Theory of acoustic band structure of periodic elastic composites

Surface wave isolation by variable depth infilled trenches

Excessive environmental vibrations generated by urban traffic pose adverse effects on nearby structures and residents. These vibrations are predominantly carried by surface waves, which are localized within the surface layer of soil. The isolation of surface waves through the embedding of periodic wave barriers in soils between the source and the receiver has gained significant attention in recent years. In this paper, a novel approach is proposed for isolating surface waves induced by urban traffic through the use of variable depth infilled trenches. This innovative design not only achieves efficient surface wave isolation but also minimizes the consumption of structural materials. Based on the measured dominant frequency range of rail transit and the available soil parameters, variable depth infilled trenches are designed with suitable dimensions. The eigenvalue equation is solved using the finite element method to derive the dispersion relations and bandgap of identical regularly spaced trenches. To study the efficacy of the proposed structure, a finite element model of the soil-infilled trench system is developed using COMSOL. The mechanism underlying the isolation of surface wave is elucidated, and the effect of variable angle α on the isolation efficiency within 40-50 Hz η40-50Hz of surface waves is studied. The results of this study reveal that for variable angle α of 15°, the surface wave isolation efficiency within 40-50 Hz η40-50Hz is 90.9 % and 92.5 % for uniformly increasing depth infilled trenches and uniformly decreasing depth infilled trenches, respectively. Although the surface wave isolation efficiencies predicted for the variable depth infilled trench arrangements are only 93.8 % and 95.5 % of those predicted for the regularly spaced identical infilled trenches, the variable depth arrangements result in a remarkable 34 % reduction in material usage. These findings highlight the potential of the proposed variable depth infilled trenches as a cost-effective and efficient solution for surface wave isolation.

Multi-functional programmable active acoustic meta-device: acoustic switch, lens, and barrier

Active acoustic metamaterials (AAMM) have garnered special attention because of their potential as multi-function devices. In this direction, the present article demonstrates a novel AAMM that can be programmed as a multi-functional Active Acoustic Meta-device (AAMD) that can switch functionalities between Acoustic Switch (AS), Acoustic Lens (AL), and Acoustic Barrier (AB). Functionality: AL corresponds to the wave vector space, and AS and AB correspond to the frequency space of the proposed AAMM. Additional functionality, such as acoustic logic gates in phase space, is also envisaged. The proposed design is found to change the dispersion diagram by acquiring different configurations while keeping the basic design parameters constant. These design parameters include constituent elements, lattice constants, and filling fractions. Further, for the said functionalities, the proposed AAMM does not rely on the deformation characteristics of the constituents. It rather capitalises on the possible relative displacements of the scatterers. As an AL, AAMM demonstrates zero angle refraction, i.e., collimation, and negative refraction of the transmitted beam at a given angle of incidence over a frequency range of 200 kHz (22.22% of the applied frequency sweep, a.f.s.). AB is shown to attenuate acoustic energy over a frequency range of 700 kHz (77.78% of a.f.s.) compared to its reference and foundation design, a statically designed Phononic Crystal (PnC). Furthermore, as AS, it operates over the entire range of applied frequency sweep (100 kHz to 1000 kHz), i.e., over the frequency range of 900 kHz (100% of a.f.s.).

Design of Locally Resonant Acoustic Metamaterials with Specified Band Gaps Using Multi-Material Topology Optimization

Locally Resonant Acoustic Metamaterials (LRAMs) have significant application potential because they can form subwavelength band gaps. However, most current research does not involve obtaining LRAMs with specified band gaps, even though such LRAMs are significant for practical applications. To address this, we propose a parameterized level-set-based topology optimization method that can use multiple materials to design LRAMs that meet specified frequency constraints. In this method, a simplified band-gap calculation approach based on the homogenization framework is introduced, establishing a restricted subsystem and an unrestricted subsystem to determine band gaps without relying on the Brillouin zone. These subsystems are specifically tailored to model the phenomena involved in band gaps in LRAMs, facilitating the opening of band gaps during optimization. In the multi-material representation model used in this method, each material, except for the matrix material, is depicted using a similar combinatorial formulation of level-set functions. This model reduces direct conversion between materials other than the matrix material, thereby enhancing the band-gap optimization of LRAMs. Two problems are investigated to test the method's ability to use multiple materials to solve band-gap optimization problems with specified frequency constraints. The first involves maximizing the band-gap width while ensuring it encompasses a specified frequency range, and the second focuses on obtaining light LRAMs with a specified band gap. LRAMs with specified band gaps obtained in three-material or four-material numerical examples demonstrate the effectiveness of the proposed method. The method shows great promise for designing metamaterials to attenuate specified frequency spectra as required, such as mechanical vibrations or environmental noise.

Valley-Selective Phonon-Magnon Scattering in Magnetoelastic Superlattices

Phonons and magnons are engineered by periodic potential landscapes in phononic and magnonic crystals, and their combined studies may enable valley phonon transport tunable by the magnetic field. Through nonreciprocal surface acoustic wave transmission, we demonstrate valley-selective phonon-magnon scattering in magnetoelastic superlattices. The lattice symmetry and the out-of-plane magnetization component control the sign of nonreciprocity. The phonons in the valleys play a crucial role in generating nonreciprocal transmission by inducing circularly polarized strains that couple with the magnons. The transmission spectra show a nonreciprocity peak near a transmission gap, matching the phononic band structure. Our results open the way for manipulating valley phonon transport through periodically varying magnon-phonon coupling.

