategy to simulate the dynamic response of phononic crystals and acoustic metamaterials. In this study, we present the spectral variational multiscale enrichment approach that allows the analysis of a broad range of material microstructures for phononic crystals and acoustic metamaterials. The spectral coarse-scale representation is proposed to capture the salient transient wave phenomena, such as wave dispersion and band gaps that occur in the short wavelength regime. A material phase based model order reduction strategy is devised at the fine-scale. By using the reduced basis for the fine-scale problem, significant numerical efficiency is achieved. Transient elastic wave propagation in two-dimensional phononic crystals and acoustic metamaterials are investigated and the proposed multiscale approach is verified against direct numerical simulations.

Complete sub-wavelength flexural wave band gaps in plates with periodic acoustic black holes

Acoustic Black Hole (ABH) effect shows promise for vibration control, but mainly limited to a relatively high frequency range. Though achievable in 1D periodic ABH structures, complete sub-wavelength band gaps (BGs) have not yet been realized in 2D configuration. Capitalizing on the unique wave propagation characteristics of the ABH, we propose a new type of plates containing periodically arranged double-layer ABH cells which offer complete and omnidirectional BGs. The phenomena originate from the combined effects of the ABH-specific local resonances and Bragg scattering, which are made possible through a dual process: a proper channeling of the wave propagation path and an impaired coupling between the ABH-induced local resonances and the global vibration of the unit cells. The former is warranted by a proper structural tailoring of the unit cells and the latter by the dynamics of the double-layer ABH design. It is shown that the BGs can be tuned through adjusting ABH parameters. Meanwhile, attaching the centers of the double ABH branches with a connecting cylinder can further broaden and lower the frequencies of the BGs as a result of the enhanced Bragg scattering. It is also demonstrated numerically and experimentally that remarkable vibration attenuation and energy insulation can be achieved in a plate with only a small number of ABH cells, thus pointing at the possibility of achieving sub-wavelength vibration control in structures with reasonable dimensions.

Natural seismic metamaterials: the role of tree branches in the birth of Rayleigh wave bandgap for ground born vibration attenuation

Natural seismic metamaterials: the role of tree branches in the birth of Rayleigh wave bandgap for ground born vibration attenuation

Eight-shaped polarization-dependent electromagnetic bandgap structure and its application as polarization reflector

AbstractIn this paper, an eight-shaped polarization-dependent electromagnetic bandgap (ES-PDEBG) structure is proposed. The unit cell of ES-PDEBG structure consists of an outer eight-shaped EBG patch with two inner square patches and three vias. Surface wave bandgap and reflection phase characteristics have been studied for the proposed structure. From the measurement results, two surface wave bandgaps with center frequencies 3.42 and 5.88 GHz are observed along the X-direction, and one surface wave bandgap with center frequency 3.69 GHz is observed along the Y-direction. The refection phase bandgap of the proposed structure is centered at 5.61 and 3.31 GHz for x- and y-polarized incident plane waves, respectively. Furthermore, the application of the proposed structure as polarization reflector is presented. The study demonstrates that the structure can act as dual-band in-polarization reflector for circularly polarized waves. In addition, incident linearly polarized waves are reflected as circularly polarized waves in four operating bands.

Continuum Flexural Metamaterial for Broadband Low-Frequency Band Gap

Despite enormous efforts being invested in the elastic wave's band gap, achieving a broadband low-frequency band gap is still a great challenge. Previous attempts to realize a broadband low-frequency band gap have focused on specific cases, such as linkage connections, the piezoelectric effect, or elastic foundations, which cannot be extended to other meaningful advances. Herein, we propose a way to achieve a broadband low-frequency band gap without any specific conditions, but with only the continuum metamaterial itself. Our proposed idea consists of a hollow cylindrical configuration and a bow-tie-shaped part, which can be easily extended to any other vibrational systems. To explain the idea, the extended mass-spring system is analytically investigated, and the idea is explained in detail based on the mass, inertia, bending, and shear-stiffness values. The proposed idea is supported by various numerical simulations. In addition, experimental realization of the broadband low-frequency band gap is carried out. It is expected that the proposed idea could be utilized to realize various vibration systems, such as a low-frequency cavity, vibration shielding, or filtering devices, which can extend vibration physics at the low-frequency regime.

