Two-dimensional Acoustic Metamaterials Research Articles

Recent Progress in Resonant Acoustic Metasurfaces.

Acoustic metasurfaces, as two-dimensional acoustic metamaterials, are a current research topic for their sub-wavelength thickness and excellent acoustic wave manipulation. They hold significant promise in noise reduction and isolation, cloaking, camouflage, acoustic imaging, and focusing. Resonant structural units are utilized to construct acoustic metasurfaces with the unique advantage of controlling large wavelengths within a small size. In this paper, the recent research progresses of the resonant metasurfaces are reviewed, covering the design mechanisms and advances of structural units, the classification and application of the resonant metasurfaces, and the tunable metasurfaces. Finally, research interest in this field is predicted in future.

Klein-Like Tunneling of Sound via Negative Index Metamaterials

Klein tunneling is a counterintuitive quantum-mechanical phenomenon, predicting perfect transmission of relativistic particles through higher-energy barriers. This phenomenon was shown to be supported at normal incidence in graphene due to pseudospin conservation. Here I show that Klein-tunneling analogy can occur in classical systems, and remarkably, does not rely on mimicking graphene's spinor wave-function structure. Instead, the mechanism requires a particular form of constitutive parameters of the penetrated medium, yielding transmission properties identical to the quantum tunneling in graphene. I demonstrate this result by simulating tunneling of sound in a two-dimensional acoustic metamaterial. More strikingly, I show that by introducing a certain form of anisotropy, the tunneling can be made unimpeded for any incidence angle, while keeping most of its original Klein dispersion properties. This phenomenon may be denoted by the omnidirectional Klein-like tunneling. The suggested tunneling mechanism and its omnidirectional variant may be useful for applications requiring lossless and direction-independent transmission of classical waves.

Elastic wave propagation in nonlinear two-dimensional acoustic metamaterials

This study describes the wave propagation in a periodic lattice which is formed by a spring-mass two-dimensional structure with local Duffing nonlinear resonators. The wave propagation characteristics of the system are evaluated by using the perturbation method to determine the dispersion relationships and wave propagation characteristics in the nonlinear two-dimensional acoustic metamaterials. A quantitative study of wave amplitude is carried out to determine the maximum allowable wave amplitude for the whole structures under the assumption of small parameters. In particular, the harmonic balance method is introduced to investigate the frequency response and effective mass of the nonlinear systems. We find that the dispersion relations and group velocity of unit cell are related to wave amplitude. Furthermore, the dual-wave vector is observed in the nonlinear systems. Numerical simulations validate the dispersion analytical results. The results can be used to tune wave propagation in the nonlinear acoustic metamaterials and provide some ideas for the study of nonlinear metamaterials.

Negative Schoch displacement of two-dimensional acoustic metamaterials with near-zero refractive index

In this paper, the Schoch displacement at the interface between different two-dimensional triangular phononic crystal metamaterial and natural material is studied by using finite element software. As is well known, the Schoch displacement is highly dependent on the surface wave and leakage wave excited at the interface between different materials. So, the negative Schoch displacement can be more easily obtained by adding a suitable thickness of covering layer at the interface between metamaterial material and natural material. The numerical results show that when the negative Schoch displacement happens, the effective parameters of metamaterials are close to zero. It means that the effective refraction index is near to zero and the reduced frequency of the incident acoustic wave is correlated with the reduced frequency of the band gap. It is also found from the results that the reduced frequency of the incident acoustic wave is located at the edge of the band gap when the negative Schoch displacement occurs. The maximum of the metamaterial effective impedance and the maximum of the reflection coefficient are almost at the same frequency. The phase of the imaginary part of the reflection coefficient has a phase mutation in π rad at the corresponding frequency. The frequency of negative Schoch displacement is located in the first band gap of <i>MK</i> direction and near the upper boundary. The Schoch displacement at the interface between conventional materials is usually positive and negligible in previous reports. In this paper, the negative Schoch displacement is obtained by using the near-zero refraction index metamaterials. This not only enriches the physics contents of Schoch effect but also provides a theoretical reference for designing the acoustic devices based on acoustic wave displacement at the interface.

Homogenization of acoustic metamaterials using retrieval methods

The effective properties of two-dimensional acoustic metamaterials are here obtained by applying two retrieval methods, referred to as the direct inversion method and the differential method. They employ the scattering coefficients at the incidence and transmission sides of the global systems immersed in a fluid. A validation case study on a one-dimensional periodic design is first presented. A two-dimensional design comprising periodic cylindrical steel inclusions in a soft elastic matrix is then examined. Homogenization issues related to different underlying assumptions in the two retrieval methods are discussed. It is shown that one of the retrieval methods (the differential method) well describes the interior of the medium, away from the interfaces, while the other (the direct inversion method) captures the interface effects. The two retrieval methods are used to build homogeneous equivalent media which are used to predict scattering coefficients. A hybrid method is introduced which combines the two methods to create effective media that are accurate approximations of their 2D counterparts.