Infrared Photodetection from 2D/3D van der Waals Heterostructures

An infrared photodetector is a critical component that detects, identifies, and tracks complex targets in a detection system. Infrared photodetectors based on 3D bulk materials are widely applied in national defense, military, communications, and astronomy fields. The complex application environment requires higher performance and multi-dimensional capability. The emergence of 2D materials has brought new possibilities to develop next-generation infrared detectors. However, the inherent thickness limitations and the immature preparation of 2D materials still lead to low quantum efficiency and slow response speeds. This review summarizes 2D/3D hybrid van der Waals heterojunctions for infrared photodetection. First, the physical properties of 2D and 3D materials related to detection capability, including thickness, band gap, absorption band, quantum efficiency, and carrier mobility, are summarized. Then, the primary research progress of 2D/3D infrared detectors is reviewed from performance improvement (broadband, high-responsivity, fast response) and new functional devices (two-color detectors, polarization detectors). Importantly, combining low-doped 3D and flexible 2D materials can effectively improve the responsivity and detection speed due to a significant depletion region width. Furthermore, combining the anisotropic 2D lattice structure and high absorbance of 3D materials provides a new strategy in high-performance polarization detectors. This paper offers prospects for developing 2D/3D high-performance infrared detection technology.

Bioinspired periodic panels optimized for acoustic insulation

The design of structures that can yield efficient sound insulation performance is a recurring topic in the acoustic engineering field. Special attention is given to panels, which can be designed using several approaches to achieve considerable sound attenuation. Previously, we have presented the concept of thickness-varying periodic plates with optimized profiles to inhibit flexural wave energy propagation. In this work, motivated by biological structures that present multiple locally resonant elements able to cause acoustic cloaking, we extend our shape optimization approach to design panels that achieve improved acoustic insulation performance using either thickness-varying profiles or locally resonant attachments. The optimization is performed using numerical models that combine the Kirchhoff plate theory and the plane wave expansion method. Our results indicate that panels based on locally resonant mechanisms have the advantage of being robust against variation in the incidence angle of acoustic excitation and, therefore, are preferred for single-leaf applications. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Quality Factor Enhancement of Piezoelectric MEMS Resonator Using a Small Cross-Section Connection Phononic Crystal

Anchor loss is usually the most significant energy loss factor in Micro-Electro-Mechanical Systems (MEMS) resonators, which seriously hinders the application of MEMS resonators in wireless communication. This paper proposes a cross-section connection phononic crystal (SCC-PnC), which can be used for MEMS resonators of various overtone modes. First, using the finite element method to study the frequency characteristics and delay line of the SCC-PnC band, the SCC-PnC has an ultra-wide bandgap of 56.6-269.6 MHz. Next, the effects of the height h and the position h₁ of the structural parameters of the small cross-connected plate on the band gap are studied, and it is found that h is more sensitive to the width of the band gap. Further, the SCC-PnC was implanted into the piezoelectric MEMS resonator, and the admittance and insertion loss curves were obtained. The results show that when the arrangement of 4 × 7 SCC-PnC plates is adopted, the anchor quality factors of the third-order overtone, fifth-order overtone, and seventh-order overtone MEMS resonators are increased by 1656 times, 2027 times, and 16 times, respectively.

A highly efficient Fabry-Perot based phononic gas sensor

In this article, a gas sensor with a single detection unit is presented which is applicable for the detection of diverse gases including CH₄, NH₃, N₂, O₂, Ar, CO₂, C₃H₈, and their different concentrations in the air background. The proposed Fabry-Perot-based phononic gas sensor is comprised of a detection layer surrounded by thin Steel sheets on both sides. It has been demonstrated that the operating frequency range, the total size of the sensor, the number of detection peaks, and the Q-factor could be adjusted by the width of the detection layer and material use. The functionality of the presented gas sensor has been investigated by the transfer matrix method and the average Q-factor of 1,140,072 and sensitivity of 0.69 MHz.kg^-1.m³ are obtained for the structure with a thickness ratio of 9:1 for the Steel and gas layers, respectively regarding pure gases. The maximum average Q-factor and sensitivity of over 10⁶ and 1.03 MHz.kg^-1.m³ are obtained for C₃H₈ gas concerning the concentration increment. The proposed sensor is simple, scalable to operate at any desired frequency range, and provides a multi-peak detection mechanism.

