Sub-wavelength Frequency Research Articles

Topological modes, vibration attenuation, and energy harvesting in electromechanical metastructures

The dynamics of topological boundary modes in both periodic and quasi-periodic electromechanical metastructures is investigated, with a focus on their applications to energy harvesting and vibration reduction. The metastructure analyzed in this study is based on a shunted array of piezoelectric patches, with electrical parameters modulated according to the 1D Aubry–André–Harper model. As a result of this modulation, a fractal spectrum is generated near the central frequency of the resonators, a hallmark of nontrivial topology that enables the emergence of digitally controllable edge states and ensuing localization phenomena at subwavelength frequencies. In this framework, a detailed analysis of the metastructure spectral characteristics is conducted to investigate the influence of the modulation parameters on mode localization, both at the boundaries and within the interior of the beam. Such localization effects are then studied in relation to the energy harvesting, attenuation, and wave transport capabilities of the system. These functionalities point toward the realization of self-powered structures with low frequency and digitally controllable vibration attenuation capabilities, and are considered of significant technological interest in applications involving elastic waves and vibrations, where the ability to precisely control and harness these phenomena could lead to innovative solutions in energy-efficient and adaptive systems.

Design, optimization, and characterization of deep sub-wavelength evanescent orders in terahertz metagratings

Resonant evanescent orders, being an exclusive deep sub-wavelength phenomenon, are well-known for confining strong EM energy at the air-grating interface when excited utilizing 1-dimensional gratings. However, stimulating prominent evanescent orders demands thoughtful design variations in grating geometry. In this pretext, we have successfully designed and optimized THz gratings that can sustain strong evanescent orders while operating in the subwavelength frequency domain. We have performed a fast Fourier transform (FFT) on the position-dependent electric field distribution of the grating to study the evanescent orders for both of the incidence polarizations (TE and TM). In order to optimize the grating performance, we have systematically increased the grating ridge height at a fixed fill factor (FF = 0.5). In such a way, excited evanescent orders are turned out to be anisotropic in nature at relatively larger grating height. We attribute such anisotropic behaviour to the effective refractive index experienced by the orthogonal THz probe.

A surface-wave seismic metamaterial filled with auxetic foam

Auxetic materials with negative Poisson's ratio (PR) exhibit superior mechanical properties with regard to energy absorption, while their potential for surface wave shielding is only in its beginnings. To attenuate surface waves in ultra-low frequencies (the starting frequency close to 0 Hz), which is the main scope of concern in seismic protection, this paper presents a novel type of seismic metamaterial (SM) with square pillars embedded as vibrators that is filled by auxetic foam. The designed SM is comprised of three commonly used construction materials, i.e., soil, concrete and auxetic foam. Combining the dispersive analysis and sound cone method, an ultra-low-frequency bandgap from 0 to 16.42 Hz is opened via the tensile resonance of the auxetic foam and the inverse dispersion effect. Furthermore, the parametric analysis further shows that filling material with a low Poisson ratio and low mass density is more favorable to widening the first complete bandgap (FCB), which means that foam is the ideal filling material for SM. The transmission spectra of the corresponding finite samples coincide well with the bandgap calculations. And the dynamic response of a scaled-down setup with a characteristic size of 1/10 of the original metamaterial is experimentally tested to validate the effectiveness of our study. We expect that this study prompts the engineering application of auxetic materials and ordinary building materials in seismic wave shielding at deep sub-wavelength frequencies.

Wave attenuation of a laminated acoustic black hole array in a load-bearing beam structure

Acoustic Black Hole (ABH) is a wedged taper in thin-walled structures that allows for a smooth and progressive retarding of bending wave speed. However, the application of ABH structures is mainly restricted by its inherent flaw, that is the impaired structural strength by digging holes. To this end, we reinvestigate the ABH concept to propose a compound layout conducive to both wave attenuation and load-bearing capacity. First, the void created by two ABH branches in a periodic double-leaf beam is filled with acoustically soft materials to retain the structural topology continuity. Based on the Rayleigh–Ritz method, a semi-analytical model considering the shear strain of the soft filler is then presented for bandgap computation and validated against finite element simulations. It is shown that the soft filler in the filled-ABH lattice could not only widen bandgaps below the characteristic frequency of ABH, but also preserve the structural bearing ability. Transmission spectra further indicate that reducing the ABH spacing will benefit to the local resonance of composite area, and the shape of ABH profile can be used to improve the broadband attenuation. We expect that this research promotes the engineering application of ABHs in vibration suppression dealing with the sub-wavelength frequencies.