Ultra-wide low-frequency band gap in a tapered phononic beam

We propose a tapered phononic beam with a broad low-frequency band gap for flexural waves. A unit cell of the phononic beam consists of two identical uniform parts and a thickness- and width-varying part sandwiched between them. Thickness and width profiles and uniform beam length are controlled to change the shear and rotational stiffnesses of the phononic beam, changing the starting and ending frequencies of the first band gap. By identifying the effects of those geometrical parameters on band structures, we determine the parameter values that enable the phononic beam to yield an ultra-broad and ultra-low band gap from 3.6 Hz to 237.9 Hz with a small lattice constant of λ/25. For experimental realization, a finite phononic beam with three unit cells is fabricated by wire electric discharge machining and its displacement transmission is measured through impact hammer tests. Particularly low transmission of -35 dB to -10 dB is observed at the band-gap frequency range. We briefly present ongoing works to enhance the structural robustness of the phononic beam by changing geometrical parameters or material of a thin and narrow part.

An elastic higher-order topological insulator based on kagome phononic crystals

Recently, the novel bulk–edge–corner correspondence of higher-order topological states had attracted increasing attention. Past research studies on higher-order topological insulators, however, have mainly concentrated on the topological multipole states within the low-frequency bandgap for airborne sound waves. In this paper, we propose a higher-order topological insulator with kagome symmetry based on two-dimensional elastic phononic crystals (PNCs), which can operate in the high-frequency bandgap. Topological corner and edge states are both achieved in well-designed finite PNCs. In addition, we demonstrate the robust characteristics of elastic topological corner and edge states in PNCs with different defects (e.g., cavities, disorders, and bends). As the analog counterpart for classical waves, the proposed PNCs provide an alternative scheme for research into the topological phases of matter in macroscopic systems.

Buckling-regulated bandgaps of soft metamaterials with chiral hierarchical microstructure

In traditional phononic metamaterials, elastic wave bandgaps are usually tuned by introducing periodic rigid inclusions in a soft matrix, but they are difficult to adapt to the changes of external mechanical environments. In this paper, inspired by the strategies of biological materials to achieve specific functions, we propose a kind of soft metamaterials with chiral and hierarchical structures. Their elastic wave bandgaps can be easily regulated in a larger space of frequency by means of the postbuckling-induced evolution of microstructures under loading. The postbuckling behavior of chiral hierarchical structures is investigated through finite element simulations and compared with those of symmetric hierarchical structures. The stress–strain curves, the phase diagram of uniaxial critical compressive strength, and the tunable elastic wave bandgaps of the proposed metamaterials are analyzed.

Scan Blindness Free Design of Wideband Wide-Scanning Open-Ended Waveguide Phased Array

A wideband wide-scanning open-ended rectangular waveguide phased array in a triangular lattice is presented. Dielectric or metamaterial wide-angle impedance matching superstrates have been widely used in phased arrays to improve the scanning performance. However these dielectric-containing covers cannot solve the problem of scan blindness caused by the surface waves, or even further aggravate the surface wave effect. The modulated surface structures, which consist of the impedance-gradient structures and the surface wave bandgap structures are designed to maximize the wideband wide-scanning performance of the array. The proposed array achieves 40% bandwidth (8–12 GHz), while covering a scanning range of ±65° in the E-plane (VSWR < 2.3) and H-plane (VSWR < 2). The practical working frequency band occupies the whole potential operating frequency band between the waveguide TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> cutoff frequency and the onset frequency of the first grating lobe. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$11\times11$ </tex-math></inline-formula> prototype is fabricated and measured. Good agreement is achieved between the simulated and measured results.

Flexural wave band gaps in a ternary periodic metamaterial plate using the plane wave expansion method

Low- and mid-frequency range vibrations usually present issues in their insulation. The development of periodic metamaterials (artificially engineered structures) has been thoroughly studied since their periodicity and geometric properties may yield good attenuation properties in such frequency ranges. Several works investigated periodic structures presenting binary or ternary material configurations using the Kirchhoff plate theory or binary material configurations using the Mindlin plate theory. In this paper, a ternary periodic metamaterials made of concentric circular inclusions of a rigid material coated with a soft material embedded in a matrix made of a low-cost recyclable polymer is investigated using the Mindlin plate theory combined with the plane wave expansion method. Computed band diagrams are compared to those obtained using the Kirchhoff plate theory and three-dimensional models. Additionally, the effect of different boundary conditions is investigated on finite structures using the finite element method. Our results assess the validity of the Mindlin plate model in such case and indicate its use in practical applications.