Ground vibration from freight railway: environmental impact and potential mitigation measure at propagation path

The freight train-induced vibrations and noise generate increasing environmental problems owing to its heavier axle loads and longer pass-by duration. To develop useful mitigation measures, the vibration characteristic induced by this type of rail transportation needs to be better learned. In the present work, firstly, the in situ measurements were carried out on two railway lines which were used for mixed freight and passenger trains. Both the track vibrations and ground vibrations resulted from different train types were measured and compared. Then, based on the dominant frequencies of ground vibrations from experimental results, the mitigation measure of periodic piles was proposed as a mitigation measure by impeding propagation. The periodic theory of solid-state physics was introduced and three-dimensional (3D) finite element (FE) simulation was employed to analyse the vibration reduction performance of periodic piles, while the attenuation zone (AZ) of the piles was also calculated. The measurement results indicate that the freight train can generate a larger level of vibrations on both the track structure and ground at the near field, especially below 10 Hz. Even though the speed of freight trains is as low as 40-55 km/h, the vibration exposure level (VEL) is higher than normal passenger trains (80-90 km/h) and EMU trains (120 km/h). The simulation results show that the proposed solution of installing periodic piles at the propagation path raises the positive influence on vibration reduction.

Two-Dimensional Phononic Crystal Based Sensor for Characterization of Mixtures and Heterogeneous Liquids

We show new approaches to developing acoustic liquid sensors based on phononic crystals. The proposed phononic crystal integrates fluidic elements. A solid block with periodic cylindrical holes contains a defect—a liquid-filled cylindrical cavity. We pay attention to acoustic excitation and the readout of the axisymmetric cylindrical resonator eigenmode of the liquid-filled defect in the middle of the phononic crystal structure. This mode solves the challenge of mechanical energy losses due to liquid viscosity. We also analyze the coupling effects between oscillations of liquid and solid systems and consider coupling issues between piezoelectric transducers and the liquid-filled cavity resonator. The numerical simulation of the propagation of acoustic waves through the phononic crystal sensor was carried out in COMSOL Multiphysics Software. The phononic crystal was made of stainless steel with mechanically drilled holes and was fabricated for experimental verification. We show that a tuning of the solid–liquid vibrational modes coupling is the key to an enhanced level of sensitivity to liquid properties. Besides (homogeneous) water–propanol mixtures, experimental studies were carried out on (disperse) water–fuel emulsions.

Probing interfacial charge transfer in the heterojunctions for photocatalysis

Photocatalytic reactions can sustainably employ inexhaustible solar energy for environmental remediation and conversion of photon energy into chemical energy, and thereby show great potential in alleviating the environmental stress and...

Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.

Numerical Analysis of Viscous Dissipation in Microchannel Sensor Based on Phononic Crystal

Phononic crystals with phononic band gaps varying in different parameters represent a promising structure for sensing. Equipping microchannel sensors with phononic crystals has also become a great area of interest in research. For building a microchannels system compatible with conventional micro-electro-mechanical system (MEMS) technology, SU-8 is an optimal choice, because it has been used in both fields for a long time. However, its mechanical properties are greatly affected by temperature, as this affects the phononic bands of the phononic crystal. With this in mind, the viscous dissipation in microchannels of flowing liquid is required for application. To solve the problem of viscous dissipation, this article proposes a simulation model that considers the heat transfer between fluid and microchannel and analyzes the frequency domain properties of phononic crystals. The results show that when the channel length reaches 1 mm, the frequency shift caused by viscous dissipation will significantly affect detecting accuracy. Furthermore, the temperature gradient also introduces some weak passbands into the band gap. This article proves that viscous dissipation does influence the band gap of phononic crystal chemical sensors and highlights the necessity of temperature compensation in calibration. This work may promote the application of microchannel chemical sensors in the future.

Band structure calculation of 2D fluid/solid and solid/fluid phononic crystal using a modified smoothed finite element method with fluid-solid interaction

Recently, a novel modified smoothed finite element method (M-SFEM) is proposed to calculate the band structures of two-dimensional (2D) in-plane elastic waves in phononic crystals (PCs) by the authors. In present work, the proposed algorithm is extended to analyze the band structures of 2D phononic crystals (PCs) with fluid/structure interaction (FSI). In order to study the phononic crystals (PCs) with FSI, this method extends the gradient smoothing technique to soften the stiffness matrix of fluid domain and solid domain. Meanwhile, according to the generalized integration rules, this method simply shifts these integration points of elements to an unconventional location in the mass matrix. In addition, different Bloch boundary conditions, viz. fluid/solid and solid/fluid, including the square and triangular lattice using M-SFEM are also investigated in the computation of PCs with FSI. Several PCs models with FSI are studied to verify the high accuracy of the M-SFEM in the analysis of band structures. In order to emerge the superiority of the proposed method, the results of finite element method (integration points on conventional location), modified finite element method (integration points on unconventional location), smoothed finite element method are all presented. Numerical analysis shows that the M-SFEM can be used to predict the band structures in PCs with FSI, and can obtained more precise results as compared to FEM and SFEM.

Bandgap characteristics of phononic crystals in steady and unsteady flows

Over the past 30 years, most phononic crystal research has been done for a stationary medium. As reported in a recent experimental study, phononic crystals cannot preserve their bandgaps in the presence of flow. In this study, the bandgap characteristics of a two-dimensional phononic crystal in steady and unsteady flows are investigated theoretically. To identify the effect of the flow on sound insulation in the bandgap frequency ranges, the acoustic reflectance spectra of phononic crystals for different types of background flows, including a uniform flow, a compressible potential flow, and a turbulent flow were calculated. For the steady flows, which include uniform and compressible potential flows, the reflectance spectra are shifted to a lower frequency by the factor 1-M² due to convection when the flow is in the same direction as the incident wave. Moreover, the reflectance spectra of a phononic crystal in a turbulent flow were evaluated for various combinations of inflow speeds and geometric parameters, such as the filling ratio and the number of layers. Due to the aerodynamic noise and fluid convection, a phononic crystal cannot work as an acoustic barrier, rather it becomes an aeroacoustic source in a turbulent flow.