Compact asymmetric treatments for perfect sound absorption in ventilated problems

This presentation introduces compact asymmetric treatments for sound absorption, i.e., simultaneous cancellation of reflection and transmission, in a lined duct of constant cross section. The treatments are composed of side by side and sub-wavelength resonators. They are thus compact, which facilitates their practical use. The simplest asymmetric treatment is formed by a pair of detuned resonators that can lead to a perfect monochromatic sound absorption. Furthermore, the combination of multiple pairs of resonators generates multiple low quality factor absorption peaks leading to an absorption plateau. Two compact asymmetric treatments are presented: one is composed of quarter-wavelength porous resonators to prove their ability to achieve perfect sub-wavelength absorption in a duct problem and the other is composed of Helmholtz resonators flush mounted on the walls of a large cross-section duct. In both cases, the evanescent coupling between the resonators has an important impact on the treatments behavior and is thus accounted for during their optimization. The experimental results are found in good agreement with the theory and a mean absorption coefficient of 99% over a large target and subwavelength frequency range is observed for each treatment.

Propagation of elastic waves in metamaterial plates with various lattices for low-frequency vibration attenuation

Elastic wave propagation characteristics of elastic metamaterial plates embedded scatterer with various lattices are explored numerically and experimentally in this study, for the attenuation of in-plane longitudinal and out-of-plane flexural waves in the subwavelength frequency region. Firstly, the mathematical models of the elastic metamaterial plates are established, and the dispersion relations are derived by the plane wave expansion (PWE) method based on Bloch's theorem. Furthermore, the applicability of the irreducible Brillouin zone (IBZ) for different lattices is also investigated through iso-frequency contours. The analysis of the bandgap formation mechanism indicates that the proposed metamaterial plates can enlarge the bandgaps (BGs) in the low-frequency range by coupling Bragg and local resonance BGs. Moreover, the influences of the scatterer shapes, geometric and material parameters on the BGs are investigated, and which combination of parameters has positive significance for opening low-frequency broadband is also discussed. The results show that the vibration transmittance obtained by experiment and numerical calculation is in good agreement with the predicted results of band structures. Therefore, the elastic metamaterial plates should be promising in the application of low-frequency wave mitigation.

Enhancing low frequency sound radiation of electrodynamic loudspeakers with acoustic metamaterials

Since the radiation resistance of a vibrating membrane in the air is proportional to frequency in the subwavelength range, low frequency (<100Hz) sound radiating devices generally require a large vibrating diaphragm and a bulky enclosure to be efficient and loud enough for practical use. The tapped horn topology, where the front radiation of an electrodynamic driver adds up with the back radiation after propagating through the internal volume of a speaker box, has been widely used in custom audio to provide low-frequency enhancement to the bass unit. Recently, people have demonstrated the application of acoustic metamaterials based on multiple Helmholtz resonators (HRs) in sound absorption, sound insulation, directivity control, impedance matching, etc. In this presentation, we show that by branching the sound path of a tapped horn speaker box with multiple Helmholtz resonators and fine-tuning the geometry of each individual element, we can produce high and relatively constant sound pressure levels at sub-wavelength frequencies, making our methodology a good candidate for compact subwoofer design. Genetic algorithm (GA) is used to bring forth optimal performance within the geometric framework. Both transfer matrix method and numerical simulation are employed to derive the sound output of a particular subwoofer.

