Acoustic Metamaterials

The control of acoustic-frequency gaps by altering the geometry of the system is analyzed in the particular case of a set of parallel solid square-section columns distributed in air on a square lattice. This system is shown to be sensitive enough to the rotation of the columns to be considered for practical sonic band-gap-width engineering. For different geometric configurations, specific interpretation models are used, taking into account the important mismatch of the impedance between the compounds. The accuracy of the plane-wave calculation is discussed in the different cases.

The impulsive acoustic dynamics of soft polymeric surface phononic crystals is investigated here in the hypersonic frequency range by near-IR time-resolved optical diffraction. The acoustic response is analysed by means of wavelet spectral methods and finite element modeling. An unprecedented class of acoustic modes propagating within the polymer surface phononic crystal and confined within 100 nm of the nano-patterned interface is revealed. The present finding opens the path to an alternative paradigm for characterizing the mechanical properties of soft polymers at interfaces and for sensing schemes exploiting polymers as embedding materials.

Metamaterials as a paradigm and laboratory for transdisciplinarity.
The course Artificial Materials, Metamaterials, and Plasmonics for Electromagnetic Applications is part of the Master's Degree in Nanotechnology Engineering starting from the 2019-2020 academic year. The Master's Degree in Nanotechnology Engineering does not have a corresponding first-level degree, therefore it naturally welcomes students who have graduated in various disciplines and has been characterized since its foundation by its evident transdisciplinary aspects. The course, which is unique in our university, aims to provide students with knowledge of artificial electromagnetic materials, metamaterials, metasurfaces, metastructures, and plasmonics, enabling them to analyze and design components and devices for electromagnetic propagation and diffusion. The course illustrates the physical principles of artificial materials, metamaterials, and plasmonic structures, which are of considerable importance in many recent applications in various disciplines, not only in the electromagnetic field, but also in the mechanical, structural, energy, environmental, and marine fields. In particular, from this point of view, the unifying elements are wave propagation, the concepts of analogy, equivalence and equivalent circuits, and homogenization. Students are led to model, from an electromagnetic point of view, certain materials and components of particular interest in applications, and to study their behavior using large-scale simulation and numerical modeling techniques for complex multifunctional structures, utilizing multiphysical properties through high-performance computing (HPC) and hybrid approaches incorporating artificial intelligence (AI). The above knowledge is particularly relevant in the fields of development, engineering, production and management, and technology transfer.

A design of actively controlled metamaterial is proposed and discussed. The metamaterial consists of layers of electrically charged nano or micro particles exposed to external magnetic field. The particles are also attached to compliant layers in a way that the designed structure exhibits two resonances: mechanical spring-mass resonance and electro-magnetic cyclotron resonance. It is shown that if the cyclotron frequency is greater than the mechanical resonance frequency, the designed structure could be highly attenuative (40–60 dB) for vibration and sound waves in very broad frequency range even for wavelength much greater than the thickness of the metamaterial. The approach opens up wide range of opportunities for design of adaptively controlled acoustic metamaterials by controlling magnetic field and/or electrical charges.

In this paper, we report about the effect of the application of a state of prestress on the band structure of a periodic phononic crystal characterized by an inertial amplification mechanism. Through a numerical example, we show the possibility of inducing negative group velocity in an isolated branch of the dispersion diagram. A 2-step Updated Lagrangian scheme is adopted to calculate the dispersion diagram of the structure. The proposed method include (i) the static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load and (ii) the Bloch-Floquet decomposition applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration. The dispersion analysis is performed in terms of small amplitude motions superimposed on a deformed state, once the desired load has been applied.

Purpose Power gain from piezoelectric harvesters depends on several parameters and one of them is to design the substructure as to increase the mechanical strain occurred in the piezoelectric material. In this study, the effect of geometrical modification of the beam on the harvested power was investigated and new geometries were offered for increased power response from cantilever type energy harvesters. Method First, the effectiveness of auxetic structures on harvested power was investigated to see the effect of the negative Poisson's ratio on harvested power. These structures are very popular in recent years on energy harvesting applications; however, their performances were generally compared to plain structures which is not a fair comparison. Rather, in this study, their performances were compared to non-auxetic nonlinear structures as well as plain geometry. Then, three new shapes inspired by re-entrant auxetic structure were presented for increased power response, and harvested power from these structures were evaluated under different conditions. Results It was shown that the power gain from auxetic structures is very high compared to plain structures; however, this increase in power could also be achieved using a non-auxetic simple rectangular structure in some cases. On the other hand, new geometries offered in this study performed better than the auxetic and non-auxetic geometries in most cases.