Control of Metro Train-Induced Vibrations in a Laboratory Using Periodic Piles

Laboratories with sensitive instruments need a low-vibration environment. It is a challenge to control the train-induced vibration impact on these instruments when a newly planned metro line is adjacent to a laboratory building. An alternative method of mitigating train-induced ground vibrations involves installing measures along the transmission path. Recent research has highlighted the potential of periodic pile barriers with specifically designed band gaps for controlling environmental vibrations. This study performed in-situ measurements of ambient vibrations inside and outside a laboratory containing various types of sensitive instruments and located adjacent to a newly designed metro line. The vibration transfer function of the laboratory was then obtained. To help design and optimize the band gaps of periodic piles, a novel band gap performance evaluation function was proposed. Finally, numerical analysis was conducted to validate the mitigation effect of the designed periodic piles. The results showed that the band gap performance evaluation function can be used to optimize the mitigation effect of periodic piles. The proposed periodic piles clearly attenuated vibrations between 52.4 and 74.3 Hz, especially those at 63 Hz. A comparison of general vibration criteria (VC) curves revealed that vibration attenuation of one level can be obtained by the designed periodic piles.

Modelling Propagating Bloch Waves in Magnetoelectroelastic Phononic Structures with Kagomé Lattice Using the Improved Plane Wave Expansion

We studied the dispersion diagram of a 2D magnetoelectroelastic phononic crystal (MPnC) with Kagomé lattice. The MPnC is composed of BaTiO3–CoFe2O4 circular scatterers embedded in a polymeric matrix. The improved plane wave expansion (IPWE) approach was used to calculate the dispersion diagram (only propagating modes) of the MPnC considering the classical elasticity theory, solid with transverse isotropy and wave propagation in the xy plane. Complete Bragg-type forbidden bands were observed for XY and Z modes. The piezoelectric and the piezomagnetic effects significantly influenced the forbidden band widths and localizations. This investigation can be valuable for elastic wave manipulation using smart phononic crystals with piezoelectric and piezomagnetic effects.

Tunable photo-responsive elastic metamaterials

The metamaterial paradigm has allowed an unprecedented space-time control of various physical fields, including elastic and acoustic waves. Despite the wide variety of metamaterial configurations proposed so far, most of the existing solutions display a frequency response that cannot be tuned, once the structures are fabricated. Few exceptions include systems controlled by electric or magnetic fields, temperature, radio waves and mechanical stimuli, which may often be unpractical for real-world implementations. To overcome this limitation, we introduce here a polymeric 3D-printed elastic metamaterial whose transmission spectrum can be deterministically tuned by a light field. We demonstrate the reversible doubling of the width of an existing frequency band gap upon selective laser illumination. This feature is exploited to provide an elastic-switch functionality with a one-minute lag time, over one hundred cycles. In perspective, light-responsive components can bring substantial improvements to active devices for elastic wave control, such as beam-splitters, switches and filters.

Band Gaps and Transmission Characteristics Analysis on a Two-Dimensional Multiple-Scatter Phononic Crystal Structure

In this paper, a novel wrap-around multi-scattering phononic crystal (PC) structure is proposed. Band gaps (BGs) and transmission characteristics of the present structure are calculated using finite element method (FEM). Through the calculations of single-scattering prototype, three complete BGs which are exhibited at low frequency and the fourth wide BG at high frequency are discovered. The transmission features and resonant spectra represented by frequency response function (FRF) shows that apparent resonance directly cause the four specific BGs. By keeping the total area of scatterers unchanged, 2 × 2, 3 × 3 and 4 × 4 scatterers are designed to obtain the change rule of BGs. Furthermore, the size ratio of 2 × 2 scatterers, the number of connection beams are investigated to obtain the regular pattern of acoustic energy transmission and attenuation. The present investigation of multiple-scatter PC structure will provide a solid support on the future design of acoustical functional materials.

A Review of Acoustic Metamaterials and Phononic Crystals

As a new kind of artificial material developed in recent decades, metamaterials exhibit novel performance and the promising application potentials in the field of practical engineering compared with the natural materials. Acoustic metamaterials and phononic crystals have some extraordinary physical properties, effective negative parameters, band gaps, negative refraction, etc., extending the acoustic properties of existing materials. The special physical properties have attracted the attention of researchers, and great progress has been made in engineering applications. This article summarizes the research on acoustic metamaterials and phononic crystals in recent decades, briefly introduces some representative studies, including equivalent acoustic parameters and extraordinary characteristics of metamaterials, explains acoustic metamaterial design methods, and summarizes the technical bottlenecks and application prospects.

