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.

Bandgap characteristics of four component periodic pile barriers in passive vibration isolation

Based on the local resonance theory, the vibration isolation performance of four-component periodic pile barriers consisting of a matrix, an outer pipe, an inner pipe, and a pile core was investigated using the finite element method (FEM). This configuration is contrasted with traditional three-component periodic pile barriers, which are composed of a matrix, a pipe, and a pile core. The four-component systems demonstrate significantly broader bandgaps compared to three-component systems. To validate the efficiency of the FEM, model test on pile barriers were conducted, facilitating a comparison between the FEM and experimental observations of bandgap characteristics. Additionally, the effects of the outer pipe's density, elastic modulus, and thickness on the complete bandgap characteristics were comprehensively studied within the four-component structure. It is found that the broadest vibration isolation band gaps occur under hexagonal arrangement pattern. In square and hexagonal lattice configurations, the density, elastic modulus, and thickness of the outer pipe pile's pile have predominantly influenced the upper bound frequency (UBF). There has been a positive correlation between the elastic modulus and the UBF, while the density and thickness have shown inverse relationships. Moreover, there exists a elastic modulus threshold, marking a transition in the displacement mode of the UBF, from the outer irreducible Brillouin zone (M or X) to the inner zone (Γ). Once the threshold is exceeded, both the vibration displacement mode and the width of bandgap remain substantially unchanged. The results obtained in the present paper are very useful for the design and application of periodic pile barriers in ambient vibration reduction.

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.).

Brillouin Klein space and half-turn space in three-dimensional acoustic crystals

The Bloch band theory and Brillouin zone (BZ) that characterize wave-like behaviors in periodic mediums are two cornerstones of contemporary physics, ranging from condensed matter to topological physics. Recent theoretical breakthrough revealed that, under the projective symmetry algebra enforced by artificial gauge fields, the usual two-dimensional (2D) BZ (orientable Brillouin two-torus) can be fundamentally modified to a non-orientable Brillouin Klein bottle with radically distinct manifold topology. However, the physical consequence of artificial gauge fields on the more general three-dimensional (3D) BZ (orientable Brillouin three-torus) was so far missing. Here, we theoretically discovered and experimentally observed that the fundamental domain and topology of the usual 3D BZ can be reduced to a non-orientable Brillouin Klein space or an orientable Brillouin half-turn space in a 3D acoustic crystal with artificial gauge fields. We experimentally identify peculiar 3D momentum-space non-symmorphic screw rotation and glide reflection symmetries in the measured band structures. Moreover, we experimentally demonstrate a novel stacked weak Klein bottle insulator featuring a nonzero Z2 topological invariant and self-collimated topological surface states at two opposite surfaces related by a nonlocal twist, radically distinct from all previous 3D topological insulators. Our discovery not only fundamentally modifies the fundamental domain and topology of 3D BZ, but also opens the door towards a wealth of previously overlooked momentum-space multidimensional manifold topologies and novel gauge-symmetry-enriched topological physics and robust acoustic wave manipulations beyond the existing paradigms.

Propagation of elastic waves in correlated dispersions of resonant scatterers

The propagation of coherent longitudinal and transverse waves in random distributions of spherical scatterers embedded in an elastic matrix is studied. The investigated frequency range is the vicinity of the resonance frequencies of the translational and rotational motion of the spheres forced by the waves, where strong dispersion and attenuation are predicted. A technique for making samples made of layers of carbide tungsten beads embedded in epoxy resin is presented, which allows control of the scatterers distribution, induce short-range positional correlations, and minimize the anisotropy of samples. Comparison between phase velocity and attenuation measurements and a model based on multiple scattering theory (MST) shows that bulk effective properties accurately described by MST are obtained from three beads layers. Besides, short-range correlations amplify the effect of mechanical resonances on the propagation of longitudinal and transverse coherent waves. As a practical consequence, the use of short-range positional correlations may be used to enhance the attenuation of elastic waves by disordered, locally resonant, elastic metamaterials, and MST globally correctly predicts the effect of short-range positional order on their effective properties.

Investigation of Bandgap Properties of a Piezoelectric Phononic Crystal Plate Based on the PDE Module in COMSOL

Aiming to address the vibration noise problems on ships, we constructed a piezoelectric phononic crystal (PC) plate structure model, solved the governing equations of the structure using the partial differential equations module (PDE) in the finite element softwareCOMSOL6.1, and obtained the corresponding energy band structure, transmission curves, and vibration modal diagrams. The application of this method to probe the structural properties of two-dimensional piezoelectric PCs is described in detail. The calculation results obtained using this method were compared with the structures obtained using the traditional plane wave expansion method (PWE) and the finite element method (FE). The results were found to be in perfect agreement, which verified the feasibility of this method. To safely and effectively adjust the bandgap within a reasonable voltage range, this paper explored the order of magnitude of the plate thickness, the influence of the voltage on the bandgap, and the dependence between them. It was found that the smaller the order of magnitude of the plate thickness, the smaller the order of magnitude of the band in which the bandgap was located. The magnitude of the driving voltage that made the bandgap change became smaller accordingly. The new idea of attaching the PC plate to the conventional plate structure to achieve a vibration damping effect is also briefly introduced. Finally, the effects of lattice constant, plate width, and thickness on the bandgap were investigated.