Metamaterials cloaking technology boasts a wide array of potential uses, spanning from military stealth applications to advancements in medical imaging. Metamaterials are specially engineered materials with unique characteristics absent in natural substances, such as negative refractive index, empowering them to manipulate electromagnetic waves in novel ways. The process of cloaking with metamaterials involves the bending of light or other electromagnetic waves around an object, effectively rendering it invisible or significantly reducing its detectability. This is accomplished through the intricate design of metamaterial structures capable of governing the flow of electromagnetic fields, diverting them away from the cloaked object. Among the most prominent applications of metamaterial cloaking is the development of invisibility cloaks. While primarily at the experimental stage, researchers have made substantial progress in crafting cloaking devices capable of concealing objects from specific wavelengths of light. These cloaks function by manipulating the path of light around an object, effectively creating the illusion of its absence. The potential applications of metamaterial cloaking encompass a broad spectrum, including invisibility, antennas and sensors, medical imaging, wireless communication, and stealth technology.

The principles by which the acoustics can be mimicked in order to reduce or cancel the vibrational field are based on anti-sound concept which can be materialized by acoustic cloaks. Geometric transformations open an elegant way towards the unconstrained control of sound through acoustic metamaterials. Acoustic cloaks can be achieved through geometric transformations which bring exotic metamaterial properties into the acoustic equations. Our paper brings new ideas concerning the technological keys for manufacturing of novel metamaterials based on the spatial compression of Cantor structures, and the architecture of 3D acoustic cloaks in a given frequency band, with application to architectural acoustics.

This paper extends upon the scalar topologies throughout our frameworks, where 16 Desmos-generated scalar visuals illustrate the phase behavior of φⁿ-modulated collapse lattices and directional coherence gates. These topologies provide the visual foundation for the Codex Scalar–Alpha framework explored in both Paper I and this expanded Paper II.
As demonstrated in Figure 4 (p.8) of the simulation atlas, the spiral convergence behavior under φⁿ encoding matches the observed freezing directionality in Codex-structured water tests and supports the modeled lattice collapse behavior presented in Section 3.2.”

We demonstrated a nanoscaled artificial phononic crystal composed of three-dimensionally ordered quantum dots (QDs) with functional acoustic properties. Femtosecond ultrasonic technique is used to investigate the lattice dynamics of this phononic nanocrystal. The measurement results indicate that three-dimensional ordering and uniformity of the QDs are important factors influencing the observed acoustic resonance at the forbidden bands. For well-arranged QDs, noticeable features of the phononic band gap and the associated phonon cavity mode can be found, while this nanocrystal also serves as an effective acoustic medium, or acoustic meta material, for low-frequency acoustic phonons.

The acoustic transmittance of two closely spaced rigid plates perforated with a square array of circular holes is studied both experimentally and numerically. The system exhibits a band of acoustic attenuation originating from hybridization between a two-dimensional resonance in the gap between the plates, and pipe modes in the holes. Misalignment of the holes in either one or both lateral dimensions shifts the centre frequency of the stop band to maintain the conditions required for zero transmission.

Controlling the phononic properties of materials provides opportunities for better thermal insulation, reduction of sound noise, and conversion of wasted heat into electricity. Phononic crystals are periodically structured media composed of two or more dissimilar materials offering a unique pathway to control the transmission of phonons, responsible for sound and heat transport. In particular, phononic crystals with cubic network structure possessing complete phononic bandgaps are highly desirable for energy applications but have not been thoroughly investigated, hampering progress in this field. Here we computationally obtained phononic band structures of 16 cubic network structures that could be made by fabrication techniques including block copolymer self-assembly and identified six structures that exhibit complete phononic bandgaps. The champion phononic bandgap structure is the so-called I-WP structure with a bandgap width of 0.41. On the basis of simulation results, design rules to tailor network structures for larger phononic bandgaps are elucidated. We expect that our results will provide guidance to develop novel materials for sonic and thermal devices.