Resonant waves and localization phenomena in lattices

Transient wave processes in mass-spring lattices excited by point oscillating sources are studied. Dispersion properties of uniform periodic three-dimensional (3D) square-cell and two-dimensional (2D) hexagonal-cell lattices including revealed star-shaped localization phenomena are analysed. The resonant-like waves and localization-like patterns in non-uniform lattices possessing predetermined and randomly distributed defects are numerically examined in order to identify the sensitivity of star-shape forms to different types of defects. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.

A finite element method towards acoustic phononic crystals by weak formulation

A weak formulation method is presented to analyze the propagation of acoustic waves in periodic crystal-like systems called phononic crystals. First, a compact circle and double split ring resonators with high impedance contrast to air background are employed to compute band structures with not only real parts of wavevectors but also imaginary parts of them. Calculating the imaginary part, which directly predicts a propagation length in band gaps, is not readily available in previous studies. It analytically enables us to more understand the behavior of evanescent mode in band gaps. Moreover, we present that the weak formulation method is advantageous in calculating equi-frequency contour.

Topological Optimization of Phononic Crystal Thin Plate by a Genetic Algorithm

Genetic algorithm (GA) is used for the topological optimization of phononic crystal thin plate composed of aluminum and epoxy resin. Plane wave expansion (PWE) method is used for calculations of band gaps. Fourier displacement property is used to calculate the structure function in PWE. The crossover rate and the mutation rate are calculated according to the adaptive GA method. Results indicate that filling rates, symmetry, polymerization degree and material parameters are key factors for design of topological configurations. The relations between the key factors and different topologies are studied in detail.

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

The differential quadrature method has been developed to calculate the elastic band gaps from the Bragg reflection mechanism in periodic structures efficiently and accurately. However, there have been no reports that this method has been successfully used to calculate the band gaps of locally resonant structures. This is because, in the process of using this method to calculate the band gaps of locally resonant structures, the non-linear term of frequency exists in the matrix equation, which makes it impossible to solve the dispersion relationship by using the conventional matrix-partitioning method. Hence, an accurate and efficient numerical method is proposed to calculate the flexural band gap of a locally resonant beam, with the aim of improving the calculation accuracy and computational efficiency. The proposed method is based on the differential quadrature method, an unconventional matrix-partitioning method, and a variable substitution method. A convergence study and validation indicate that the method has a fast convergence rate and good accuracy. In addition, compared with the plane wave expansion method and the finite element method, the present method demonstrates high accuracy and computational efficiency. Moreover, the parametric analysis shows that the width of the 1st band gap can be widened by increasing the mass ratio or the stiffness ratio or decreasing the lattice constant. One can decrease the lower edge of the 1st band gap by increasing the mass ratio or decreasing the stiffness ratio. The band gap frequency range calculated by the Timoshenko beam theory is lower than that calculated by the Euler-Bernoulli beam theory. The research results in this paper may provide a reference for the vibration reduction of beams in mechanical or civil engineering fields.

Slow light in ultracompact photonic crystal decoder

In this study, merging two photonic crystal-based structures, a new design for an all-optical 2-to-4 decoder has been proposed. The switching operation is based on the Kerr effect and refractive index modification. The structure consists of one nonlinear ring resonator and three nonlinear cavities that have been modified for entering the slow-light regime in order to enhance coupling through waveguides. The maximum group index of 94 has been obtained for the proposed slow-light waveguides. With this approach, the maximum and minimum normalized output powers for logic 0 and 1 are 4% and 82%, respectively. The data transfer rate of the decoder is 220 GHz, and the size of the structure is 24×9.5  μm². The maximum insertion loss and cross talk are -7.45  dB and -16.38  dB, respectively. Considering the above characteristics, the proposed decoder can be qualified as a part of optical integrated circuits.

Elastic Wave Propagation of Two-Dimensional Metamaterials Composed of Auxetic Star-Shaped Honeycomb Structures

In this paper, the wave propagation in phononic crystal composed of auxetic star-shaped honeycomb matrix with negative Poisson’s ratio is presented. Two types of inclusions with circular and rectangular cross sections are considered and the band structures of the phononic crystals are also obtained by the finite element method. The band structure of the phononic crystal is affected significantly by the auxeticity of the star-shaped honeycomb. Some other interesting findings are also presented, such as the negative refraction and the self-collimation. The present study demonstrates the potential applications of the star-shaped honeycomb in phononic crystals, such as vibration isolation and the elastic waveguide.

A Review of Tunable Acoustic Metamaterials

Acoustic metamaterial science is an emerging field at the frontier of modern acoustics. It provides a prominent platform for acoustic wave control in subwavelength-sized metadevices or metasystems. However, most of the metamaterials can only work in a narrow frequency band once fabricated, which limits the practical application of acoustic metamaterials. This paper highlights some recent progress in tunable acoustic metamaterials based on various modulation techniques. Acoustic metamaterials have been designed to control the attenuation of acoustic waves, invisibility cloaking, and acoustic wavefront engineering, such as focusing via manipulating the acoustic impedance of metamaterials. The reviewed techniques are promising in extending the novel acoustics response into wider frequency bands, in that tunable acoustic metamaterials may be exploited for unusual applications compared to conventional acoustic devices.