Band gap characteristics of new composite multiple locally resonant phononic crystal metamaterial

Locally resonant phononic crystal (LRPC) exhibit elastic wave band gap characteristics within a specific low-frequency range, but their band gap width is relatively narrow, which has certain limitations in practical engineering applications. In order to open a lower frequency band gap and broaden the band gap range, this paper proposes a new composite multiple locally resonant phononic crystal (CMLRPC). Firstly, the band structure of the CMLRPC is calculated by using the finite element method, and then the formation mechanism of the band gap of the CMLRPC is studied by analyzing its vibration mode, and the band gap width is expanded by adjusting the size of the single primitive cell in the supercell model of the CMLRPC. Secondly, an equivalent mass-spring system model for CMLRPC is established to calculate the starting frequency and cut-off frequency of the band gap, and the calculated results are in good agreement with the finite element calculation. Finally, the frequency response function of the CMLRPC is calculated and its attenuation characteristics are analyzed. Within the band gap frequency range, the attenuation values of the CMLRPC are mostly above 20 dB, indicating a good attenuation effect. Compared with traditional LRPC, this new CMLRPC opens multiple band gaps in the frequency range of 200 Hz, with a wider band gap width and better attenuation effect. In addition, considering both the contact between single primitive cell and the adjustment of their spacing in the supercell model of the CMLRPC, lower and wider band gap can be obtained. The research results of this paper provide a new design idea and method for obtaining low-frequency band gap in LRPC, and can provide reference for the design of vibration reduction and isolation structures in the field of low-frequency vibration control.

Research on Fabrication of Phononic Crystal Soft-Supported Graphene Resonator

In aviation, aerospace, and other fields, nanomechanical resonators could offer excellent sensing performance. Among these, graphene resonators, as a new sensitive unit, are expected to offer very high mass and force sensitivity due to their extremely thin thickness. However, at present, the quality factor of graphene resonators at room temperature is generally low, which limits the performance improvement and further application of graphene resonators. Enhancing the quality factor of graphene resonators has emerged as a pressing research concern. In a previous study, we have proposed a new mechanism to reduce the energy dissipation of graphene resonators by utilizing phononic crystal soft-supported structures. We verified its feasibility through theoretical analysis and simulations. This article focuses on the fabrication of a phononic crystal soft-supported graphene resonator. In order to address the issues of easy fracture, deformation, and low success rate in the fabrication of phononic crystal soft-supported graphene resonators, we have studied key processes for graphene suspension release and focused ion beam etching. Through parameter optimization, finally, we have obtained phononic crystal soft-supported graphene resonators with varying cycles and pore sizes. Finally, we designed an optical excitation and detection platform based on Fabry-Pérot interference principle and explored the impact of laser power and spot size on phononic crystal soft-supported graphene resonators.

A Novel 3D-Printed Negative-Stiffness Lattice Structure with Internal Resonance Characteristics and Tunable Bandgap Properties

The bandgap tuning potential offered by negative-stiffness lattice structures, characterized by their unique mechanical properties, represents a promising and burgeoning field. The potential of large deformations in lattice structures to transition between stable configurations is explored in this study. This transformation offers a novel method for modifying the frequency range of elastic wave attenuation, simultaneously absorbing energy and effectively generating diverse bandgap ranges. In this paper, an enhanced lattice structure is introduced, building upon the foundation of the normal negative-stiffness lattice structures. The research examined the behavior of the suggested negative-stiffness lattice structures when subjected to uniaxial compression. This included analyzing the dispersion spectra and bandgaps across different states of deformation. It also delved into the effects of geometric parameter changes on bandgap properties. Furthermore, the findings highlight that the normal negative-stiffness lattice structure demonstrates restricted capabilities in attenuating vibrations. In contrast, notable performance improvements are displayed by the improved negative-stiffness lattice structure, featuring distinct energy band structures and variable bandgap ranges in response to differing deformation states. This highlights the feasibility of bandgap tuning through the deformation of negatively stiffened structures. Finally, the overall metamaterial structure is simulated using a unit cell finite element dynamic model, and its vibration transmission properties and frequency response patterns are analyzed. A fresh perspective on the research and design of negative-stiffness lattice structures, particularly focusing on their bandgap tuning capabilities, is offered in this study.

Graphene-based phononic crystal lenses: Machine learning-assisted analysis and design

The advance of artificial intelligence and graphene-based composites brings new vitality into the conventional design of acoustic lenses which suffers from high computation cost and difficulties in achieving precise desired refractive indices. This paper presents an efficient and accurate design methodology for graphene-based gradient-index phononic crystal (GGPC) lenses by combing theoretical formulations and machine learning methods. The GGPC lenses consist of two-dimensional phononic crystals possessing square unit cells with graphene-based composite inclusions. The plane wave expansion method is exploited to obtain the dispersion relations of elastic waves in the structures and then establish the data sets of the effective refractive indices in structures with different volume fractions of graphene fillers in composite materials and filling fractions of inclusions. Based on the database established by the theoretical formulation, genetic programming, a superior machine learning algorithm, is introduced to generate explicit mathematical expressions to predict the effective refractive indices under different structural information. The design of GGPC lenses is conducted with the assistance of the machine learning prediction model, and it will be illustrated by several typical design examples. The proposed design method offers high efficiency, accuracy as well as the ability to achieve inverse design of GGPC lenses, thus significantly facilitating the development of novel phononic crystal lenses and acoustic energy focusing.

GaAs/GaP Superlattice Nanowires for Tailoring Phononic Properties at the Nanoscale: Implications for Thermal Engineering

The possibility to tune the functional properties of nanomaterials is key to their technological applications. Superlattices, i.e., periodic repetitions of two or more materials in one or more dimensions, are being explored for their potential as materials with tailor-made properties. Meanwhile, nanowires offer a myriad of possibilities to engineer systems at the nanoscale, as well as to combine materials that cannot be put together in conventional heterostructures due to the lattice mismatch. In this work, we investigate GaAs/GaP superlattices embedded in GaP nanowires and demonstrate the tunability of their phononic and optoelectronic properties by inelastic light scattering experiments corroborated by ab initio calculations. We observe clear modifications in the dispersion relation for both acoustic and optical phonons in the superlattices nanowires. We find that by controlling the superlattice periodicity, we can achieve tunability of the phonon frequencies. We also performed wavelength-dependent Raman microscopy on GaAs/GaP superlattice nanowires, and our results indicate a reduction in the electronic bandgap in the superlattice compared to the bulk counterpart. All of our experimental results are rationalized with the help of ab initio density functional perturbation theory (DFPT) calculations. This work sheds fresh insights into how material engineering at the nanoscale can tailor phonon dispersion and open pathways for thermal engineering.