Wide Rayleigh waves bandgap engineered metabarriers for ground born vibration attenuation

The present study proposes two types of engineered resonant metabarrier designs for ground born vibration attenuation at subwavelength frequency region. By establishing analytical and full-scale 3D numerical models, the effectiveness of metabarrier in attenuating incoming Rayleigh surface waves in the earthquake frequency range of interest is investigated. The metabarrier designs are comprised of a cylindrical steel mass encapsulated inside a hollow concrete setup mounted with low-stiffness rubber bearings. The interaction of surface ground motion caused by the propagation of Rayleigh waves with the vertical resonant mode of metabarriers result in the trapping and/or mode conversion of Rayleigh waves into bulk shear waves that propagate deep into the ground. This so-called wave hybridization or the local resonance phenomena induces an extremely wide low frequency bandgap from both designs that is found effective in attenuating incoming Rayleigh waves at the deep-subwavelength scale. By varying the height and arrangement types of resonant metabarriers, the seismic metawedge phenomena are also investigated. In the bandgap frequency range, the Rayleigh waves attenuation is validated by performing a full-scale 3D numerical frequency response analysis including an actual earthquake record (Imperial Valle-1940 El-Centro) based time history analysis. The findings reported indicate such metabarriers can be embedded into the ground surrounding civil infrastructures to be protected from earthquake hazards.

Low frequency topologically protected wave transport in sinusoidal lightweight acoustic metamaterials

Topological phononic crystals and acoustic metamaterials have attracted enormous research attention in recent years due to the presence of robust and disorder-immune wave propagation. In this study, a sinusoidal lightweight elastic topological insulator with protected interface modes is investigated at a subwavelength frequency region. By a wave dispersion study, the dual Dirac cones are observed at a subwavelength frequency region due to the employment of two distinct cylinders connected with sinusoidal ligaments. Both cylindrical masses and sinusoidal ligaments are found responsible for opening low-frequency bandgaps that manipulate elastic wave wavelengths almost 30 times larger than the lattice size. Consequently, the subwavelength bandgap closing-and-reopening phenomenon with phase transitions is further captured and opposite signs of the valley Chern numbers are obtained for different structural parameters. A supercell structure is constructed based on the phase transition, and dual topologically protected interface modes (TPIMs) are captured with different quality factors. The comparison of topologically protected interface modes shows that TPIM I is in a higher and wider frequency range, while TPIM II is positioned in a comparatively narrow and extremely low-frequency range. Finally, the robust elastic wave propagation along various designated paths is demonstrated. The proposed lightweight topologically protected phononic lattice may spark future investigation of topological edge states in metadevices at a subwavelength frequency region.

Inertial amplification band-gap generation by coupling a levered mass with a locally resonant mass

Inertial amplification has been utilized in phononic media as a mechanism for the generation of large band gaps at low subwavelength frequencies. A unique feature in an inertial-amplification band gap is that it may exhibit two coupled peaks in the imaginary wavenumber portion of its band diagram. This unique double-attenuation band gap has been shown to emerge from a periodic arrangement of a levered mass whose motion is directly connected to that of an independent degree of freedom in the system through the motion of the lever base. Here we demonstrate a double-attenuation band gap emerging specifically from a modal coupling of the levered mass with a conventional local-resonance mass separately attached to the base. This presents a fundamentally distinct mechanical mechanism for the shaping of inertially-amplified band gaps and provides a pathway for realising a combination of strength and breadth in the wave attenuation characteristics. We theoretically present this concept, analytically identify critical conditions for the coupling of the attenuation peaks, and provide a series of parametric sweeps to further highlight the phenomenon and guide design. For example, we find a design with a relatively elevated level of minimum attenuation over practically the entire width of a band gap with a relative size of 130%, and another design with a smaller band gap but a 15-fold increase in the minimum attenuation strength compared to a pure IA chain.

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.