Realizing polarization band gaps and fluid-like elasticity by thin-plate elastic metamaterials

The flexible manipulation of elastic waves that exhibit abundant polarization characteristics in solid structures can be realized through ingenious microstructure design, thus accomplishing various unique physical properties. This paper proposes a lightweight, thin-plate elastic metamaterial with transverse, longitudinal, and torsional wave polarization band gaps. Due to the spatial asymmetry of the unit cell, the band gaps do not overlap and can achieve the selective suppression of elastic waves exhibiting different polarization forms. In addition, the stopband of the flexural vibrational overlaps the passband of the longitudinal vibration, allowing a fluid-like elasticity capable of transmitting longitudinal waves but not transverse waves to be realized via a multicellular elastic rod-like structure with integrated multiple unit cells. A corresponding rod-like structure was fabricated and verified, achieving a fluid-like elasticity through vibrational measurements. Furthermore, the unit cell behaves a negative moment of inertia characteristic in the torsional wave band gap, which can effectively attenuate the torsional vibrational propagation of the rod-like structure with integrated multiple unit cells in another form. This proposed elastic metamaterial structure can provide a practical implementation scheme for the separation and manipulation of elastic waves in different polarization forms in solid structures.

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.

Longitudinal vibration wave in the composite elastic metamaterials containing Bragg structure and local resonator

In this paper, a novel composite acoustical hyperstructure of Bragg structure with local resonator is investigated theoretically for discussing the scattering performance of longitudinal vibration wave, its bandgaps are calculated using the established mathematical model. For confirming the veritable existence of bandgap and verifying the correctness of established mathematical model, the transmission spectrum of composite acoustical hyperstructure is also studied using finite-element method, and comparing the vibration transmission spectrum with bandgaps, the results indicate that the established theoretical model can correctly predict longitudinal wave bandgaps. Moreover, the bandgaps and modes shapes are calculated and compared with an unalloyed Bragg structure for probing the dispersion mechanics of composite acoustical hyperstructure, it turned out that local resonator can add one bandgap at the base of Bragg structure and the total bandgaps can be broadened. Further, for discussing the effect of spring of local resonator on bandgaps, bandgap of local resonator with different spring is calculated, the results showed that the total width of BG is larger when Young’s modulus is 1E and 16E, the total width are 772.48 and 774.30 Hz, respectively; as Young’s modulus is 0.5E and 2E, the width of BG are lower, 753.79 and 754.23 Hz, respectively. In view of longitudinal vibration wave inducing structural distortion and vibration energy conversion, the dynamic properties of composite acoustical hyperstructure are studied via strain energy density, the results indicate that reaction formation of local resonator can dissipate strain energy, when the local resonator is not activated (or waveless along with Bragg structure), un-dissipation strain energy.

Topology optimization of periodic barriers for surface waves

Dispersion engineering is always the important topic in the field of artificial periodic structures. In particular, topology optimization of composite structures with expected bandgaps plays a key role. However, most reported studies focused on topology optimization for bulk waves, and the optimization for surface wave bandgaps (SWBGs) is still missing. In this paper, we develop a topology optimization framework based on the genetic algorithm and finite element method to design periodic barriers embedded in semi-infinite space for reducing surface waves on demand. The objective functions for SWBGs are proposed based on the energy distribution properties of surface waves. The numerical results show that the optimization framework has stable convergence for this problem and is effective to optimize SWBGs. Considering large SWBGs and low filling fraction of solids, we investigate single- and multi-objective optimizations, respectively, and obtain novel wave barriers with good performance. The beneficial configuration features and mechanism of broadband SWBGs from the optimized results are explored. The results indicate that for the first-order SWBG, most optimized structures consist of a main scatterer at the center and some subsidiary scatterers near the surface. The rigid body resonance of the main scatterer determines the lower edge of SWBG, and the subsidiary scatterers can regulate the upper edge. Higher-order SWBGs are generated from the interaction of multiple scatterers, whose relative distance has a great influence on the position of SWBGs. The optimized structures can make the surface waves propagate far away from the surface within the frequencies of bandgaps, leading to a strong attenuation of surface vibration. In practice, our topological optimization framework is promising in designing high-performance surface wave devices and novel isolating structures for earthquake or environmental vibration in civil engineering.