In this paper, we show that acoustoelasticity in hyperelastic materials can be understood using the framework of nonlinear wave mixing, which, when coupled with an induced static stress, leads to a change in the phase velocity of the propagating wave with no change in frequency. By performing Floquet wave eigenvalue analysis, we also show that band gaps for periodic composites, acting as 1-D phononic crystals, can be tuned using this static stress. In the presence of second-order elastic nonlinearities, the phase velocity of propagating waves in the phononic structure changes, leading to observable shifts in the band gaps. Finally, we present numerical examples as evidence that the band gaps are tuned by both the direction of the stress and its magnitude.

This study presents a deep-learning framework for predicting and optimizing the bandgap properties of 2D acoustic metamaterials with arbitrary-shaped unit cells. The convolutional neural network (CNN) presented in this work achieves exceptional accuracy, with coefficients of determination (R-2) exceeding 0.99, in predicting both bandgap widths and positions. We improve model interpretability using SHapley Additive exPlanations (SHAP), revealing how geometric features, including concave and convex curvatures, impact bandgap properties. Additionally, an inverse design process utilizing particle swarm optimization technique identifies metamaterial geometries that meet specific bandgap ratio targets, with prediction errors consistently below 0.25 %. The implementation code is available on GitHub, ensuring reproducibility and facilitating future research. This framework offers a powerful tool for designing and optimizing next-generation acoustic metamaterials.

Both the medical and building authority requirements not to exceed a night-time indoor sound pressure level of 30 dB(A) in bedrooms and to ensure a sufficient hygienic minimum air exchange repeatedly pose major challenges for building professionals. The newly developed "attached soundproof window" can be a solution for this. The "attached soundproof window" ensures both sufficient air exchange, with low heat losses thanks to heat recovery, as well as very good sound insulation of up to 20 dB sound level differ-ence in the case of a fully open window. The advantages of an "attached soundproof window" also in-clude excellent summer thermal insulation, thermal bridge-free installation on the façade and all without reducing sound insulation. This article presents the operating principle of the "attached soundproof win-dow" and shows which applications can be derived from it. In this article, the acoustic improvements that can be achieved are discussed based on measurement results.

We consider the low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals). Exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived. We apply our formulas to the well-known phenomenon of the drop of the speed of sound in mixtures. For air bubbles in water we obtain a perfect agreement with the recent results of coherent potential approximation obtained by M. Kafesaki, R. S. Penciu, and E. N. Economou [Phys. Rev. Lett. 84, 6050 (2000)] if the filling of air bubbles is far from close packing. When air spheres almost touch each other, the approximation gives 10 times lower speed of sound than the exact theory does.

A two-dimensional phononic crystal with asymmetric scatterers is used for the study of Anderson localization of sound along one-dimensional disorder produced by random orientation of metallic rods. An exponentially weak transmission of ultrasound is demonstrated for the waves propagating along the direction of disorder. In the perpendicular direction where the scatterers are ordered, sound propagates as extended wave. The PT-symmetry of the system is broken by dissipative viscous losses and asymmetric shape of the scatterers. Nonreciprocal transmission of sound is observed for both, ordered and disordered, directions. In the localized regime, the nonreciprocity is manifested through different values of localization length for sound propagating in the opposite directions.

Anomalous scattering and redirection of sound in narrow liquid channels ANDRII BOZHKO, ARKADII KROKHIN, University of North Texas, VICTOR M. GARCíA-CHOCANO, JOS É S ÁNCHEZ-DEHESA, Universidad Politècnica de València -Propagation of sonic waves through a finite-length channel clad between two identical liquid-immersed metal plates with accounting for excitation of coupled surface Rayleigh waves propagating near metal-liquid interfaces is studied. The transmission coefficient is calculated for the wide range of frequencies of the incident sound wave, f = 0.2 ÷ 1.4 MHz. At discrete frequencies the transmission and reflection is anomalously suppressed that is shown to be accompanied by unusual redirection of sound from the liquid into metal at the edges of the channel. Proposed theory is in excellent agreement with experimental data obtained for water channels formed by Al and Cu plates.

A homogenization theory, representing the low-frequency limit, is developed for a phononic crystal of cylinders embedded in a viscous fluid. The decay coefficient of sound due to viscosity is calculated analytically for any two-dimensional Bravais lattice and cross section of the cylinders. It is shown that due to the formation of a viscous boundary layer around each cylinder, the losses are enhanced by two to three orders of magnitude as compared to the losses in the free fluid. Also, the decay coefficient in a phononic crystal scales with frequency as √ ω, unlike ω 2 scaling known for free viscous fluid. In the low-frequency limit a phononic crystal with asymmetric unit cell behaves like a dissipative homogeneous metafluid with anisotropic viscosity.

