Double Negative Acoustic Metamaterial Research Articles

Localization of waves in double-negative acoustic metamaterial multilayers with thickness disorder

The investigation of double-negative acoustic metamaterials for, among other things, achieving acoustic damping and the suppression of the localization of waves in acoustic systems constitutes an interesting field of study. Vibrational waves in one-dimensional random systems containing double-negative acoustic metamaterials are investigated in this study. Participation number is used to analyze the localization of waves in acoustic metamaterial multilayers with thickness disorder. PN is observed to become very large inside the DN band near the characteristic frequency where the effective mass approaches zero. For acoustic metamaterial multilayers following the Fibonacci sequence, the frequency dependence of their transmittance was numerically investigated.

Viscoelastic reduced enhanced isotropic continua as acoustic metamaterials.

We consider a linear enhanced viscoelastic continuum of general nature but of specific type. Namely, we consider a reduced elastic continuum, satisfying Lagrange equations, where the strain energy depends on a certain (special) vectorial generalized coordinate, but does not depend on its gradient, and then add linear dissipation to the existing elastic connections. We may also represent this model as a 'bearing continuum', where all the connections are present (described by one vectorial generalized coordinate), enriched in each point by a 'distributed dynamic absorber' (described by 'special' vectorial generalized coordinate). We look for free harmonic waves in this infinite medium and obtain a reduced spectral problem for the vectorial generalized coordinate of the bearing continuum, for anarbitrary number of degrees of freedom. It was shown earlier that under certain symmetry conditions in the elastic case we obtain a single negative acoustic metamaterial, i.e. a medium that has band gaps. Further, we considerisotropic and gyrotropic reduced media, described by two three-dimensional vectorial generalized coordinates. First, we generalize results of previous studies for more complex elastic coupling, discovering a polarized shear wave, which has both bandgaps and zones of anomalous refraction. Then we introduce linear dissipation of different kinds. We find that viscosity yields in existence of travelling harmonic waves for all frequencies, possibly except for some points. Logarithmic decrement, infinite for the elasticmaterial in bandgaps, becomes finite and decreases as the dissipation increases, at least for small viscosity. An important observation is: an infinitesimal dissipation in most cases transforms bandgaps into zones of travelling evanescent waves that partially are zones of anomalous refraction (decreasing parts of dispersion curves), where the medium is a double negative acoustic metamaterial. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Tri-Band Negative Modulus Acoustic Metamaterial With Nested Split Hollow Spheres

We presented tri-band negative modulus acoustic metamaterials (AM), whose operation characteristics could be flexibly designed by changing the three hole sizes (i.e., a1, a2, and a3) of the tri-layer nested split hollow spheres (NSHSs). We demonstrate numerically that tri-band negative modulus can be obtained and each resonant frequency corresponds to the hole size of each split hollow sphere. However, for the case when a1> a2> a3, the negative modulus band in the high frequency region vanishes. An effective sound-force analogue model with coupling interaction is further developed for the accurate prediction of the three resonant frequencies based on equating the tri-layer NSHSs to three spring oscillators in series. As a result of the analytical formulas, three resonant frequencies could be precisely controlled, and a nested AM with a tri-band negative modulus can be flexibly constructed. The proposed AM could be easily extended to multiple operation bands and can be further coupled with negative mass density structures for constructing multi-band double-negative AMs.

Reduced linear viscoelastic isotropic Cosserat medium with rotational viscosity: an acoustic metamaterial

In this paper we investigate the influence of rotational viscosity on the plane shear-rotational wave propagation in the linear isotropic reduced Cosserat medium. In such a continuum body points possess independent rotational and translational degrees of freedom, but the material does not resist to the gradient of microrotation. Stress tensor is asymmetric, but the couple stress is zero. For the elastic reduced Cosserat medium a band gap is present, where no running waves exist, and the logarithmic decrement is infinitely large. It was shown before that introducing viscoelasticity we may qualitatively change the dispersion behaviour. This work investigates the case of rotational viscosity, related to the difference between micro- and macrorotation. We show that in this case running decaying waves appear in the band gap domain, and their logarithmic decrement becomes finite. The dispersion relation for the real part of the wave number has a decreasing part. This means that the group velocity of these waves is opposed to their phase velocity, the behaviour characterizing double negative acoustic metamaterials.