Stiffening and dynamics of a two-dimensional active elastic solid

This work deals with the mechanical properties and dynamics of an active elastic solid defined as a two-dimensional network of active stochastic particles interacting by nonlinear hard springs. By proposing a discrete model, it is numerically found that when activity in the system is turned on, the active solid stiffens as a function of propulsion forces, thus deviating from equilibrium mechanics. To understand this effect a minimal stochastic model is offered, and a physical explanation based on spatial symmetry-breaking is put forward. In addition, the dynamics of the active solid in the absence of an external stress is also studied. From this, three main features are observed to emerge, namely, a collective behavior within the active solid, a time-density fluctuation, and oscillating dynamics of the internal stresses towards a steady state.

Advances in Tunable Bandgaps of Piezoelectric Phononic Crystals

Bandgaps of traditional phononic crystals (PCs) are determined using structural geometric parameters and material properties, and they are difficult to tune in practical applications. Piezoelectric PCs with lead zirconium titanate piezoelectric ceramics (abbreviated to piezoelectric PCs) have multi-physics coupling effects and their bandgaps can be tuned through external circuits to expand the application range of the PCs. First, the typical structures of piezoelectric PCs are summarized and analyzed. According to the structure, common tunable piezoelectric PCs can be roughly divided into three categories: PCs that only contain piezoelectric materials (single piezoelectric PCs), PCs composed of embedded piezoelectric materials in elastic materials (composite piezoelectric PCs), and PCs that are composed of an elastic base structure and attached piezoelectric patches (patch-type piezoelectric PCs). Second, the tuning methods of bandgaps for piezoelectric PCs are summarized and analyzed. Then, the calculation methods of the bandgaps of piezoelectric PCs are reviewed and analyzed. Finally, conclusions are drawn on the research status of piezoelectric PCs, shortcomings of the existing research are discussed, and future development directions are proposed.

A promising ultra-sensitive CO2 sensor at varying concentrations and temperatures based on Fano resonance phenomenon in different 1D phononic crystal designs

Detecting of the levels of greenhouse gases in the air with high precision and low cost is a very urgent demand for environmental protection. Phononic crystals (PnCs) represent a novel sensor technology, particularly for high-performance sensing applications. This study has been conducted by using two PnC designs (periodic and quasi-periodic) to detect the CO2 pollution in the surrounding air through a wide range of concentrations (0-100%) and temperatures (0-180 °C). The detection process is physically dependent on the displacement of Fano resonance modes. The performance of the sensor is demonstrated for the periodic and Fibonacci quasi-periodic (S3 and S4 sequences) structures. In this regard, the numerical findings revealed that the periodic PnC provides a better performance than the quasi-periodic one with a sensitivity of 31.5 MHz, the quality factor (Q), along with a figure of merit (FOM) of 280 and 95, respectively. In addition, the temperature effects on the Fano resonance mode position were examined. The results showed a pronounced temperature sensitivity with a value of 13.4 MHz/°C through a temperature range of 0-60 °C. The transfer matrix approach has been utilized for modeling the acoustic wave propagation through each PnC design. Accordingly, the proposed sensor has the potential to be implemented in many industrial and biomedical applications as it can be used as a monitor for other greenhouse gases.

Enhanced Sensitivity of Binary/Ternary Locally Resonant Porous Phononic Crystal Sensors for Sulfuric Acid Detection: A New Class of Fluidic-Based Biosensors

This research presented a comprehensive study of a one-dimensional (1D) porous silicon phononic crystal design as a novel fluidic sensor. The proposed sensor is designed to detect sulfuric acid (H₂SO₄) within a narrow concentration range of 0-15%. Sulfuric acid is a mineral acid extensively utilized in various physical, chemical, and industrial applications. Undoubtedly, its concentration, particularly at lower levels, plays a pivotal role in these applications. Hence, there is an urgent demand for a highly accurate and sensitive tool to monitor even the slightest changes in its concentration, which is crucial for researchers. Herein, we presented a novel study on the optimization of the phononic crystal (PnC) sensor. The optimization process involves a comparative strategy between binary and ternary PnCs, utilizing a multilayer stack comprising 1D porous silicon (PSi) layers. Additionally, a second comparison is conducted between conventional Bragg and local resonant PnCs to demonstrate the design with the highest sensitivity. Moreover, we determine the optimum values for the materials' thickness and number of periods. The results revealed that the ternary local resonant PnC design with the configuration of {silicone rubber/[PSi1/PSi2/PSi3]^N/silicone rubber} is the optimal sensor design. The sensor provided a super sensitivity of 2.30 × 10⁷ Hz for a concentration change of just 2%. This exceptional sensitivity is attributed to the presence of local resonant modes within the band gap of PnCs. The temperature effects on the local resonant modes and sensor performance have also been considered. Furthermore, additional sensor performance parameters such as quality factor, figure of merit, detection limit, and damping rate have been calculated to demonstrate the effectiveness of the proposed liquid sensor. The transfer matrix method was utilized to compute the transmission spectra of the PnC, and Hashin's expression was employed to manipulate the porous silicon media filled with sulfuric acid at various concentrations. Lastly, the proposed sensor can serve as an efficient tool for detecting acidic rain, contaminating freshwater, and assessing food and liquid quality, as well as monitoring other pharmaceutical products.

Analysis of Vibration-Damping Characteristics and Parameter Optimization of Cylindrical Cavity Double-Plate Phononic Crystal

For the application of low-frequency vibration damping in industry, a cylindrical cavity double-layer plate-type local resonance phononic crystal structure is proposed to solve low-frequency vibration in mechanical equipment. Initially, using COMSOL 5.4 software, the bending wave band gap is calculated in conjunction with elastic dynamics theory and the BOLOCH theorem to be 127-384 Hz. Then the mechanism of bending wave gap is analyzed by combining element mode shape and an equivalent model. Subsequently, the bending vibration transmission characteristics of the crystal plate are explained, and the vibration-damping characteristics are illustrated in combination with the time-frequency domain. An experimental system is constructed to verify the vibration-damping properties of crystal plates; the experimental results and simulation results are verified with each other. Finally, the element structural parameters are optimized using the RSM. Fifty-four sets of experiments are designed based on six structural factors and three levels, and the expressions between the bending wave band gap and six structural factors are obtained. Combining the particle swarm algorithm, the optimization is performed with the band gap width as the target. This method is shown to be more accurate than the commonly used interior point method. The structure of cylindrical-cavity-type phononic crystal and the parameter optimization method proposed in this paper provide a certain reference for the design of local-resonance-type phononic crystal.

