Periodic Array Of Resonators Research Articles

Decomposition-assisted analysis of transmission in periodic resonator arrays using mode-matching method.

This paper focuses on analysing acoustic structures containing locally reacting resonators, aiming to establish a framework for discussing sound properties related to scattering and transmission in a periodic resonator array. The paper introduces an analytical model for the input surface impedance of non-uniform resonator arrays, which is a challenging task when addressing sound propagation to the opposite side of the array. To address this challenge, a mode-matching method is employed within a one-dimensional periodic structure combined with the decomposition of the initial mirror-symmetric system into symmetric and antisymmetric sub-systems. This procedure leads to simplified analytical solutions of transmission problems about non-uniform resonator arrays, and its accuracy is verified through numerical simulations. The proposed method provides insights into mode shapes and amplitudes, thereby complementing numerical simulations and enabling a comprehensive understanding of sound fields beyond conventional results such as pressure fields and sound absorption coefficients alone. The model of a periodic varying-height resonator array presented herein involves developing mathematical equations or simulations to capture the physical characteristics and interactions of the resonators. This approach empowers researchers to predict and comprehend the non-uniform array's transmission behaviour and performance characteristics, with diverse applications spanning various systems, including electromagnetic devices.

Investigation of a new magnetorheological elastomer metamaterial plate with continuous programmable properties for vibration manipulation

Metamaterial plates have attracted considerable attention due to their unprecedented elastic wave manipulation abilities. Currently, the band gap and other properties of traditional metamaterial plates are fixed, and the material parameters of most metamaterials cannot be dynamically and continuously adjusted. To address this issue, a two-dimensional (2D) magnetorheological elastomer (MRE) programmable metamaterial plate (MREPMP) with local resonance was proposed. The proposed MREPMP was composed of a thin steel plate and a periodic array of resonators, consisting of MREs and electromagnetic mass blocks. It not only has a compact structural design, but also enables real-time vibration control and programming wave manipulation by altering the amplitude of the current. The dispersion relation of the proposed MREPMP was theoretically calculated based on the plane wave expansion (PWE) method and the simulated transmissibility was numerically calculated using the finite element method in COMSOL. Subsequently, a prototype of the MREPMP was fabricated, and vibration tests were conducted to assess its programmable vibration manipulation functionalities. Two different types of defect paths were used as excitations and the corresponding real-time vibration manipulation performance was analyzed. The simulation results agree with the experimental results, showing that the MREPMP can dynamically tune the band gap and activate different waveguides through continuous online programming. This paper opens up a new idea for tunable manipulation of wave propagation.

An acoustic metasurface by applying planar periodic arrays of resonators with a multiple folded long neck for broadband sound absorption

An acoustic metasurface gives a broadband sound absorption by a planar periodic array combining small resonant modules tuned at different frequencies. The resonant module is often applied by a Helmholtz resonator, a membrane backed by an airtight cavity and a quarter wavelength closed tube, which have equivalent small area to a fraction of the wavelength. The author has studied the sound absorption of resonators by applying a multiple folded long neck and an airtight cavity for a thin sound-absorbing structure with high sound absorption at low frequencies below 100 Hz. In this paper, the author prototypes an acoustic metasurface by planar periodic array of Helmholtz resonators at various resonant frequency tuned by this neck and cavity of the resonator as a unit cell, and discusses the sound absorption characteristics. The prototyped acoustic metasurface gives a 40 % - 70 % sound absorption from 125 Hz to 250 Hz when it is combined with a 6.4 mm thickness of top plate including a 24 mm - 96 mm length of the multiple folded long neck and a 43.2 mm depth of the airtight cavity. And, more broadband sound absorption will be discussed by a theoretical analysis.