High-Q Interstitial Square Coupled Microring Resonators Arrays

The properties of the square array of coupled Microring Resonators (MRRs) with interstitial rings are studied. Dispersion behavior of the interstitial square coupled MRRs is obtained through the transfer matrix method with the Floquet-Bloch periodic condition. Analytical formulas of the eigen wave vectors, band gaps and eigen mode vectors are derived for the special cases of the interstitial square coupled MRRs array with identical couplers and the regular square coupled MRRs array without the interstitial rings. Then, the eigen modes' field distribution are calculated for each of the four eigen wave vectors for a given frequency through the secular equation. Finally, numerical simulation is performed for an interstitial square coupled MRRs array with identical couplers and a regular square coupled MRRs array. The simulation result verifies the analytical analysis. Finally, the loaded quality factors of the interstitial 5-ring configuration, the regular 4-ring configuration and the 1-ring configuration are obtained. It is found that the loaded quality factor of the interstitial 5-ring configuration is up to 20 times and 8 times as high as those of the 1-ring configuration and the regular 4-ring configuration respectively, mainly due to the degenerated eigen modes at the resonant frequency. Thus, the interstitial square coupled MRRs array has the great potential to form high-quality integrated photonics components, including filters and resonance based sensing devices like the parity-time symmetric sensors.

Flexural wave propagation and vibration isolation characteristics of sandwich plate-type elastic metamaterials

Sandwich structures are widely used in the fields of aerospace, automobile as well as ship and offshore structures because of their excellent mechanical performances such as lightweight, high specific strength and high specific stiffness. In this study, the flexural wave band gaps and vibration isolation characteristics of sandwich plate-type elastic metamaterials are numerically and experimentally investigated. The proposed sandwich plate-type elastic metamaterials are constituted of local resonant stubs periodically deposited on a sandwich plate with periodic thin-wall aluminium tube cores. An efficient finite element method combined with a solid-shell coupling method and Bloch periodic boundary conditions is presented and validated by experimental measurements to calculate the dispersion relations and the acceleration frequency responses of sandwich plate-type elastic metamaterials. The influences of geometric parameters on the flexural wave band gaps are performed and discussed. Results show that the proposed sandwich plate-type elastic metamaterials can yield flexural wave band gaps in the low-frequency range and show significant performance on the flexural vibration isolation. Moreover, the flexural wave band gaps can be effectively modulated by the geometric parameters.

Seismic metasurfaces on porous layered media: Surface resonators and fluid-solid interaction effects on the propagation of Rayleigh waves

Seismic surface wave mitigation using metamaterials is a growing research field propelled by intrinsic theoretical value and possible application prospects. Up to date, the complexity of site conditions found in engineering practice, which can include layered stratigraphy and variable water table level, has been discarded in the development of analytical frameworks to favor the derivation of simple, yet effective, closed-form dispersion laws. This work provides a further step towards the analytical study of “seismic metasurfaces” in real site conditions considering the propagation of Rayleigh waves through a layered porous substrate equipped with local resonators. To this aim, we combine classical elasticity theory, Biot’s poroelasticity and an effective medium approach to describe the metasurface dynamics and its coupling with the poroelastic substrate. The developed framework naturally includes simpler configurations like seismic metasurfaces atop homogeneous dry or saturated soils. Apart from known phenomena like wave-resonance hybridization and surface wave band gaps, we predict the existence of an extended frequency range where surface waves are attenuated due to energy leakage in the form of slow pressure waves, as a result of the fluid-solid interaction. Besides, we demonstrate that the surface wave band gap and the related surface-to-shear wave conversion is robust to variations in the water table level. Conversely, when the dry and saturated layers have different material parameters, for example, due to different porosity ratios, the surface-to-shear wave conversion can be accompanied by the excitation of higher-order surface modes, which remain channeled below the metasurface. These analytical findings, augmented and confirmed by numerical simulations, evidence the importance of accounting for fluid-solid interaction in the dynamics of seismic metasurfaces.