Low Frequency Attenuation Characteristics of Two-Dimensional Hollow Scatterer Locally Resonant Phonon Crystals

The finite element method (FEM) was applied to study the low frequency band gap characteristics of a designed phonon crystal plate formed by embedding a hollow lead cylinder coated with silicone rubber into four epoxy resin short connecting plates. The energy band structure, transmission loss and displacement field were analyzed. Compared to the band gap characteristics of three traditional phonon crystal plates, namely, the square connecting plate adhesive structure, embedded structure and fine short connecting plate adhesive structure, the phonon crystal plate of the short connecting plate structure with a wrapping layer was more likely to generate low frequency broadband. The vibration mode of the displacement vector field was observed, and the mechanism of band gap formation was explained based on the spring mass model. By discussing the effects of the width of the connecting plate, the inner and outer radii and height of the scatterer on the first complete band gap, it indicated that the narrower the width of the connecting plate, the smaller the thickness; the smaller the inner radius of the scatterer, the larger the outer radius; and the higher the height, the more conducive it is to the expansion of the band gap.

Refraction, beam splitting and dispersion of GHz surface acoustic waves by a phononic crystal

We exploit a time-resolved ultrafast optical technique to study the propagation of point-excited surface acoustic waves on a microscopic two-dimensional phononic crystal in the form of a square lattice of holes in a silicon substrate. Constant-frequency images and the dispersion relation are extracted, and the latter measured in detail in the region around the phononic band gap. Mode conversion and refraction at the interface between the phononic crystal and surrounding non-structured silicon substrate is studied at constant frequencies. Symmetric phonon beam splitting, for example, is shown to lead to a striking Maltese-cross pattern when phonons exit a square region of phononic crystal excited near its center.

Dynamics of time-modulated, nonlinear phononic lattices

The propagation of acoustic and elastic waves in time-varying, spatially homogeneous media can exhibit different phenomena when compared to traditional spatially varying, temporally homogeneous media. In the present work, the response of a one-dimensional phononic lattice with time-periodic elastic properties is studied with experimental, numerical and theoretical approaches in both linear and nonlinear regimes. The system consists of repelling magnetic masses with grounding stiffness controlled by electrical coils driven with electrical signals that vary periodically in time. For small-amplitude excitation, in agreement with linear theoretical predictions, wave-number band gaps emerge. The underlying instabilities associated to the wave-number band gaps are investigated with Floquet theory and the resulting parametric amplification is observed in both theory and experiments. In contrast to genuinely linear systems, large-amplitude responses are stabilized via the nonlinear nature of the magnetic interactions of the system, and results in a family of nonlinear time-periodic states. The bifurcation structure of the periodic states is studied. It is found the linear theory correctly predicts parameter values from which the time-periodic states bifurcate from the zero state. In the presence of an external drive, the parametric amplification induced by the wave-number band gap can lead to bounded and stable responses that are temporally quasiperiodic. Controlling the propagation of acoustic and elastic waves by balancing nonlinearity and external modulation offers a new dimension in the realization of advanced signal processing and telecommunication devices. For example, it could enable time-varying, cross-frequency operation, mode- and frequency-conversion, and signal-to-noise ratio enhancements.

Mechanically-tunable bandgap closing in 2D graphene phononic crystals

We present a tunable phononic crystal which can be switched from a mechanically insulating to a mechanically conductive (transmissive) state. Specifically, in our simulations for a phononic lattice under biaxial tension (σ xx = σ yy = 0.01 N m-1), we find a bandgap for out-of-plane phonons in the range of 48.8-56.4 MHz, which we can close by increasing the degree of tension uniaxiality (σ xx/σ yy) to 1.7. To manipulate the tension distribution, we design a realistic device of finite size, where σ xx/σ yy is tuned by applying a gate voltage to a phononic crystal made from suspended graphene. We show that the bandgap closing can be probed via acoustic transmission measurements and that the phononic bandgap persists even after the inclusion of surface contaminants and random tension variations present in realistic devices. The proposed system acts as a transistor for MHz-phonons with an on/off ratio of 105 (100 dB suppression) and is thus a valuable extension for phonon logic applications. In addition, the transition from conductive to isolating can be seen as a mechanical analogue to a metal-insulator transition and allows tunable coupling between mechanical entities (e.g. mechanical qubits).

Phononic Crystal Made of Silicon Ridges on a Membrane for Liquid Sensing

We propose the design of a phononic crystal to sense the acoustic properties of a liquid that is constituted by an array of silicon ridges on a membrane. In contrast to other concepts, the ridges are immersed in the liquid. The introduction of a suitable cavity in the periodic array gives rise to a confined defect mode with high localization in the cavity region and strong solid-liquid interaction, which make it sensitive to the acoustic properties of the liquid. By using a finite element method simulation, we theoretically study the transmission and cavity excitation of an incident flexural wave of the membrane. The observation of the vibrations of this mode can be achieved either outside the area of the phononic crystal or just above the cavity. We discuss the existence of the resonant modes, as well as its quality factor and sensitivity to liquid properties as a function of the geometrical parameters. The performance of the proposed sensor has then been tested to detect the variation in NaI concentration in a NaI-water mixture.

Simulation study of gas sensor using periodic phononic crystal tubes to detect hazardous greenhouse gases

Here, we investigate a gas sensor model based on phononic crystals of alternating tubes using the transfer matrix method to detect hazardous greenhouse gases. The effect of the thicknesses and cross-sections of all tubes on the performance of the proposed sensor is studied. The results show that longitudinal acoustic speed is a pivotal parameter rather than the mass density variations of the gas samples on the position of the resonant peaks due to its significant impact on the propagation of the acoustic wave. The suggested sensor can be considered very simple and low-cost because it does not need a complicated process to deposit multilayers of different mechanical properties' materials.