Reduced Linear Constrained Elastic and Viscoelastic Homogeneous Cosserat Media as Acoustic Metamaterials

We consider the reduced constrained linear Cosserat continuum, a particular type of a Cosserat medium, for three different material behaviors or symmetries: the isotropic elastic case, a special type of elastic transversely isotropic case, and the isotropic viscoelastic case. Such continua, in which stresses do not work on rates of microrotation gradients, behave as acoustic metamaterials for the (pure) shear waves and also for one branch of the mixed wave in the considered anisotropic material case. In elastic media, those waves do not propagate for frequencies exceeding a certain threshold, whence these media exhibit a single negative acoustic metamaterial behavior in this range. In the isotropic viscoelastic case, dissipation destroys the bandgap and favors wave propagation. This curious effect is, probably, due to the fact that the bandgap is associated not with the dissipation, but with the wave localization which can be destroyed by the viscosity. The dispersion curve is now decreasing in some part of the former bandgap, above a certain frequency, whence the medium is a double negative acoustic metamaterial. We prove the existence of a boundary wavenumber in the viscoelastic case and estimate its value. Below the characteristic frequency corresponding to the boundary of the elastic bandgap, the wave attenuation (logarithmic decrement) is a growing function of the viscous dissipation parameter. Above this frequency, the attenuation decreases as the viscosity increases.

Reversed Doppler effect based on hybridized acoustic Mie resonances

The realization of reversed Doppler effects in double-negative acoustic metamaterials remains challenging. This paper demonstrates the reversed Doppler effect associated with sound wave propagation in negative group velocity in hybridized metamaterial (HM) system using a simple Mie-resonator configuration. Double-negative acoustic parameters act simultaneously on the effective dynamic bulk modulus and mass density within overlapped frequency region of multiple Mie resonances. Notably, while ordinary media exhibits higher received frequency during the approach and lower during the recession, we observe that in HM the detected signals show redshift compared to the emitted frequency when approaching to the source while depict blue shift when receding from the source. On this basis, the HM exhibits negative phase velocity with reversed wavefronts and negative refraction effect for certain frequency range. Focusing of sound waves emitted from a point source is further realized with a flat lens composed by such a HM slab.

Tunable Two-Layer Dual-Band Metamaterial with Negative Modulus.

A tunable dual-band acoustic metamaterial (AM) with nested two-layer split hollow spheres (TLSHSs) is presented here, which was achieved by adjusting the hole diameter and the ratio of the two layers’ volumes. This work comprises theoretical and numerical studies. Based on sound-force analogy (SFA), TLSHSs can be considered equivalent to a model of two spring oscillators in series. The equations of two resonant frequencies were derived, which precisely provided the relation between two resonant frequencies and the hole diameter as well as the ratio of the two layers’ volumes. The analytical formulas and simulation results by the finite element method (FEM) showed that there were two resonant frequencies for the TLSHSs, and their dynamic modulus became negative near the resonant frequencies. As the the diameter of two holes increased, both of the resonant frequencies underwent a blue shift. As the relative volume ratio increased, both of the resonant frequencies underwent a red shift. The calculation and simulation results were in good agreement. This kind of precisely controllable dual-band AM with negative modulus can easily be coupled to other structures with negative mass density, thereby achieving a double-negative AM in an expected frequency range.