Elastic waves in periodically heterogeneous two-dimensional media: locally periodic and anti-periodic modes

Propagation of anti-plane waves through a discrete square lattice and through a continuous fibrous medium is studied. In the long-wave limit, for periodically heterogeneous structures the solution can be periodic or anti-periodic across the unit cell. It is shown that combining periodicity and anti-periodicity conditions in different directions of the translational symmetry allows one to detect different types of modes that do not arise in the purely periodic case. Such modes may be interpreted as counterparts of non-classical waves appearing in phenomenological theories. Dispersion diagrams of the discrete square lattice are evaluated in a closed analytical from. Dispersion properties of the fibrous medium are determined using Floquet–Bloch theory and Fourier series approximations. Influence of a viscous damping is taken into account.

Broadband All-angle Negative Refraction by Optimized Phononic Crystals

All-angle negative refraction (AANR) of phononic crystals and its frequency range are dependent on mechanical properties of constituent materials and their spatial distribution. So far, it is impossible to achieve the maximum operation frequency range of AANR theoretically. In this paper, we will present a numerical approach for designing a two-dimensional phononic crystal with broadband AANR without negative index. Through analyzing the mechanism of AANR, a topology optimization problem aiming at broadband AANR is established and solved by bi-directional evolutionary structural optimization method. The optimal steel/air phononic crystal exhibits a record AANR range over 20% and its refractive properties and focusing effects are further investigated. The results demonstrate the multifunctionality of a flat phononic slab including superlensing effect near upper AANR frequencies and self-collimation at lower AANR frequencies.

3-D phononic crystals with ultra-wide band gaps

In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure evaluations is accomplished by a combination of a fast mixed variational eigenvalue solver and distributed Graphic Processing Unit (GPU) parallel computations. The TO algorithm utilizes the material distribution-based approach and a gradient-based optimizer. The design sensitivity for the mixed variational eigenvalue problem is derived using the adjoint method and is implemented through highly efficient vectorization techniques. We present optimized results for two-material simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC) crystal structures and show that in each of these cases different initial designs converge to single inclusion network topologies within their corresponding primitive cells. The optimized results show that large phononic stop bands for bulk wave propagation can be achieved at lower than close packed spherical configurations leading to lighter unit cells. For tungsten carbide - epoxy crystals we identify all angle all mode normalized stop bands exceeding 100%, which is larger than what is possible with only spherical inclusions.

Predictive Synthesis of Freeform Carbon Nanotube Microarchitectures by Strain-Engineered Chemical Vapor Deposition

High-throughput fabrication of microstructured surfaces with multi-directional, re-entrant, or otherwise curved features is becoming increasingly important for applications such as phase change heat transfer, adhesive gripping, and control of electromagnetic waves. Toward this goal, curved microstructures of aligned carbon nanotubes (CNTs) can be fabricated by engineered variation of the CNT growth rate within each microstructure, for example by patterning of the CNT growth catalyst partially upon a layer which retards the CNT growth rate. This study develops a finite-element simulation framework for predictive synthesis of complex CNT microarchitectures by this strain-engineered growth process. The simulation is informed by parametric measurements of the CNT growth kinetics, and the anisotropic mechanical properties of the CNTs, and predicts the shape of CNT microstructures with impressive fidelity. Moreover, the simulation calculates the internal stress distribution that results from extreme deformation of the CNT structures during growth, and shows that delamination of the interface between the differentially growing segments occurs at a critical shear stress. Guided by these insights, experiments are performed to study the time- and geometry-depended stress development, and it is demonstrated that corrugating the interface between the segments of each microstructure mitigates the interface failure. This study presents a methodology for 3D microstructure design based on "pixels" that prescribe directionality to the resulting microstructure, and show that this framework enables the predictive synthesis of more complex architectures including twisted and truss-like forms.

Architected Materials with Ultra-Low Porosity for Vibration Control

Periodic structures with extremely low porosities capable of forming large band gaps-frequency ranges with strong wave attenuation-are designed by patterning an elastic sheet with an array of alternating crack-like pores separated by small ligaments. The results indicate that the presence and size of the band gaps are controlled by the smallest geometric -feature in the system (which can be easily controlled by tuning the aspect ratio of the pores), providing an important guideline for the design of systems with the -desired response.

Realization of Complex 3D Phononic Crystals with Wide Complete Acoustic Band Gaps

Phononic crystals offer unique band structures for acoustic wave propagation. Fabricating intricate threedimensional phononic crystals allows a new class of devices with complex phononic band structures beyond capabilities of two-dimensional designs. We have successfully fabricated novel 3D phononic crystals with 1 mm lattice constant and minimum feature sizes as low as 100 micron using high-resolution stereolithography printing. Here we report the first theoretical calculations and experimental results demonstrating wide complete 3D phononic band gaps not attainable by corresponding 2D structures with the same lattice geometry. Longitudinal and shear wave propagation is suppressed by more than -60 dB in frequency bands as wide as 400 kHz to 1 MHz.