Unlocking Novel Ultralow-Frequency Band Gap: Assembled Cellular Metabarrier for Broadband Wave Isolation

Admittedly, the design requirements of compactness, low frequency, and broadband seem to constitute an impossible trinity, hindering the further development of elastic metamaterials (EMMs) in wave shielding engineering. To break through these constraints, we propose theoretical combinations of effective parameters for wave isolation based on the propagation properties of Lamb waves in the EMM layer. Accordingly, we design compact EMMs with a novel ultralow-frequency bandgap, and the role of auxeticity in the dissociation between the dipole mode and the toroidal dipole mode is clearly revealed. Finally, under the guidance of the improved gradient design, we integrate multiple bandgaps to assemble metamaterial barriers (MMBs) for broadband wave isolation. In particular, the original configuration is further optimized and its ultralow-frequency and broadband performance are proven by transmission tests. It is foreseeable that our work will provide a meaningful reference for the application of the new EMMs in disaster prevention and protection engineering.

Work extraction from single-mode thermal noise by measurements: How important is information?

Our goal in this article is to elucidate the rapport of work and information in the context of a minimal quantum-mechanical setup: a converter of heat input to work output, the input consisting of a single oscillator mode prepared in a hot thermal state along with a few much colder oscillator modes. The core issues we consider, taking account of the quantum nature of the setup, are as follows: (i) How and to what extent can information act as a work resource or, conversely, be redundant for work extraction? (ii) What is the optimal way of extracting work via information acquired by measurements? (iii) What is the bearing of information on the efficiency-power tradeoff achievable in such setups? We compare the efficiency of work extraction and the limitations of power in our minimal setup by different, generic, measurement strategies of the hot and cold modes. For each strategy, the rapport of work and information extraction is found and the cost of information erasure is allowed for. The possibilities of work extraction without information acquisition, via nonselective measurements, are also analyzed. Overall, we present, by generalizing a method based on optimized homodyning that we have recently proposed, the following insight: extraction of work by observation and feedforward that only measures a small fraction of the input is clearly advantageous to the conceivable alternatives. Our results may become the basis of a practical strategy of converting thermal noise to useful work in optical setups, such as coherent amplifiers of thermal light, as well as in their optomechanical and photovoltaic counterparts.

Design and Robustness Evaluation of Valley Topological Elastic Wave Propagation in a Thin Plate with Phononic Structure

Based on the concept of band topology in phonon dispersion, we designed a topological phononic crystal in a thin plate for developing an efficient elastic waveguide. Despite that various topological phononic structures have been actively proposed, a quantitative design strategy of the phononic band and its robustness assessment in an elastic regime are still missing, hampering the realization of topological acoustic devices. We adopted a snowflake-like structure for the crystal unit cell and determined the optimal structure that exhibited the topological phase transition of the planar phononic crystal by changing the unit cell structure. The bandgap width could be adjusted by varying the length of the snow-side branch, and a topological phase transition occurred in the unit cell structure with threefold rotational symmetry. Elastic waveguides based on edge modes appearing at interfaces between crystals with different band topologies were designed, and their transmission efficiencies were evaluated numerically and experimentally. The results demonstrate the robustness of the elastic wave propagation in thin plates. Moreover, we experimentally estimated the backscattering length, which measures the robustness of the topologically protected propagating states against structural inhomogeneities. The results quantitatively indicated that degradation of the immunization against the backscattering occurs predominantly at the corners in the waveguides, indicating that the edge mode observed is a relatively weak topological state.

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.

Excitation and detection of acoustic phonons in nanoscale systems

Phonons play a key role in the physical properties of materials, and have long been a topic of study in physics. While the effects of phonons had historically been considered to be a hindrance, modern research has shown that phonons can be exploited due to their ability to couple to other excitations and consequently affect the thermal, dielectric, and electronic properties of solid state systems, greatly motivating the engineering of phononic structures. Advances in nanofabrication have allowed for structuring and phonon confinement even down to the nanoscale, drastically changing material properties. Despite developments in fabricating such nanoscale devices, the proper manipulation and characterization of phonons continues to be challenging. However, a fundamental understanding of these processes could enable the realization of key applications in diverse fields such as topological phononics, information technologies, sensing, and quantum electrodynamics, especially when integrated with existing electronic and photonic devices. Here, we highlight seven of the available methods for the excitation and detection of acoustic phonons and vibrations in solid materials, as well as advantages, disadvantages, and additional considerations related to their application. We then provide perspectives towards open challenges in nanophononics and how the additional understanding granted by these techniques could serve to enable the next generation of phononic technological applications.

Engineering nanoscale hypersonic phonon transport

Controlling vibrations in solids is crucial to tailor their elastic properties and interaction with light. Thermal vibrations represent a source of noise and dephasing for many physical processes at the quantum level. One strategy to avoid these vibrations is to structure a solid such that it possesses a phononic stop band, that is, a frequency range over which there are no available elastic waves. Here we demonstrate the complete absence of thermal vibrations in a nanostructured silicon membrane at room temperature over a broad spectral window, with a 5.3-GHz-wide bandgap centred at 8.4 GHz. By constructing a line-defect waveguide, we directly measure gigahertz guided modes without any external excitation using Brillouin light scattering spectroscopy. Our experimental results show that the shamrock crystal geometry can be used as an efficient platform for phonon manipulation with possible applications in optomechanics and signal processing transduction.