At low frequencies, a phononic crystal behaves like a homogeneous medium. Different variants of homogenization technique have been recently proposed to calculate the effective elastic parameters of periodic medium. Here, we develop a homogenization theory for a phononic crystal of solid rods in a viscous fluid. Using the plane wave expansion method, we derive analytical formula for the decay coefficient of low frequency sound propagating in a 2D Bravais lattice with arbitrary unit cell. It is shown that due to the formation of a viscous boundary layer around each cylinder, the losses are enhanced by two to four orders of magnitude as compared to the losses in the free fluid. This enhancement depends on the filling fraction of solid rod and it becomes very strong for almost touching scatterers when sound propagates through narrow slits between the neighbouring rods. Also, the decay coefficient in a phononic crystal scales with frequency as ω2, unlike scaling √ω known for free viscous...

A homogenization theory, representing the low-frequency limit, is developed for a phononic crystal of cylinders embedded in a viscous fluid. The decay coefficient of sound due to viscosity is calculated analytically for any two-dimensional Bravais lattice and cross section of the cylinders. It is shown that due to the formation of a viscous boundary layer around each cylinder, the losses are enhanced by two to three orders of magnitude as compared to the losses in the free fluid. Also, the decay coefficient in a phononic crystal scales with frequency as √ ω, unlike ω 2 scaling known for free viscous fluid. In the low-frequency limit a phononic crystal with asymmetric unit cell behaves like a dissipative homogeneous metafluid with anisotropic viscosity.

Anomalous scattering and redirection of sound in narrow liquid channels ANDRII BOZHKO, ARKADII KROKHIN, University of North Texas, VICTOR M. GARCíA-CHOCANO, JOS É S ÁNCHEZ-DEHESA, Universidad Politècnica de València -Propagation of sonic waves through a finite-length channel clad between two identical liquid-immersed metal plates with accounting for excitation of coupled surface Rayleigh waves propagating near metal-liquid interfaces is studied. The transmission coefficient is calculated for the wide range of frequencies of the incident sound wave, f = 0.2 ÷ 1.4 MHz. At discrete frequencies the transmission and reflection is anomalously suppressed that is shown to be accompanied by unusual redirection of sound from the liquid into metal at the edges of the channel. Proposed theory is in excellent agreement with experimental data obtained for water channels formed by Al and Cu plates.

We consider the low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals). Exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived. We apply our formulas to the well-known phenomenon of the drop of the speed of sound in mixtures. For air bubbles in water we obtain a perfect agreement with the recent results of coherent potential approximation obtained by M. Kafesaki, R. S. Penciu, and E. N. Economou [Phys. Rev. Lett. 84, 6050 (2000)] if the filling of air bubbles is far from close packing. When air spheres almost touch each other, the approximation gives 10 times lower speed of sound than the exact theory does.

Nature has always represented a fundamental source of inspiration to solve mankind's scientific challenges and engineering tasks. For instance, it has been shown that a hierarchical organization over multiple length scales allows enhanced quasi-static mechanical properties, while the relative orientation of adjacent chiral centers strongly affects the physical properties of a polymer, and internal heterogeneous architectures may result in shape changing systems, to cite a few examples. In this paper, we discuss how bio-inspiration may be used to enhance the potential of phononic crystals and acoustic metamaterials.

The vast majority of acoustic wave propagation in phononic band studies has been usually carried out by scattering inclusions embedded in a viscoelastic medium, such as air or water. In this study, we present calculated band structure results for the two-dimensional square array geometry of a solid cylindrical scatterer surrounded by a liquid crystal (LC) matrix. Liquid crystals provide a unique combination of liquidlike and crystal-like properties as well as anisotropic properties. The purpose of using LC material is to take advantage of longitudinal acoustic waves propagating parallel (||) and perpendicular (\) to the nematic liquid crystal (NLC) director n. The compound used in this study was a room temperature NLC, called 5CB (4-pentyl-4 0 -cyanobiphenyl). The acoustic band structure of a two-dimensional phononic crystal containing a 5CB NLC and lithium tantalate was investigated by the plane wave expansion method. The theoretical results show that the solid/LC system can be tuned in a favorable configuration for adjusting or shifting acoustic band gaps.