Low frequency sound isolation by a metasurface of Helmholtz ping-pong ball resonators

We study both numerically and experimentally an acoustic metasurface based on coupled Helmholtz resonators to obtain broadband low-frequency spectral responses for acoustic insulation. A hierarchical approach is proposed, starting from single and coupled Helmholtz resonators, up to a periodic array of resonators. To this end, we performed numerical simulations using the finite element method, in which the resonators are modeled as drilled rigid spheres in airborne environment and experimental demonstrations based on ping-pong balls as Helmholtz resonators in an acoustic reverberation box. We showed the alteration of the low-frequency response of acoustic insulation resulting from inter-unit coupling in acoustic metasurfaces, and the apparition of additional attenuation by inserting a plexiglass board as support for the structure.

Bandgaps for flexural waves in infinite beams and plates with a periodic array of resonators

ABSTRACT The subject of seismic metamaterials, inspired from novel ideas in optics and acoustics, has attracted great attention in the last decade for potential applications in earthquake engineering. Simple structure systems, like beams and plates, with periodically attached mechanical resonators provide a simple physical model to interpret the existence of certain frequency bandgap in dispersion relations and to simulate the mechanism of flexural energy attenuation. In this work, we consider simple structure systems of beams and plates with periodically attached resonators. The resonator is composed of a spring, a damper and a mass attached along the beam direction. We utilize the Timoshenko beam model and the Mindlin plate theory to incorporate the shear effect. The plane wave expansion method together with the Bloch theorem is used to expand the governing field into an eigenvalue problem of an infinite complex system, allowing us to characterize the band structures of the dispersion relations. Local resonance and Bragg bandgaps are identified and examined. The effect of thickness ratios, the damping ratio and the shear modulus are exemplified to demonstrate how these factors will affect the formation of bandgaps. This formulation demonstrates a feasibility that a periodic array of mechanical resonators together with suitable material and geometric parameters of beams and plates can be designed to tune with the dispersion behavior in the control of flexure waves. This study may open up new potential in the control of wave propagation in complex continuum systems through the interaction of adequately designed resonators.

Design of Wideband Beamforming Metasurface With Alternate Absorption

In this paper, we propose a periodic structure that is capable of alternating between absorption and radiation mode. The designed periodic structure consists of an array of $6\times 6$ square shaped unit cell. Each unit cell consists of a multi-layered structure, with dimensions of $0.5\lambda \times 0.5\lambda $ . The resonators are placed on the top layer and the feeding network is designed and implemented on the bottom layer. The ground layer is sandwiched between the two dielectric substrates. All resonators are connected to a $50\Omega $ feed-line using the corporate feeding technique. To achieve broadband absorption, lumped resistors are inserted into the resonators. The proposed metasurface structure achieves broadband radiation, with low RCS and high gain, in the propagation direction whereas broadband absorption is achieved, when it is exposed to a free space plane wave. Moreover, the metamaterial absorber has stable absorptivity for an incident angle of (0°–30°). To verify the in-band absorption and radiation of the proposed design, a $6\times 6$ periodic array of resonators has been fabricated and experimentally verified in an anechoic chamber. The measured results validate the performed simulations.

Superlensing effect for flexural waves on phononic thin plates composed by spring-mass resonators

This paper demonstrates the superlensing effect of flexural waves by phononic plates with the negative index of refraction. The phononic plate consists of a square lattice of spring-mass resonators attached to an infinite thin plate. The periodic resonator array induces a resonant band gap between the first and second dispersion curves of band structures calculating by a plane wave expansion method. All-angle negative refraction phenomenon has been found for a propagation mode under specific elastic parameters of spring-mass resonators. Furthermore, a flat lens composed by a finite number of spring-mass resonators is designed to focus elastic fields of a point-like excitation operating at this propagating mode. Multiple scattering simulations show that the image resolution of the designed flat lens is about 0.15λ, overcoming the Rayleigh diffraction limit of traditional imaging systems.

An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces.