Acoustic computing: At tunable pseudospin-1 Hermitian Dirac-like cone

Hermitian Dirac-like cones are proposed for creating acoustic logic gates herein. The predictive phenomenon of creating Dirac-like cones near a bipolar antisymmetric deaf band was found to be useful for acoustic computing of Boolean algebra. Unlike previous approaches, Dirac-like cone creates exclusive opportunity to perform all possible Boolean algebra computation with valid inputs. The phenomenon is demonstrated in two-dimensional phononic crystals (PnCs), consisting of tunable square columns in air media. By predictive tuning of the deaf bands, a triply to doubly degenerated Dirac-like cone is reported to form and is particularly useful for acoustic computing. It is only possible when a bottom band has a negative curvature that is lifted from a nearby doubly degenerated band with positive curvature, which is again degenerated with a deaf band. On the contrary, similar computing possibilities are difficult when the bottom band degenerates with the deaf band and the top band is lifted. Using these phenomena, acoustic logic gates are designed to perform Boolean algebra through AND, NAND, OR, and NOR gate operations. A simple one degree of freedom system and a complex six degrees of freedom system are proposed and demonstrated in which simple rotation of the PnCs activates a specific gate.

Complex Band Structure of 2D Piezoelectric Local Resonant Phononic Crystal with Finite Out-Of Plane Extension

In this study, a new type of 2D piezoelectric phononic crystal with a square hollow and convex structures is designed and established. A theoretical study of the piezoelectric phononic crystal is presented in this article to investigate the transmission properties of waves in terms of complex dispersion relations. Based on the finite discretization technique and plane wave expansion, the formula derivation of the real band structure is achieved as well as the complex band diagrams are obtained. The numerical results are presented to demonstrate the multiple broadband complete bandgaps produced by the designed piezoelectric phononic crystal and the propagation characteristics of the elastic waves for different directions. In addition, the transmission loss in the ΓX direction is calculated to verify the band structure. Finally, the effects of the thickness and the square hollow side length on the band structure are discussed.

Ultra-sensitive gas sensor based fano resonance modes in periodic and fibonacci quasi-periodic Pt/PtS2 structures

Ultra-sensitive greenhouse gas sensors for CO₂, N₂O, and CH₄ gases based on Fano resonance modes have been observed through periodic and quasi-periodic phononic crystal structures. We introduced a novel composite based on metal/2D transition metal dichalcogenides (TMDs), namely; platinum/platinum disulfide (Pt/PtS₂) composite materials. Our gas sensors were built based on the periodic and quasi-periodic phononic crystal structures of simple Fibonacci (F(5)) and generalized Fibonacci (FC(7, 1)) quasi-periodic phononic crystal structures. The FC(7, 1) structure represented the highest sensitivity for CO₂, N₂O, and CH₄ gases compared to periodic and F(5) phononic crystal structures. Moreover, very sharp Fano resonance modes were observed for the first time in the investigated gas sensor structures, resulting in high Fano resonance frequency, novel sensitivity, quality factor, and figure of merit values for all gases. The FC(7, 1) quasi-periodic structure introduced the best layer sequences for ultra-sensitive phononic crystal greenhouse gas sensors. The highest sensitivity was introduced by FC(7, 1) quasiperiodic structure for the CH₄ with a value of 2.059 (GHz/m.s^-1). Further, the temperature effect on the position of Fano resonance modes introduced by FC(7, 1) quasi-periodic PhC gas sensor towards CH₄ gas has been introduced in detail. The results show the highest sensitivity at 70 °C with a value of 13.3 (GHz/°C). Moreover, the highest Q and FOM recorded towards CH₄ have values of 7809 and 78.1 (m.s^-1)^-1 respectively at 100 °C.

Longitudinal Wave Locally Resonant Band Gaps in Metamaterial-Based Elastic Rods Comprising Multi-Degree-of-Freedom DAVI Resonators

The wave propagation and vibration transmission in metamaterial-based elastic rods with periodically attached multi-degree-of-freedom (MDOF) dynamic anti-resonant vibration isolator (DAVI) resonators are investigated. A methodology based on a combination of the transfer matrix (TM) method and the Bloch theorem is developed, yielding an explicit formulation for the complex band structure calculation. The bandgap behavior of the periodic structure arrayed with single-degree-of-freedom (SDOF) DAVI resonators and two-degree-of-freedom (2DOF) DAVI resonators are investigated, respectively. A comparative study indicates that the structure consisting of SDOF DAVI resonators periodically jointed on the metamaterial-based elastic rod can obtain an initial locally resonant band gap 500 Hz smaller than the one given in the published literature. The periodic structure containing 2DOF DAVI resonators has an advantage over the periodic structure with SDOF DAVI resonators in achieving two resonance band gaps. By analyzing the equivalent dynamic mass of a DAVI resonator, the underlying mechanism of achieving a lower initial locally resonant band gap by this periodic structure is revealed. The parameters of the 2DOF DAVI resonator are optimized to obtain the lowest band gap of the periodic structure. The numerical results show that, with the optimal 2DOF DAVI parameters, the periodic structure can generate a much lower initial locally resonant band gap compared with the case before the optimization.

Simultaneous negative reflection and refraction and reverse-incident right-angle collimation of sound in a solid-fluid phononic crystal

The square lattice phononic crystal (PnC) has been used extensively to demonstrate metamaterial effects. Here, positive and negative refraction and reflection are observed simultaneously due to the presence of Umklapp scattering of sound at the surface of PnC and square-like equifrequency contours (EFCs). It is found that a shift in the EFC of the third transmission band away from the center of the Brillouin zone results in an effectively inverted EFC. The overlap of the EFC of the second and third band produce quasimomentum-matching conditions that lead to multi-refringence phenomena from a single incident beam without the introduction of defects into the lattice. Additionally, the coupling of a near-normal incident wave to a propagating almost perpendicular Bloch mode is shown to lead to strong right-angle redirection and collimation of the incident acoustic beam. Each effect is demonstrated both numerically and experimentally for scattering of ultrasound at a 10-period PnC slab in water environment.