An acoustic metamaterial has been constructed using 3D printing. It contained an array of air-filled channels, whose size and shape could be varied within the design and manufacture process. In this paper we analyze both numerically and experimentally the properties of this polymer metamaterial structure, and demonstrate its use for the imaging of a sample with sub-wavelength dimensions in the audible frequency range.

We investigate experimentally and theoretically the acoustic phonon propagation in two-dimensional phononic crystal membranes. Solid-air and solid-solid phononic crystals were made of square lattices of holes and Au pillars in and on 250 nm thick single crystalline Si membrane, respectively. The hypersonic phonon dispersion was investigated using Brillouin light scattering. Volume reduction (holes) or mass loading (pillars) accompanied with second-order periodicity and local resonances are shown to significantly modify the propagation of thermally activated GHz phonons. We use numerical modeling based on the finite element method to analyze the experimental results and determine polarization, symmetry, or three-dimensional localization of observed modes.

The design and fabrication of phononic crystals (PnCs) hold the key to control the propagation of heat and sound at the nanoscale. However, there is a lack of experimental studies addressing the impact of order / disorder on the phononic properties of PnCs. Here, we present a comparative investigation of the influence of disorder on the hypersonic and thermal properties of 2-dimensional PnCs. PnCs of ordered and disordered lattices are fabricated of circular holes with equal filling fractions in free-standing Si membranes. Ultrafast pump and probe spectroscopy (asynchronous optical sampling) and Raman thermometry based on a novel two-laser approach are used to study the phononic properties in the GHz and THz regime, respectively. Finite element method simulations of the phonon dispersion relation and three dimensional displacement fields furthermore enable the unique identification of the different hypersonic vibrations. The increase of surface roughness and the introduction of short range disorder are shown to modify the phonon dispersion and phonon coherence in the hypersonic (GHz) range without affecting the room temperature thermal conductivity. Based on these findings we suggest a criteria for predicting phonon coherence as function of roughness and disorder.

We investigate experimentally and theoretically the acoustic phonon propagation in two-dimensional phononic crystal membranes. Solid-air and solid-solid phononic crystals were made of square lattices of holes and Au pillars in and on 250 nm thick single crystalline Si membrane, respectively. The hypersonic phonon dispersion was investigated using Brillouin light scattering. Volume reduction (holes) or mass loading (pillars) accompanied with second-order periodicity and local resonances are shown to significantly modify the propagation of thermally activated GHz phonons. We use numerical modeling based on the finite element method to analyze the experimental results and determine polarization, symmetry, or three-dimensional localization of observed modes.

This presentation demonstrates that acoustic metamaterials can be used as an alternative to conventional acoustic materials to absorb acoustic modes in a hollow vessel, where the volume available for the acoustic treatment is limited and the geometry is complex. The metamaterials are placed in the limited available volume around the chamber. The metamaterials proposed here are based on periodic neck-cavity systems. Owing to the fact that the cavities are small and of complex shapes, numerical thermo-visco-acoustic simulations are used to simulate the acoustics of the metamaterials. Since these simulations are time consuming, they are paired with the analytical transfer matrix method. Here, only a periodic cell of the metamaterial is solved numerically. From this solution, the transfer matrix of the periodic cell is derived and periodized. Following this approach, the shape and geometric parameters of the thermo-visco-acoustic metamaterial are optimized in terms of the absorbed modes...

We propose a tunable four-channel acoustic demultiplexer, based on a fork-shaped phononic crystal (PnC) structure, having four output ports. A square lattice of cylindrical water inclusions in a mercury matrix, separate by ultra-thin elastically solid shells, characterizes the PnC platform. We used a plane wave expansion (PWE) method to calculate the PnC band diagram. There are four cylindrical resonant cavities of different inner radii, filled with the methyl nonafluorobutyl ether (MNE), placed in correspondence of the throat of each output port. Using the finite difference time domain (FDTD) numerical approach, we show that the proposed device can demultiplex a given broadband acoustic signal to four narrowband channels of ultra-high quality factors and interchannel cross talks less than −32 dB. Moreover, simulations show that the proposed device besides its demultiplexing functionality has the potential of sensing pressure and temperature and also the capability of determining the properties of the cavity fluid.