Experimental realization of aqueous double negative metamaterials in near-megahertz range

Ultrasound is strongly attenuated and aberrated by the skull, principally due to the complex structure and acoustic impedance mismatch of skull which generates strong scattering. Analytical models and finite element methods have shown that negative index metamaterials matching skull properties can enable the transmission of US which enhances bidirectional transmission of ultrasonic signal for imaging. However, it is difficult to realize double-negative metamaterials in near-megahertz range experimentally because of the limitation of fabrication and characterization methods. Here we show the experimental realization of waterborne double negative acoustic metamaterials by coupling micrometer-size membrane-based negative density metamaterials with Helmholtz resonator-based negative modulus materials. Numerical simulation and experimental verification consistently exhibit the double negative behavior between 230 kHz and 410 kHz. We demonstrated the feasibility of creating ultrasonic-range metamaterials for non-invasive ultrasound imaging and neuron stimulation.

Systematic design and realization of double-negative acoustic metamaterials by topology optimization

Double-negative acoustic metamaterials (AMMs) offer the promising ability of superlensing for applications in ultrasonography, biomedical sensing and nondestructive evaluation. However, the systematic design and realization of broadband double-negative AMMs are stilling missing, which hinder their practical implementations. In this paper, under the simultaneous increasing or non-increasing mechanisms, we develop a unified topology optimization framework involving different microstructure symmetries, minimal structural feature sizes and dispersion extents of effective parameters. The optimization framework is applied to conceive the heuristic resonance-cavity-based and space-coiling metamaterials with broadband double negativity. Meanwhile, we demonstrate the essences of double negativity derived from the novel artificial multipolar LC (inductor-capacitor circuit) and Mie resonances which can be induced by controlling mechanisms in optimization. Furthermore, abundant numerical simulations validate the corresponding double negativity, negative refraction, enhancement of evanescent waves and subwavelengh imaging. Finally, we experimentally show the desired broadband subwavelengh imaging by using the 3D-printed optimized space-coiling metamaterial. The present design methodology provides an ideal approach for constructing the constituent “atoms” of metamaterials according to any artificial physical and structural requirements. In addition, the optimized broadband AMMs and superlens lay the structural foundations of subwavelengh imaging technology.

Dynamical effective parameters of elastic superlattice with strong acoustic contrast between the constituents

Analytical formulas are obtained for frequency-dependent effective elastic modulus and effective mass density for a periodic layered structure. The proposed homogenization procedure is valid at sufficiently high frequencies well above the lowest band gap in the acoustic spectrum of the structure. It is shown that frequency-dependent effective parameters may take negative values either in different regions of frequencies or in the same quite narrow region. This property demonstrates that the 1D elastic structure may behave in the limit of small Bloch wave vectors as a double-negative acoustic metamaterial.

Inverse Doppler Effects in Pipe Instruments

Music is older than language, and for most of human history music holds our culture together. The pipe instrument is one of the most popular musical instruments of all time. Built on the foundation of previous flute and flute-like acoustic metamaterial models, we herein report the experimental results of the inverse Doppler effects discovered in two common pipe instruments - recorder and clarinet. Our study shows that the inverse Doppler effects can be detected at all seven pitches of an ascending musical scale when there is a relative motion between a microphone (observer) and abovementioned two pipe instruments (source). The calculated effective refractive indices of these two pipe instruments are negative and varying across a set of pitches, exhibiting a desired characteristic of broadband acoustic metamaterials. This study suggests that recorder and clarinet may be the earliest man-made acoustic metamaterials known so far, offering a new explanation why pipe instruments have enjoyed wide popularity in Europe and Asia over the past hundreds and thousands years. This newly discovered phenomenon would also offer a clue into designing next-generation smart broadband double-negative acoustic metamaterials with varying refractive index.

Multibands acoustic metamaterial with multilayer structure

A multiband acoustic metamaterial (AM) with negative modulus is presented. To realize the multibands, we conduct the unit structure of a resonator with multilayers in which we adjust the number of layers of local resonance cells, namely, multilayer split hollow spheres or cubes (SHSs or SHCs). The results obtained by the finite element method show that a single-layer SHS has one transmission dip and the resonance generates a negative modulus; two-layer SHSs exhibit two transmission dips, while three-layer SHSs and three-layer SHCs have three transmission dips and their dynamic modulus become negative near the resonant frequency. Thus, the number of multiband resonant frequencies is regulated by adjusting the number of layers. This regulation is independent of the sphere and cube of the resonance cell, and this structure is simple. The developed multiband AM can easily be coupled to other structures with negative mass density, thereby obtaining a double-negative AM. It is also applicable in fields such as cloak or sub-wavelength imaging.