Waves Propagating in Nano-Layered Phononic Crystals with Flexoelectricity, Microstructure, and Micro-Inertia Effects

The miniaturization of electronic devices is an important trend in the development of modern microelectronics information technology. However, when the size of the component or the material is reduced to the micro/nano scale, some size-dependent effects have to be taken into account. In this paper, the wave propagation in nano phononic crystals is investigated, which may have a potential application in the development of acoustic wave devices in the nanoscale. Based on the electric Gibbs free energy variational principle for nanosized dielectrics, a theoretical framework describing the size-dependent phenomenon was built, and the governing equation as well as the dispersion relation derived; the flexoelectric effect, microstructure, and micro-inertia effects are taken into consideration. To uncover the influence of these three size-dependent effects on the width and midfrequency of the band gaps of the waves propagating in periodically layered structures, some related numerical examples were shown. Comparing the present results with the results obtained with the classical elastic theory, we find that the coupled effects of flexoelectricity, microstructure, and micro-inertia have a significant or even dominant influence on the waves propagating in phononic crystals in the nanoscale. With increase in the size of the phononic crystal, the size effects gradually disappear and the corresponding dispersion curves approach the dispersion curves obtained with the conventional elastic theory, which verify the results obtained in this paper. Thus, when we study the waves propagating in phononic crystals in the micro/nano scale, the flexoelectric, microstructure, and micro-inertia effects should be considered.

Discretization Approach for the Homogenization of Three-Dimensional Solid-Solid Phononic Crystals in the Quasi-Static Limit: Density and Elastic Moduli

With the application of a homogenization theory, based on the Fourier formalism (which provides efficient and exact formulas by which to determine all the components of the effective stiffness and mass density tensors, valid in the regime of large wavelengths), a new approach to calculate the effective quasi-static response in three-dimensional solid-solid phononic crystals is reported. The formulas derived in this work for calculating the effective elastic parameters show a dependence, in terms of summations over the vectors, of the reciprocal lattice by the discretization of the volume of the inclusion in small parts (e.g., small cubes), to obtain a system of equations from which we define the effective response. In particular, we present the numerical results calculated for several cubic lattices with solid constituents and different shapes of inclusions in the unit cell versus the filling fraction, as well as for fixed values of it. By this means, we analyzed the effect of the type of Bravais lattice of the materials, and the geometry of the inclusions that constitute the three-dimensional phononic array, on the resulting effective anisotropy. Finally, our theory confirms other well-known results with previous homogenization theories as a particular case study. In this regard, the examples and results shown here can be useful for the design of metamaterials with predetermined elastic properties.

Extremely low frequency wave localization via elastic foundation induced metamaterial with a spiral cavity

We proposed a metamaterial which exhibits elastic wave localization at extremely low frequencies. First, we opened an extremely low bandgap via elastic foundations. Subsequently, we investigated wave localization by imposing normal defect, which is widely used to capture waves in conventional wave localization systems. However, there were limitations: wave localization was not achieved when a weak bandgap is generated, and the operating frequency of localization is still in the upper part of the bandgap. To overcome wave localization via the normal defect, we proposed a novel metamaterial with a spiral cavity which can tune the resonating frequency depending on the length of the spiral path. By imposing on the spiral cavity inside the elastic foundation-induced metamaterial, we can shift the resonating frequency of the cavity down. Finally, we carried out wave simulations, not only to support the previous eigenfrequency study for the supercell, but also to verify that the finite-size metamaterial can also achieve wave localization at the extremely low frequencies. Through wave simulations, we could observe wave localization even at 77.3 Hz, which is definitely the lower part of the extremely low bandgap.

Nonlinear solitary waves in particle metamaterials with local resonators

In this work, solitary wave solutions of particle mechanical metamaterials are studied, in which the mass-in-mass structure with local resonators is considered. The Hertzian contact theory is used to describe adjacent particles in a precompressed granular chain. The governing wave equations are decoupled, and the expressions of bright, dark, and peaked solitary waves are derived, respectively. According to the results, both the wave velocity and prestress can affect the propagation of solitary waves. The amplitudes of bright and peaked solitary waves are smaller when a larger prestress is applied, which are different from the dark solitons. Furthermore, the wave widths become larger as the prestress increases.

A Ternary Seismic Metamaterial for Low Frequency Vibration Attenuation

Structural vibration induced by low frequency elastic waves presents a great threat to infrastructure such as buildings, bridges, and nuclear structures. In order to reduce the damage of low frequency structural vibration, researchers proposed the structure of seismic metamaterial, which can be used to block the propagation of low frequency elastic wave by adjusting the frequency range of elastic wave propagation. In this study, based on the concept of phononic crystal, a ternary seismic metamaterial is proposed to attenuate low frequency vibration by generating band gaps. The proposed metamaterial structure is periodically arranged by cube units, which consist of rubber coating, steel scatter, and soft matrix (like soil). The finite element analysis shows that the proposed metamaterial structure has a low frequency band gap with 8.5 Hz bandwidth in the range of 0-20 Hz, which demonstrates that the metamaterial can block the elastic waves propagation in a fairly wide frequency range within 0-20 Hz. The frequency response analysis demonstrates that the proposed metamaterial can effectively attenuate the low frequency vibration. A simplified equivalent mass-spring model is further proposed to analyze the band gap range which agrees well with the finite element results. This model provides a more convenient method to calculate the band gap range. Combining the proposed equivalent mass-spring model with finite element analysis, the effect of material parameters and geometric parameters on the band gap characteristic is investigated. This study can provide new insights for low frequency vibration attenuation.

Mechanical Shunt Resonators-Based Piezoelectric Metamaterial for Elastic Wave Attenuation

The conventional piezoelectric metamaterials with operational-amplifier-based shunt circuits have limited application due to the voltage restriction of the amplifiers. In this research, we report a novel piezoelectric metamaterial beam that takes advantage of mechanical shunt resonators. The proposed metamaterial beam consisted of a piezoelectric beam and remote mechanical piezoelectric resonators coupled with electrical wires. The local resonance of the remote mechanical shunt resonators modified the mechanical properties of the beam, yielding an elastic wave attenuation capability. A finite-length piezoelectric metamaterial beam and mechanical shunt resonators were considered for conceptual illustration. Significant elastic wave attenuation can be realized in the vicinity of the resonant frequency of the shunt resonators. The proposed system has the potential in the application of wave attenuation under large-amplitude excitations.