We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper, we consider the effect of the flexural motion of the resonators, adapting a recently established asymptotic methodology that leads to an explicit scalar hyperbolic equation governing the propagation of Rayleigh-like waves. Compared with classical approaches, the asymptotic model yields a significantly simpler dispersion relation, with closed-form solutions, shown to be accurate for surface wave-speeds close to that of the Rayleigh wave. Special attention is devoted to the effect of various junction conditions joining the beams to the elastic half-space which arise from considering flexural motion and are not present for the case of purely compressional resonators. Such effects are shown to provide significant and interesting features and, in particular, the choice of junction conditions dramatically changes the distribution and sizes of stop bands. Given that flexural vibrations in thin beams are excited more readily than compressional modes and the ability to model elastic surface waves using the scalar wave equation (i.e. waves on a membrane), the paper provides new pathways towards novel experimental set-ups for elastic metasurfaces.

Flexural wave band gaps in metamaterial plates: A numerical and experimental study from infinite to finite models

The proposed numerical design approach investigates both infinite and finite models and includes an experimental validation of elastic wave absorption and vibration suppression for flexural wave band gaps in metamaterial plates. The resonant metamaterial is obtained using a 2-dimensional periodic array of resonators (mass-screws) mounted to a thin homogeneous plate. The sensitivity analysis of the band gap frequency range takes into account the uncertainties of all the design parameters of the metamaterial plate. The theoretical approach uses the finite element method (FEM) to compare the predicted band gaps, which are derived from infinite and finite models of the metamaterial. An automatic method is proposed to detect the frequency ranges of band gaps in the finite metamaterial based on the behavior of the corresponding bare plate. Directional plane wave excitation and point force excitation are applied to evaluate the efficiency of the detection method. The results of these analyses are compared with experimental measurements. The frequency ranges of experimental vibration attenuation are in good agreement with the theoretically predicted complete and directional band gaps.

Nonlocal boundary conditions for corrugated acoustic metasurface with strong near-field interactions

The propagation of long-wavelength sound in the presence of a metasurface made by arranging acoustic resonators periodically upon or slightly above an impervious substrate is studied. The method of two-scale asymptotic homogenization is used to derive effective boundary conditions, which account for both the surface corrugation and the low-frequency resonance. This method is applied to periodic arrays of resonators of any shape operating in the long-wavelength regime. The approach relies on the existence of a locally periodic boundary layer developed in the vicinity of the metasurface, where strong near-field interactions of the resonators with each other and with the substrate take place. These local effects give rise to an effective surface admittance supplemented by nonlocal contributions from the simple and double gradients of the pressure at the surface. These phenomena are illustrated for the periodic array of cylindrical Helmholtz resonators with an extended inner duct. Effects of the centre-to-centre spacing and orientation of the resonators' opening on the nonlocality and apparent resonance frequency are studied. The model could be used to design metasurfaces with specific effective boundary conditions required for particular applications.

Band gap formation in thin plates with a periodic array of resonators

A resonator assembly consisting of a two-dimensional periodic array (mass-screws) mounted to a thin homogenous plate was used to investigate the vibration characteristics of locally resonant (LR) phononic plates. The numeric simulations employed the finite element method to calculate the band structures of the proposed periodic plates and to analyze the effect of geometry parameters on the evolution of the flexural band gap behavior. To experimentally validate the predictions for these theoretical examinations, two measurements with the LR phononic plates were obtained with respective lattice constants a = 40 and 50 mm. The tested plate was clamped on one side to a shaking table to generate a plane wave, propagating in the Ox-direction. Obtained experimental measurements of the wave attenuation in this direction are in good agreement with the theoretical frequency of both complete and directional band gaps.

On the sonic composites with scatterers made from auxetic material

AbstractA finite size periodic array of resonators made from auxetic material embedded into an epoxy matrix is analyzed in this paper. According to the Bragg's theory, the sound attenuation band is due to the superposition of multiple reflected waves inverse proportional to the central distance between resonators. The sound attenuation in such composites is studied using a method that combines the features of the cnoidal method and the genetic algorithm [1‐3]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Extraordinary absorption by a thin dielectric slab backed with a metasurface

The absorption of electromagnetic waves by a thin dielectric slab backed by a metasurface has been comprehensively studied and discussed at microwave frequencies. The metasurface consists of a metallic plate decorated with a periodic distribution of coaxial- or annular-type cavities. Analytical expressions for the absorbance have been obtained by using a mode-matching method. For $P$-polarized waves it is predicted that a low-frequency peak of perfect absorption is possible by properly choosing the lossy component of the permittivity of the dielectric slab, with the position of this peak being easily tunable by the cavity length. It is also shown that non-Bravais lattices, containing several cavities in the unit cell, and the excitation of guided waves by the periodic array of resonators are complementary absorption mechanisms in the studied structures.