Systematic Design and Realization of Double-Negative Acoustic Metamaterials by Topology Optimization

Double-negative acoustic metamaterials (AMMs) offer the promising ability of superlensing for applications in ultrasonography, biomedical sensing and nondestructive evaluation. However, the systematic design and realization of broadband double-negative AMMs is stilling missing, which hinders their practical implementations. In this paper, under the simultaneous increasing or non-increasing mechanisms, we develop a unified topology optimization framework involving the different microstructure symmetries, minimal structural feature sizes and dispersion extents of effective parameters. The optimization framework is applied to discover the heuristic resonance-cavity-based and space-coiling metamaterials with broadband double negativity. Meanwhile, we demonstrate the essences of double negativity derived from the novel artificial multipolar LC (inductor-capacitor circuit) and Mie resonances which can be induced by controlling mechanisms in optimization. Furthermore, abundant numerical simulations validate the corresponding double negativity, negative refraction, enhancements of evanescent waves and subwavelengh imaging. Finally, we experimentally show the desired broadband subwavelengh imaging by using the 3D-printed optimized space-coiling metamaterial. The present design methodology provides an ideal approach for constructing the constituent atoms of metamaterials according to any manual physical and structural requirements. In addition, the optimized broadband AMMs and superlens can truly lay the structural foundations of subwavelengh imaging technology.

The Effect of Geometrical Parameters on Resonance Characteristics of Acoustic Metamaterials with Negative Effective Modulus

There has been an explosion of interest in acoustic metamaterial in the last ten years. The tunable negative acoustic metamaterial is an important issue for designing metamaterials. The acoustic metamaterial is restricted by the narrow bandgap of sound waves for the local resonance of metamaterial unit cells. By shifting the sizes of the unit cell, the acoustic metamaterial could potentially overcome the limit of the narrow resonance frequency. In this research, we focus on the resonant behavior of split hollow sphere (SHS) in the waveguide. Firstly, we analyze the resonance characteristics of SHS and get an analytical formula for the effect of geometrical parameters on the resonance frequency. Furthermore, the resonance frequency of SHS is verified with finite-element method analysis based on COMSOL Multiphysics simulation. The results are in good agreement with theory model. It is observed that there is a blue shift of the resonance frequency with the gradual increase of the neck radius of SHS, a V-type response curve with the increase of inner radius of SHS, and a red shift with the increase of outer radius of SHS. Using the method of estimate of resonance, we could get a precisely controllable unit structure with negative effective modulus and offer a way to optimize the realization of double negative acoustic metamaterial.

Viscothermal Losses in Double-Negative Acoustic Metamaterials

V. M. G.-C. and J. S.-D. acknowledge the support from the Spanish Ministerio de Economia y Competitividad (MINECO), and the European Union Fondo Europeo de Desarrollo Regional (FEDER) through Project No. TEC 2014-53088-C3-1-R.

One class of single negative acoustic metamaterials

We consider linear elastic complex media the point-body motion of which is described by two vectorial generalized coordinates and the elastic energy contains a term coupling them. All constraints are holonomic and ideal. The dynamics of this continuum is determined by modified Lagrange equations. We specify a class of media whose strain energy depends only on one of the vectorial generalized coordinates, but does not depend on its gradient. We call this generalized coordinate “special.” On the partial frequency of the special generalized coordinates under some conditions for the inertial and elastic characteristics, the medium behaves as a system of independent harmonic oscillators, and under other conditions, only the trivial solution exists. It is shown that independently of the nature of generalized coordinates, if the inertial and elastic tensors satisfy certain requirements, there exists a band gap of frequencies for most of the dispersion curves; i.e., the medium is a single negative acoustic metamaterial in this band of frequencies. The partial frequency of the “special” coordinate limits the band gap. For a specific class of parameters, apart from this, there exists a decreasing part of the dispersion curve; i.e., the medium is also a double negative acoustic metamaterial in a certain domain of frequencies.