Parametric Optimization of Local Resonant Sonic Crystals Window on Noise Attenuation by Using Taguchi Method and ANOVA Analysis

Local resonant sonic crystals (LRSCs) window as a novel design has recently been proposed to achieve a good balance between noise mitigation, natural ventilation and natural lighting. In an effort to explore the feasibilities of such designs in civil residential buildings, an optimization methodology was proposed to develop a more compact LRSCs window with high noise attenuation performance in the present study. Specifically, the Taguchi method was adopted for the design of experiments on the parameters of interest and their corresponding levels, and SN ratio analysis was then applied for the parametric evaluations on the noise attenuation on specified frequencies in traffic noise (concentrated sound energy frequency range: 630–1000 Hz). Three optimal sets of design parameters on the interested frequencies, namely, 630 Hz, 800 Hz and 1000 Hz were obtained. ANOVA analysis was conducted to quantificationally identify the design parameters with statistical significance and remarkable contribution to the desired performance. Results indicate that the slit size has the most significant influence on the overall noise attenuation performance, followed by cavity width. An optimal set of design parameters to achieve the overall best noise reduction performance in the frequency range of 630–1000 Hz was finally determined by combining the SN ratio and ANOVA analysis. A prototype of the final optimized LRSCs window was then fabricated and tested in a semi-anechoic chamber. Good agreement was found between the experiment and numerical simulation. In comparison to the benchmark case, the final optimized design can achieve a further noise reduction by 2.84 dBA, 3.48 dBA and 5.56 dBA for the frequencies of 630 Hz, 800 Hz and 1000 Hz, respectively. The overall noise reduction for the interested frequency range can be promoted by 3.28 dBA. The results indicate that the proposed optimization methodology is practical and efficient in designing a high-performance LRSCs window or improving similar applications.

Low-Frequency Bandgaps of the Lightweight Single-Phase Acoustic Metamaterials with Locally Resonant Archimedean Spirals

In order to achieve the dual needs of single-phase vibration reduction and lightweight, a square honeycomb acoustic metamaterials with local resonant Archimedean spirals (SHAMLRAS) is proposed. The independent geometry parameters of SHAMLRAS structures are acquired by changing the spiral control equation. The mechanism of low-frequency bandgap generation and the directional attenuation mechanism of in-plane elastic waves are both explored through mode shapes, dispersion surfaces, and group velocities. Meanwhile, the effect of the spiral arrangement and the adjustment of the equation parameters on the width and position of the low-frequency bandgap are discussed separately. In addition, a rational period design of the SHAMLRAS plate structure is used to analyze the filtering performance with transmission loss experiments and numerical simulations. The results show that the design of acoustic metamaterials with multiple Archimedean spirals has good local resonance properties, and forms multiple low-frequency bandgaps below 500 Hz by reasonable parameter control. The spectrograms calculated from the excitation and response data of acceleration sensors are found to be in good agreement with the band structure. The work provides effective design ideas and a low-cost solution for low-frequency noise and vibration control in the aeronautic and astronautic industries.

Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates

Phonon spectra of a two-dimensional (2D) solid dusty plasma modulated by 2D square and triangular periodic substrates are investigated using Langevin dynamical simulations. The commensurability ratio, i.e., the ratio of the number of particles to the number of potential well minima, is set to 1 or 2. The resulting phonon spectra show that propagation of waves is always suppressed due to the confinement of particles by the applied 2D periodic substrates. For a commensurability ratio of 1, the spectra indicate that all particles mainly oscillate at one specific frequency, corresponding to the harmonic oscillation frequency of one single particle inside one potential well. At a commensurability ratio of 2, the substrate allows two particles to sit inside the bottom of each potential well, and the resulting longitudinal and transverse spectra exhibit four branches in total. We find that the two moderate branches come from the harmonic oscillations of one single particle and two combined particles in the potential well. The other two branches correspond to the relative motion of the two-body structure in each potential well in the radial and azimuthal directions. The difference in the spectra between the square and triangular substrates is attributed to the anisotropy of the substrates and the resulting alignment directions of the two-body structure in each potential well.

Acoustic Add-Drop filter involving a ring resonator based on a One-Dimensional surface phononic crystal

By employing two parallel one-dimensional surface phononic crystals for spoof surface acoustic waves and a circular ring resonator, an acoustic add-drop filter is numerically designed and its operation in the air environment is both numerically and experimentally investigated. Finite Element Method is used for band structure calculations and frequency domain simulations of filter operation. For frequencies around 40 kHz, a surface band is observed when a one-dimensional array of cylindrical cavities with a period of 2.7 mm, whose radius is 1.1 mm are embedded in the solid surface by 30% of the radius from their center. When a surface phononic crystal is close to a circular ring resonator containing 100 cavities in total with a radius of 42.9 mm, at a distance of 1.5 periods, frequency-domain Finite-Element simulations at 41.528 kHz reveal that drop port output maximum is observed, whereas through and add outputs are minimum. The corresponding drop port transmission peak has a width and quality factor of 25 Hz and 1661, respectively. In addition, the contrast ratio between the drop and through port outputs at the peak frequency is calculated as 0.77. Experimentally obtained port output data are in agreement with numerical results. The proposed acoustic add-drop filter can be used in areas such as ultrasonic sensors, acoustic signal processing and acoustic logic.

Vibration Band Gap Characteristics of Two-Dimensional Periodic Double-Wall Grillages

In this article, the wave finite element method (WFEM) is used to calculate the band gap characteristics of two-dimensional (2D) periodic double-wall grillages (DwGs), which are verified by the grillage model vibration measurement experiment and finite element calculation. To obtain the band gap characteristics of periodic DwGs, the finite element calculation model is established according to the lattice and energy band theory and the characteristic equation of the periodic unit cell under the given wave vector condition is solved based on Bloch theorem. Then, the frequency transfer functions of finite-length manufactured and finite element models are obtained to verify the band gap characteristics of periodic DwGs. Finally, the effects of material parameters and structural forms on band gap characteristics and transfer functions are analyzed, which can provide a reference for engineering structure vibration and noise reduction design.