Topological Design of Cellular Phononic Band Gap Crystals

This paper systematically investigated the topological design of cellular phononic crystals with a maximized gap size between two adjacent bands. Considering that the obtained structures may sustain a certain amount of static loadings, it is desirable to ensure the optimized designs to have a relatively high stiffness. To tackle this issue, we conducted a multiple objective optimization to maximize band gap size and bulk or shear modulus simultaneously with a prescribed volume fraction of solid material so that the resulting structures can be lightweight, as well. In particular, we first conducted the finite element analysis of the phononic band gap crystals and then adapted a very efficient optimization procedure to resolve this problem based on bi-directional evolutionary structure optimization (BESO) algorithm in conjunction with the homogenization method. A number of optimization results for maximizing band gaps with bulk and shear modulus constraints are presented for out-of-plane and in-plane modes. Numerical results showed that the optimized structures are similar to those obtained for composite case, except that additional slim connections are added in the cellular case to support the propagation of shear wave modes and meanwhile to satisfy the prescribed bulk or shear modulus constraints.

Bio-inspired heterogeneous composites for broadband vibration mitigation

Structural biological materials have developed heterogeneous and hierarchical architectures that are responsible for the outstanding performance to provide protection against environmental threats including static and dynamic loading. Inspired by this observation, this research aims to develop new material and structural concepts for broadband vibration mitigation. The proposed composite materials possess a two-layered heterogeneous architecture where both layers consist of high-volume platelet-shape reinforcements and low-volume matrix, similar to the well-known "brick and mortar" microstructure of biological composites. Using finite element method, we numerically demonstrated that broadband wave attenuation zones can be achieved by tailoring the geometric features of the heterogeneous architecture. We reveal that the resulting broadband attenuation zones are gained by directly superimposing the attenuation zones in each constituent layer. This mechanism is further confirmed by the investigation into the phonon dispersion relation of each layer. Importantly, the broadband wave attenuation capability will be maintained when the mineral platelet orientation is locally manipulated, yet a contrast between the mineral platelet concentrations of the two constituent layers is essential. The findings of this work will provide new opportunities to design heterogeneous composites for broadband vibration mitigation and impact resistance under mechanically challenging environmental conditions.

Phononic band structure in carbon microtube composites

The phononic band structure of hollow carbon microtubes immersed in a soft medium presents GHz narrow band pass frequencies which may be used as an acoustic filter.

Localization of acoustic modes in periodic porous silicon structures

The propagation of longitudinal acoustic waves in multilayer structures based on porous silicon and the experimental measurement of acoustic transmission for the structures in the gigahertz range are reported and studied theoretically. The considered structures exhibit band gaps in the transmission spectrum and these are localized modes inside the band gap, coming from defect layers introduced in periodic systems. The frequency at which the acoustic resonances appear can be tuned by changing the porosity and/or thickness of the defect layer.

Transforming wave propagation in layered media via instability-induced interfacial wrinkling

The ability to control wave propagation in highly deformable layered media with elastic instability-induced wrinkling of interfacial layers is presented. The onset of a wrinkling instability in initially straight interfacial layers occurs when a critical compressive strain is achieved. Further compression beyond the critical strain leads to an increase in the wrinkle amplitude of the interfacial layer. This, in turn, gives rise to the formation of a system of periodic scatterers, which reflect and interfere with wave propagation. We demonstrate that the topology of wrinkling interfacial layers can be controlled by deformation and used to produce band gaps in wave propagation and, hence, to selectively filter frequencies. Remarkably, the mechanism of frequency filtering is effective even for composites with similar or identical densities, such as polymer-polymer composites. Since the microstructure change is reversible, the mechanism can be used for tuning and controlling wave propagation by deformation.

Numerical simulation of effective phase velocity and attenuation of shear elastic wave propagation in unidirectional composite materials

In this paper, a simple simulation approach is presented for calculating the effective phase velocity and attenuation coefficient of elastic shear waves propagating in composite materials with randomly distributed unidirectional inclusions. As an application of the developed numerical approach, the phase velocities and attenuation coefficients of the coherent waves in four different types of composite material are simulated for various incident frequencies up to π. Numerical results are compared with theoretical predictions obtained from three representative theoretical models. While all theoretical results agree very well with numerical values at low incident frequencies, the discrepancies increase with the increased incident frequency and volume fraction of inclusions. It has been found that within the frequency and volume fraction ranges considered in this work, the generalized self-consistent model by Kanaun and Levin [18] seems to provide the most accurate estimations.

Homogenization theory for periodic distributions of elastic cylinders embedded in a viscous fluid

A multiple-scattering theory is applied to study the homogenization of clusters of elastic cylinders distributed in a isotropic lattice and embedded in a viscous fluid. Asymptotic relations are derived and employed to obtain analytical formulas for the effective parameters of homogenized clusters in which the underlying lattice has a low filling fraction. It is concluded that such clusters behave, in the low frequency limit, as an effective elastic medium. Particularly, it is found that the effective dynamical mass density follows the static estimate; i.e., the homogenization procedure does not recover the non-linear behavior obtained for the inviscid case. Moreover, the longitudinal and transversal sound speeds do not show any dependence on fluid viscosity. Numerical simulations performed for clusters made of brass cylinders embedded in glycerin support the reliability of the effective parameters resulting from the homogenization procedure reported here.