Development of a multi-objective artificial tree (MOAT) algorithm and its application in acoustic metamaterials

Although there are many algorithms that can solve the multi-objective optimization problems (MOPs) efficiently, each algorithm has its own disadvantages. The emergence of new algorithms is beneficial to make up the deficiencies of existing algorithms. Inspired by the organic matter transport process and the branch update theory of the banyan, this work proposed a new bio-inspired algorithm, named the multi-objective artificial tree (MOAT) algorithm to solve the MOPs. In MOAT, an improved crossover operator and an improved self-evolution operator are introduced to update solutions, a adaptive grid method is applied to manage the non-dominated solutions, and the strategy of variable number of branches in population is adopted to enhance the accuracy of this algorithm. Many typical test functions and seven well-known multi-objective algorithms, including MOEAD, NSGAII, MOPSO, GDE3, eMOEA, IBEA and MPSO/D, are applied to study the accuracy and efficiency of MOAT. Experimental tests show that the results of MOAT are better than those of the seven algorithms, and the performance of MOAT is demonstrated. In addition, this new algorithm is also applied to solve the MOPs of two-dimensional acoustic metamaterials (AMs). The key parameters of AMs are optimized by MOAT to mitigate impact load and reduce structural mass, and the performance of these AMs is significantly improved.

Tunable Dirac cones in two-dimensional acoustic metamaterials with matryoshka structure.

Dirac cones of an acoustic system are the foundation of most topological phase transitions and topological states and have recently become a research hotspot. Although the Dirac cones, Dirac-like cones, double Dirac cones, and semi-Dirac points are all skillfully designed, it is still indispensable to realize a tunable Dirac cone in a novel acoustic structure. This paper proposes two-dimensional acoustic metamaterials with matryoshka structure to achieve tunable Dirac cones and topological spin states. Dirac points can be obtained on the dispersion curves owing to the high symmetry. The concentric circular scattering units of the matryoshka structure are arranged in honeycomb lattices. By a rotating-scatterer mechanism to break the symmetry, the Dirac cone at K (K') is split and the topological spin states appear at the band valley. The existence of a topological transition with opposite Chern numbers as the rotating angle varies is also verified, and helical edge states are obtained along the interfaces separating the topologically opposite spin states insulators. Moreover, the frequency of the Dirac cone is tuned by rotating the inner structure in a double-layer matryoshka structure.

Study of Two-Dimensional Acoustic Metamaterial Based on Lattice System

This article presents a comprehensive study of two-dimensional acoustic metamaterial based on mass-in-mass lattice model with both one resonator and multi-resonators. We demonstrate the dynamic anisotropic property of a two-dimensional lattice system and the existence of multiple stop bands of mass-in-mass lattice systems with more than one resonator. A two-dimensional stable lattice plate structure, composed of unit mass-in-mass cells is proposed, and been studied by adapting both an exact model and a continuum model. The dispersion surfaces and stop band obtained by the exact model show that the stop band of this metamaterial exists, and it can be shifted and operated upon. In contrast, the dispersion surface obtained through the continuum model describes the acoustic mode well, but is only accurate at low frequencies for the optical mode. By attaching a secondary resonator to the primary resonator, an additional stop band is achieved. Finally, an acoustic metamaterial plate which has more than one stop band is proposed and studied numerically. Good agreement has been achieved between theoretical and numerical analyses.

Elastic wave and vibration bandgaps in two-dimensional acoustic metamaterials with resonators and disorders

The vibration properties of two-dimensional (2D) finite acoustic metamaterials (AMs) consisting of discrete masses and springs are investigated in this paper. In order to clarify the mechanisms of the bandgaps in AMs, the infinite symmetrical systems are also studied, especially the impact of the physical asymmetry caused by the discrepant stiffness coefficients of the springs connecting the unit-cells. Although the asymmetry cannot change the bandgap width, the change of the phase velocity and the generation of the shear mode have been proven analytically. To study the vibration properties of the finite AM model, the effective mass of each unit-cell is used. The effective mass properties of the unit-cell with single resonator and multi-resonators in 2D AMs subjected to a time-harmonic excitation are discussed. The effects of the number of the unit-cells, multi-resonators in each unit-cell, graded resonators in the finite AM model on the vibration suppression are thoroughly examined by the frequency response analysis. Numerical results show that the degree of the vibration attenuation is related to the size of the model and the number of the bandgaps changes corresponding to the disorders of the local resonators. Furthermore, imperfections or defects are introduced into the finite AM system. Wave propagation and guiding in a finite model for straight waveguide are investigated and discussed. The defect states induced by changing the central resonator of a supercell are demonstrated. Defect bands are obtained and their location is illustrated.