Topology optimization of an acoustic metamaterial with negative bulk modulus using local resonance

During the past decade, materials that display novel properties in the acoustic realm, so-called acoustic metamaterials, have attracted much attention, since these properties can provide promising opportunities to design new acoustic devices that cannot be made with natural materials. Although acoustic metamaterials that exhibit negative mass density or negative bulk modulus, and double-negative acoustic metamaterials, have been obtained experimentally by trial and error, our aim is to develop a topology optimization method for the direct design of acoustic metamaterials, based on the concept of local resonant mechanisms, which ensures that the lattice constant is orders of magnitude functionally smaller than the corresponding sonic wavelength, and avoids unwanted effects of Bragg scattering mechanisms. This paper proposes a level set-based topology optimization method for the structural design of acoustic metamaterials that achieve an extremely negative bulk modulus at certain prescribed frequencies. Level set-based topology optimization methods can directly provide clear boundaries in optimal configurations that avoid the presence of grayscales. The optimization problem is formulated for a two-dimensional wave propagation problem, with the objective being to minimize the effective bulk modulus at chosen target frequencies. An effective medium description based on S-parameters is introduced to describe the acoustic metamaterial. Finite element method (FEM) is used to solve the Helmholtz equation for acoustic waves, sensitivities are obtained with the adjoint variable method (AVM), and a reaction-diffusion equation is used to update the level set function. Several numerical examples with prescribed target frequencies and different initial shapes are provided to demonstrate that the proposed method can provide clear, optimized structures for the design of negative bulk modulus acoustic metamaterials.

Double-negative acoustic metamaterial based on hollow steel tube meta-atom

We presented an acoustic “meta-atom” model of hollow steel tube (HST). The simulated and experimental results demonstrated that the resonant frequency is closely related to the length of the HST. Based on the HST model, we fabricated a two-dimensional (2D) acoustic metamaterial (AM) with negative effective mass density, which put up the transmission dip and accompanied inverse phase in experiment. By coupling the HST with split hollow sphere (SHS), another kind of “meta-atom” with negative effective modulus in the layered sponge matrix, a three-dimensional (3D) AM was fabricated with simultaneously negative modulus and negative mass density. From the experiment, it is shown that the transmission peak similar to the electromagnetic metamaterials exhibited in the double-negative region of the AM. We also demonstrated that this kind of double-negative AM can faithfully distinguish the acoustic sub-wavelength details (λ/7) at the resonance frequency of 1630 Hz.

Double-negative acoustic metamaterials based on quasi-two-dimensional fluid-like shells

A structured cylindrical scatterer with low-frequency resonances in both the effective bulk modulus and the dynamical mass density is designed and characterized. The proposed scattering unit is made of a rigid cylinder surrounded by a fluid-like shell embedded in a two-dimensional waveguide of height less than the length of the cylindrical scatterer. It is demonstrated that the acoustic metamaterials based on this building unit have negative acoustic parameters in a broad range of frequencies. It is also shown that double-negative behavior can be tailored by adjusting the dimensions and properties of the materials forming the structured scattering unit.

Acoustic metamaterial exhibiting four different sign combinations of density and modulus

We fabricated a double negative acoustic metamaterial which consisted of Helmholtz resonators and membranes. Experimental data on the transmission and dispersion relation are presented. The system exhibited three frequencies where the acoustic state makes sharp transitions from density negative (ρ-NG) to double negative (DNG), modulus negative (B-NG), and double positive (DPS) in sequence with the frequency. We observed a wide range of negative refractive indexes from −0.06 to −3.7 relative to air, which will allow for new acoustic transformation techniques.