Effect of geometric uncertainties and variations on the one-dimensional sound transmission in a duct with periodic resonator array

Sound transmission in a one-dimensional duct with periodic resonator array is characterized by Bragg stopband due to periodicity and resonance stopband due to resonator. Involved geometric parameters affecting the acoustic characteristics are resonator spacing, resonator length, widths or areas of main duct and resonator. Distortions of such geometric parameters are due to uncertainties in manufacturing and due to intentional design variations for focusing on a target frequency range. A side-branch array was taken as the test example. Stopband information was obtained by four-pole matrix and Bloch wave theory. Area and length ratios between side-branch and main duct periodicity properties were varied from zero to unity. Randomized distortions were generated from either Gaussian or uniform random distribution. As a deterministic distortion, sine function was employed. Simulation results showed that bandwidths and frequencies of stopbands were highly affected by the length ratio. Along with the increase of random distortion rate or function period of deterministic distortions, sound transmission at stopbands decreases, while passband transmission increases. It was also shown that one can change the bandwidth and/or frequency of stopbands as desired for sound reduction. (Work partially supported by BK21 project and NCRC (NRF 2011-0018242))

Negative Effective Gravity in Water Waves by Periodic Resonator Arrays

Based on analytic derivations and numerical simulations, we show that near a low resonant frequency water waves cannot propagate through a periodic array of resonators (bottom-mounted split tubes) as if water has a negative effective gravitational acceleration g(e) and positive effective depth h(e). This gives rise to a low-frequency resonant band gap in which water waves can be strongly reflected by the resonator array. For a damping resonator array, the resonant gap can also dramatically modify the absorption efficiency of water waves. The results provide a mechanism to block water waves and should find applications in ocean wave energy extraction.

Resonance continuum coupling in high-permittivity dielectric metamaterials

A detailed investigation of resonance-continuum coupling is carried out both experimentally and theoretically in metamaterials based on high-permittivity dielectric subwavelength resonators. An original experimental scheme is designed at microwave frequencies, which mimics a periodic array of resonators. Fano resonances are discussed in the framework of temporal coupled mode theory for the cases where one or two resonator modes couples to the continuum. Fano lineshapes are unambiguously demonstrated experimentally for the single-mode case in agreement with theoretical modeling. Numerical evidence of resonance trapping is shown in the two-mode case when modes with the same symmetry coincide in frequency.

Superlenses, metamaterials, and negative refraction

The purpose of this paper is threefold. The first aim is to discuss the superlensing effect in left-handed material presented originally by Veselago [Sov. Phys. Usp.10, 509 (1968)] and Pendry [Phys. Rev. Lett.85, 3966 (2000)] for n=-1. Our discussion is based on an integral expression for the electromagnetic fields (i.e., the Extinction Theorem), and it allows us to demonstrate that such superlensing effect does not exist. The second aim is to discuss some basic questions about structured metamaterials formed by periodic resonator arrays. We will show that a set of antennas can never emulate a negative refractive index material. The third, concurrent, aim is to discuss the experimental evidence for negative refraction in structured periodic materials. We present another possible explanation of the experimental results concerning negative refraction that is based on the coherent interference of wavelets originated in the subwavelength structures.

Thin-film sensing with planar asymmetric metamaterial resonators

We propose rectangular asymmetric double split resonators with field confining tips for use as thin-film sensors. In contrast to frequency selective surfaces, which consist of two-dimensional, periodic resonator arrays, only a single unit cell placed inside a rectangular waveguide is sufficient for sensing. Compared to circular structures, the rectangular design offers a miniaturization. Furthermore, the tips at the end of the resonator arms concentrate the field components into a small area, increasing the volumetric sensitivity of the device.