Surface elastic waves whispering gallery modes based subwavelength tunable waveguide and cavity modes of the phononic crystals

We studied the characteristics of a phononic crystal which consists of hollow pillars mounted on the surface of semi-infinite substrate. In this study, the existence of surface waves whispering gallery modes referred as localized cavity modes of the hollow pillars at the subwavelength frequency spectrum is reported. The interaction of the hollow pillars with the surface waves induce localized cavity modes and by tuning the inner radius of the hollow pillars these confined modes can be adjusted/tuned inside the bandgap region, thus introducing new applications for the surface waves based phononic crystals and acoustic metamaterial devices. These subwavelength confined cavity modes possess high-q narrow passband characteristics induced by the interaction of cavity modes with the surface waves propagating at the surface of semi-infinite substrate. We demonstrate the subwavelength waveguiding and other functionalities of these localized cavity modes by tuning the inner radius of the hollow pillars and allowing the specific wavelength frequencies to pass through the monochannel, multichannel, and linear cavity based compact waveguides. To make the study more general, we demonstrate the wave multiplexing phenomena for the identical frequencies (diameters of the hollow pillars are kept constant) for all types of waveguides. However, by varying the inner radii of the hollow pillars, the high-q localized frequencies can be tuned. All the physical phenomena presented shows excellent agreement and it indicates promising applications for the manipulation of surface waves in the surface acoustic waves devices, surface waves sensor and actuator technology, and other photonic/phononic and metamaterial applications.

Enhancement of Deep-Subwavelength Band Gaps in Flat Spiral-Based Phononic Metamaterials Using the Trampoline Phenomena

Abstract Elastic and acoustic metamaterials can sculpt dispersion of waves through resonances. In turn, resonances can give rise to negative effective properties, usually localized around the resonance frequencies, which support band gaps at subwavelength frequencies (i.e., below the Bragg-scattering limit). However, the band gaps width correlates strongly with the resonators’ mass and volume, which limits their functionality in applications. Trampoline phenomena have been numerically and experimentally shown to broaden the operational frequency ranges of two-dimensional, pillar-based metamaterials through perforation. In this work, we demonstrate trampoline phenomena in lightweight and planar lattices consisting of arrays of Archimedean spirals in unit cells. Spiral-based metamaterials have been shown to support different band gap opening mechanisms, namely, Bragg-scattering, local resonances and inertia amplification. Here, we numerically analyze and experimentally realize trampoline phenomena in planar metasurfaces for different lattice tessellations. Finally, we carry out a comparative study between trampoline pillars and spirals and show that trampoline spirals outperform the pillars in lightweight, compactness and operational bandwidth.

Conductor-backed dielectric metasurface thermal emitters for mid-infrared spectroscopy

A conductor-backed dielectric metasurface thermal emitter at mid-IR frequencies with narrowband emissivity is experimentally demonstrated. The metasurface emitter consists of a high permittivity silicon resonator on top of a ground plane, whose resonant mechanism is explained using image theory. The resonator, placed close to a copper ground plane, is designed to produce a magnetic resonance, resulting in a low-profile device with a single emission peak in its subwavelength frequency range. The thermal emitter is next fabricated using common CMOS processes. Frequency dependent optical constants of plasma-enhanced chemical vapor deposited films of Si, SiO2, and evaporated Cu are also reported in the mid-IR range. Narrowband thermal emission is successfully obtained at around 7.22μm (41.5 THz), which corresponds to the absorption band of SO2. The Q-factor of about 37 is achieved with a peak emissivity of 0.65, which is significantly higher compared to the reported Q-factors of state-of-the-art plasmonic resonators.

Fundamental Bounds on Transmission Through Periodically Perforated Metal Screens With Experimental Validation

This paper presents a study of transmission through arrays of periodic sub-wavelength apertures. Fundamental limitations for this phenomenon are formulated as a sum rule, relating the transmission coefficient over a bandwidth to the static polarizability. The sum rule is rigorously derived for arbitrary periodic apertures in thin screens. By this sum rule we establish a physical bound on the transmission bandwidth which is verified numerically for a number of aperture array designs. We utilize the sum rule to design and optimize sub-wavelength frequency selective surfaces with a bandwidth close to the physically attainable. Finally, we verify the sum rule and simulations by measurements of an array of horseshoe-shaped slots milled in aluminum foil.