The possibilities of Sonic Crystals (SCs) as acoustic barriers have been intensively investigated during the last decade. A SC consists of a periodic array of scatterers embedded in a host fluid medium. These periodic structures provide a new wave control mechanism based on the structuring of the considered system, not on its acoustics properties. Perhaps, the most known property is the presence of the so-called band gaps (BG), defined as ranges of frequencies where the transmission of waves is forbidden inside the periodic structure. This property is used in finite structures to produce bands of frequencies of large transmission loss. However, both its central frequency and its width mainly depend on the geometry of the array being both angular dependent. Therefore, several strategies have been developed during last years to obtain acoustic screens based on SC with better performance. Basically, the path has been twofold: (i) seeking different arrangements of scatterers or (ii) bri...

Purpose Power gain from piezoelectric harvesters depends on several parameters and one of them is to design the substructure as to increase the mechanical strain occurred in the piezoelectric material. In this study, the effect of geometrical modification of the beam on the harvested power was investigated and new geometries were offered for increased power response from cantilever type energy harvesters. Method First, the effectiveness of auxetic structures on harvested power was investigated to see the effect of the negative Poisson's ratio on harvested power. These structures are very popular in recent years on energy harvesting applications; however, their performances were generally compared to plain structures which is not a fair comparison. Rather, in this study, their performances were compared to non-auxetic nonlinear structures as well as plain geometry. Then, three new shapes inspired by re-entrant auxetic structure were presented for increased power response, and harvested power from these structures were evaluated under different conditions. Results It was shown that the power gain from auxetic structures is very high compared to plain structures; however, this increase in power could also be achieved using a non-auxetic simple rectangular structure in some cases. On the other hand, new geometries offered in this study performed better than the auxetic and non-auxetic geometries in most cases.

In recent years, acoustic metamaterials (AMMs) have been developed to create more ergonomic designs that can be integrated into the built environment. For instance, embedding metamaterials in windows has facilitated effective ventilation and sound insulation. Presently, European standards provide specific guidelines for evaluating the insulation properties of façades, enabling the characterisation of both active and passive noise management solutions to ensure a healthy indoor environment. However, these standards primarily focus on closed partitions, limiting their applicability to noise management open systems. This study employs the ISO 10140 measurement method to assess a vertical metamaterial-based partition, namely an acoustic metawindow (AMW) unit, that, when open, allows noise insulation and ventilation contemporarily. The standardised level difference (Dn,e) is used to assess the performance of the open AMW unit's noise insulation. The results demonstrate the applicability of ISO 10140 for assessing an open AMW unit's performance, showcasing a Dn,e,w = 27 dB in the frequency range 1000-5000 Hz and an improvement over an open standard window ranging from 3 to 15 dB. This initial exploration could pave the way for more inclusive regulations considering ventilated sound-insulating devices as vertical partitions in the built environment and more comprehensive assessment methods for AMMs-based ventilated systems.

Control of guided waves has applications across length scales ranging from surface acoustic wave devices to seismic barriers. Resonant elastodynamic metasurfaces present attractive means of guided wave control by generating frequency stop-bandgaps using local resonators. This work addresses the systematic design of these resonators using a density-based topology optimization formulated as an eigenfrequency matching problem that tailors antiresonance eigenfrequencies. The effectiveness of our systematic design methodology is presented in a case study, where topologically optimized resonators are shown to prevent the propagation of the S0 wave mode in an aluminum plate.

In the last years, many papers have reported the results of researchers on acoustic metamaterials. The study of acoustic metamaterials represents a new research field in noise control. Metamaterials are artificial structures with periodical elements, made by the arrangement of scatterers in a square or triangular lattice configuration. The reason for such sound attenuation is due to the destructive interference of waves in the band of frequencies and the propagating wave has a decaying amplitude, which causes the sound attenuation to take place in the "bandgap" region. Metamaterials are structures designed and built to control the propagation of the waves. So the metamaterials are new materials obtained by the interaction of artificial objects and geometric structures of regular shape. The term metamaterials was coined nearly a decade, the word metamaterial is made of two words: meta and material. The word meta, from "metamorfosi" means a change in conditions, in this context it means later. The prefix "meta" originates from the Greek word for "after" or "beyond". The latest applications are in the room acoustics, noise barriers. This paper describes the state of art of the applications of the metamaterials in the acoustics field and the applications of metamaterials for the sound attenuation of an acoustic barrier are reported. The acoustic measurements were done in a scale model (1:10). The sound attenuation is shown in particular frequencies range, in the function of the distance of the barrier elements.