Lamb waves in phononic crystal slabs: truncated plane parallels to the axis of periodicity

A theoretical study is presented on the propagation properties of Lamb wave modes in phononic crystal slabs consisting of a row or more of parallel square cylinders placed periodically in the host material. The surfaces of the slabs are parallel to the axis of periodicity. The dispersion curves of Lamb wave modes are calculated based on the supercell method. The finite element method is employed to calculate the band structures and the transmission power spectra, which are in good agreement with the results by the supercell method. We also have found that the dispersion curves of Lamb waves are strongly dependent on the crystal termination, which is the position of the cut plane through the square cylinders. There exist complete or incomplete (truncated) layers of square cylinders with the change of the crystal termination. The influence of the crystal termination on the band gaps of Lamb wave modes is analyzed by numerical simulations. The variation of the crystal termination leads to obvious changes in the dispersion curves of the Lamb waves and the widths of the band gaps.

Numerical simulation of nonlinear field distributions in two-dimensional optical superlattices

A finite difference method in real space is presented for calculating nonlinear optical processes in two-dimensional optical superlattices. The focused second-harmonic generation under the local quasi-phase-matched condition is calculated as an example. The field distribution of both the fundamental and the harmonic wave can be simulated well using this method, and the result agrees well with previous theoretical predictions and experimental studies. It is shown that this method is a simple and rapid technique to analysis nonlinear processes in optical superlattices.

Matryoshka locally resonant sonic crystal

The results of numerical modeling of sonic crystals with resonant array elements are reported. The investigated resonant elements include plain slotted cylinders as well as their various combinations, in particular, Russian doll or Matryoshka configurations. The acoustic band structure and transmission characteristics of such systems have been computed with the use of finite element methods. The general concept of a locally resonant sonic crystal is proposed that utilizes acoustic resonances to form additional band gaps that are decoupled from Bragg gaps. An existence of a separate attenuation mechanism associated with the resonant elements that increases performance in the lower frequency regime has been identified. The results show a formation of broad band gaps positioned significantly below the first Bragg frequency. For low frequency broadband attenuation, a most optimal configuration is the Matryoshka sonic crystal, where each scattering unit is composed of multiple concentric slotted cylinders. This system forms numerous gaps in the lower frequency regime, below Bragg bands, while maintaining a reduced crystal size viable for noise barrier technology. The finding opens alternative perspectives for the construction of sound barriers in the low frequency range usually inaccessible by traditional means including conventional sonic crystals.

Lamb waves in two-dimensional phononic crystal plate with anisotropic inclusions

An analysis is given to the band structure of the two-dimensional phononic crystal plate constituted of a square array of elastic anisotropic, circular Pb cylinders embedded in elastic isotropic epoxy. The numerical results show that the band gap can be tuned by rotating the anisotropic material orientation. It is found that the influence of anisotropy on band gap of Lamb wave is clearly different from that on the band gap of bulk waves. The thickness of the system under study is a sensitive parameter to affect the influence of anisotropic materials on the normalized gap width.

Reduction in the thermal conductivity of single crystalline silicon by phononic crystal patterning

Phononic crystals (PnCs) are the acoustic wave equivalent of photonic crystals, where a periodic array of scattering inclusions located in a homogeneous host material causes certain frequencies to be completely reflected by the structure. In conjunction with creating a phononic band gap, anomalous dispersion accompanied by a large reduction in phonon group velocities can lead to a massive reduction in silicon thermal conductivity. We measured the cross plane thermal conductivity of a series of single crystalline silicon PnCs using time domain thermoreflectance. The measured values are over an order of magnitude lower than those obtained for bulk Si (from 148 W m(-1) K(-1) to as low as 6.8 W m(-1) K(-1)). The measured thermal conductivity is much smaller than that predicted by only accounting for boundary scattering at the interfaces of the PnC lattice, indicating that coherent phononic effects are causing an additional reduction to the cross plane thermal conductivity.

Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs

We demonstrate planar structures that can provide simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical (or phoxonic) crystal slabs. Different phoxonic crystal (PxC) structures, composed of square, hexagonal (honeycomb), or triangular arrays of void cylindrical holes embedded in silicon (Si) slabs with a finite thickness, are investigated. Photonic band gap (PtBG) maps and the complete phononic band gap (PnBG) maps of PxC slabs with different radii of the holes and thicknesses of the slabs are calculated using a three-dimensional plane wave expansion code. Simultaneous phononic and photonic band gaps with band gap to midgap ratios of more than 10% are shown to be readily obtainable with practical geometries in both square and hexagonal lattices, but not for the triangular lattice.

Imaging off-plane shear waves with a two-dimensional phononic crystal lens

A two-dimensional flat phononic crystal (PC) lens for focusing off-plane shear waves is proposed. The lens consists of a triangular lattice hole-array, embedded in a solid matrix. The self-collimation effect is employed to guide the shear waves propagating through the lens along specific directions. The Dirichlet-to-Neumann maps (DtN) method is employed to calculate the band structure of the PC, which can avoid the problems of bad convergence and fake bands automatically in the void-solid PC structure. When the lens is illuminated by the off-plane shear waves emanating from a point source, a subwavelength image appears in the far-field zone. The imaging characteristics are investigated by calculating the displacement fields explicitly using the multiple scattering method, and the results are in good agreement with the ray-trace predictions. Our results may provide insights for designing new phononic devices.