Between Science and Art: Thin Sound Absorbers Inspired by Slavic Ornaments

Acoustic metamaterials have opened promising opportunities for manipulation of low-frequency sound and development of compact structures with a broadband acoustic performance for noise mitigation applications, room, and architectural acoustics. So far, several mechanisms have been studied to achieve broadband sound absorption at subwavelength frequencies, when the system thickness is much smaller than the wavelength of sound waves. In this paper, we analyze two other approaches based on the use of interacting and coupled resonators with the aim to further reduce a structural thickness. We numerically demonstrate that properly designed panels with interacting resonators allow extending a single-peak absorption to broadband frequencies, while coupled resonators enable achieving broadband absorption at several frequency ranges. The developed designs are inspired by ancient Slavic folk patterns, attracting attention by their delicate ligature, multi-layered structure, and concealed meaning. Our results open new possibilities for creating acoustic metamaterials with art effects, which provide meaning to occupied space and make these metamaterials more appealing for applications.

Subwavelength Interferometric Control of Absorption in Three-port Acoustic Network

Utilizing the effect of losses, we show that symmetric 3-port devices exhibit coherent perfect absorption of waves and we provide the corresponding conditions on the reflection and transmission coefficients. Infinite combinations of asymmetric inputs with different amplitudes and phase at each port as well as a completely symmetric input, are found to be perfectly absorbed. To illustrate the above we study an acoustic 3-port network operating in a subwavelength frequency both theoretically and experimentally. In addition we show how the output from a 3-port network is altered, when conditions of perfect absorption are met but the input waves phase and amplitude vary. In that regard, we propose optimized structures which feature both perfect absorption and perfect transmission at the same frequency by tuning the amplitudes and phases of the input waves.

Spider web-structured labyrinthine acoustic metamaterials for low-frequency sound control

Attenuating low-frequency sound remains a challenge, despite many advances in this field. Recently-developed acoustic metamaterials are characterized by unusual wave manipulation abilities that make them ideal candidates for efficient subwavelength sound control. In particular, labyrinthine acoustic metamaterials exhibit extremely high wave reflectivity, conical dispersion, and multiple artificial resonant modes originating from the specifically-designed topological architectures. These features enable broadband sound attenuation, negative refraction, acoustic cloaking and other peculiar effects. However, hybrid and/or tunable metamaterial performance implying enhanced wave reflection and simultaneous presence of conical dispersion at desired frequencies has not been reported so far. In this paper, we propose a new type of labyrinthine acoustic metamaterials (LAMMs) with hybrid dispersion characteristics by exploiting spider web-structured configurations. The developed design approach consists in adding a square surrounding frame to sectorial circular-shaped labyrinthine channels described in previous publications (e.g. ()). Despite its simplicity, this approach provides tunability in the metamaterial functionality, such as the activation/elimination of subwavelength band gaps and negative group-velocity modes by increasing/decreasing the edge cavity dimensions. Since these cavities can be treated as extensions of variable-width internal channels, it becomes possible to exploit geometrical features, such as channel width, to shift the band gap position and size to desired frequencies. Time transient simulations demonstrate the effectiveness of the proposed metastructures for wave manipulation in terms of transmission or reflection coefficients, amplitude attenuation and time delay at subwavelength frequencies. The obtained results can be important for practical applications of LAMMs such as lightweight acoustic barriers with enhanced broadband wave-reflecting performances.

Spider web-inspired acoustic metamaterials

Spider silk is a remarkable example of bio-material with superior mechanical characteristics. Its multilevel structural organization of dragline and viscid silk leads to unusual and tunable properties, extensively studied from a quasi-static point of view. In this study, inspired by the Nephila spider orb web architecture, we propose a design for mechanical metamaterials based on its periodic repetition. We demonstrate that spider-web metamaterial structure plays an important role in the dynamic response and wave attenuation mechanisms. The capability of the resulting structure to inhibit elastic wave propagation in sub-wavelength frequency ranges is assessed, and parametric studies are performed to derive optimal configurations and constituent mechanical properties. The results show promise for the design of innovative lightweight structures for tunable vibration damping and impact protection, or the protection of large scale infrastructure such as suspended bridges.