In the last years, many papers have reported the results of researchers on acoustic metamaterials. The study of acoustic metamaterials represents a new research field in noise control. Metamaterials are artificial structures with periodical elements, made by the arrangement of scatterers in a square or triangular lattice configuration. The reason for such sound attenuation is due to the destructive interference of waves in the band of frequencies and the propagating wave has a decaying amplitude, which causes the sound attenuation to take place in the "bandgap" region. Metamaterials are structures designed and built to control the propagation of the waves. So the metamaterials are new materials obtained by the interaction of artificial objects and geometric structures of regular shape. The term metamaterials was coined nearly a decade, the word metamaterial is made of two words: meta and material. The word meta, from "metamorfosi" means a change in conditions, in this context it means later. The prefix "meta" originates from the Greek word for "after" or "beyond". The latest applications are in the room acoustics, noise barriers. This paper describes the state of art of the applications of the metamaterials in the acoustics field and the applications of metamaterials for the sound attenuation of an acoustic barrier are reported. The acoustic measurements were done in a scale model (1:10). The sound attenuation is shown in particular frequencies range, in the function of the distance of the barrier elements.

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The elastodynamic response of finite 3D phononic structures is analyzed by means of comparing experimental findings obtained through a laser Doppler vibrometry-based methodology and theoretical computations performed with the Layer-Multiple-Scattering method. The recorded frequency-gap spectrum of the phononic slabs exhibited a good agreement of theory to experiment. Along these lines, a newly developed technique, based on laser doppler vibrometry, has been proposed and validated for the dispersion efficiency in 3D phononic metamaterials.

In this letter, we report the theoretical study on phonon transport in monocrystalline silicon thin-films having unfilled or metal-filled circular holes (i.e., phononic crystals, PnCs) and show that the thermal conductivity, j, at 1 K can be maximally reduced by using a multiscale structure, which allows us control over the porosity of the structure. The circular scatterers are placed in the square (SQ) and hexagonal (HX) pattern with a fixed 100 nm interhole spacing, and the pit diameter is varied between 10 and 90 nm. Each of the corresponding silicon PnCs shows reduced j compared to the unpatterned film. The SQ-PnC having tungsten-filled pits shows the greatest reduction in j when we consider only the effects of coherent scattering. Furthermore, we have computed j for the PnC where the unit cell, of 100 nm and 500 nm sizes, comprises the Sierpinski gasket (SG) with circular holes of different diameters (depending on the fractal order) in the same cell. It is observed that the j for the 2nd (100 nm cell) and 3rd order (500 nm cell) SG-PnC is comparable to the SQ-and HX-PnC with a pit diameter of 90 nm. When we add the effect of the diffuse boundary scattering in j, there is a lowering in j compared to that when only the coherent effects are considered. The additional j-reduction due to boundary scattering for the SQ-PnC and HX-PnC (both with 90 nm diam) as well as the 2nd and 3rd order SG-PnCs is 47%, 40%, 80%, and 60%, respectively.

In this paper, we report about the effect of the application of a state of prestress on the band structure of a periodic phononic crystal characterized by an inertial amplification mechanism. Through a numerical example, we show the possibility of inducing negative group velocity in an isolated branch of the dispersion diagram. A 2-step Updated Lagrangian scheme is adopted to calculate the dispersion diagram of the structure. The proposed method include (i) the static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load and (ii) the Bloch-Floquet decomposition applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration. The dispersion analysis is performed in terms of small amplitude motions superimposed on a deformed state, once the desired load has been applied.

In this paper, we report about the effect of the application of a state of prestress on the band structure of a periodic phononic crystal characterized by an inertial amplification mechanism. Through a numerical example, we show the possibility of inducing negative group velocity in an isolated branch of the dispersion diagram. A 2-step Updated Lagrangian scheme is adopted to calculate the dispersion diagram of the structure. The proposed method include (i) the static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load and (ii) the Bloch-Floquet decomposition applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration. The dispersion analysis is performed in terms of small amplitude motions superimposed on a deformed state, once the desired load has been applied.