Two-dimensional structure-embedded acoustic lenses based on periodic acoustic black holes

Recent studies have introduced a new class of two-dimensional acoustic metamaterials whose dispersion and propagation properties result from the use of geometric inhomogeneities in the form of Acoustic Black Holes (ABH). The ABH is an element able to smoothly bend acoustic rays and slow down elastic bending waves, therefore providing a variety of unconventional dispersion and propagation properties that are typically observed in more complex multi-material and locally resonant designs. Our approach enables full integration of acoustic lenses in thin-walled structural elements while preserving the structural character. The lenses are capable of different high-level functionalities such as focusing, collimation, and negative refraction. Numerical and experimental results show that such structures exhibit broadband operating conditions that span both the metamaterial and the phononic range.

Dirac cones in two-dimensional acoustic metamaterials

Dirac cones show many extraordinary properties, including Klein tunneling, pseudo-diffusive behavior, phase reconstruction, and topological edge states, and are thus attracting increasing research attention. However, no studies of Dirac cones on a subwavelength scale have been reported to date. In this paper, subwavelength-scale Dirac cones are realized using acoustic metamaterials that consist of hexagonal arrays of hexagonal columns with Helmholtz resonators. We have calculated the band structures of the three types of unit cells that are yielded by space group symmetry operations of the triangular Helmholtz resonators. The results show that these acoustic metamaterials with Helmholtz resonators can be used successfully to reduce the Dirac cone frequencies. Subwavelength Dirac cones of acoustic metamaterials with p6 mm or p6 symmetries are robust to rotation, while subwavelength Dirac cones of acoustic metamaterials with p31m symmetry are sensitive to rotation. In addition, the Dirac cone frequency decreases gradually with increasing filling ratio, which indicates a possible way to control wave propagation on the subwavelength scale. Numerical simulation results show that acoustic metamaterials can behave like zero-refractive-index media and can be applied to acoustic tunneling. The acoustic metamaterials designed in this work offer a route towards the design of functional acoustic devices operating on subwavelength scales.

Topology and shape optimization of broadband acoustic metamaterials and phononic crystals

A time-dependent adjoint approach for obtaining sensitivity derivatives for shape and topology optimizations of two-dimensional acoustic metamaterials and phononic crystals is presented. The acoustic wave propagation problem is solved in the time-domain using a Streamline Upwind/Petrov Galerkin formulation. Topology parameterization is accomplished using the homogenization method, and shape optimization is subsequently used afterwards to fine tune the geometries. The combined strategy is compared with penalty-based topology optimization. The gradient-based design procedure is suitable for large numbers of design variables, and results are shown for achieving effective material properties and noise reductions, respectively.

Models and general wave properties of two-dimensional acoustic metamaterials and media

For two-dimensional linear acoustic metamaterials and media represented in the form of periodic structures made of complex cells, a general model is proposed, formulas are derived for the effective parameters and energy characteristics, and the restrictions imposed on such media are formulated. They are divided into four main types, differing in general wave properties; the differentiating features of each type are shown. Several new schemes of negative and hyperbolic types of discrete and continuous metamaterials are presented, for which the dispersion dependences are constructed and the corresponding “wave” equations are written.

Dynamic effective models of two-dimensional acoustic metamaterials with cylindrical inclusions

Based on analytical solutions of elastic waves scattered by a coated cylinder in an infinite elastic matrix, we construct the localization relations for averaged displacement and stress fields in each phase. Dynamic effective mass, in-plane bulk modulus and shear modulus are defined, respectively, as the ratio between the force and acceleration, bulk stress and bulk strain, maximum shear stress and maximum shear strain. Analytic expressions for dynamic effective parameters of two-dimensional acoustic metamaterials are derived. Numerical examples are given to analyze dynamic effective properties of composites with coated inclusions. It is demonstrated that the proposed model can predict negative values of effective mass and effective bulk and shear modulus, and discover the underlying mechanisms of negative effective material parameters. The proposed model will be helpful in designing new acoustic metamaterials.

Extreme Acoustic Metamaterial by Coiling Up Space

We show that by coiling up space using curled perforations, a two-dimensional acoustic metamaterial can be constructed to give a frequency dispersive spectrum of extreme constitutive parameters, including double negativity, a density near zero, and a large refractive index. Such an approach has band foldings at the effective medium regime without using local resonating subwavelength structures, while the principle can be easily generalized to three dimensions. Negative refraction with a double negative prism and tunneling with a density-near-zero metamaterial are numerically demonstrated.

Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials

A kind of two-dimensional acoustic metamaterial is designed so that it exhibits strong anisotropy along two orthogonal directions. Based on the rectangular equal frequency contour of this metamaterial, magnifying lenses for acoustic waves, analogous to electromagnetic hyperlenses demonstrated recently in the optical regime, can be realized. Such metamaterial may offer applications in imaging for systems that obey scalar wave equations.

Anisotropic mass density by two-dimensional acoustic metamaterials

We show that specially designed two-dimensional arrangements of full elastic cylinders embedded in a nonviscous fluid or gas define (in the homogenization limit) a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic. Here, analytic expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit. Both show an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell, and their multiple scattering interactions. Several examples of these metamaterials are reported and discussed.