Complete band gaps in two-dimensional phononic crystal slabs

Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

Phononic-Crystal-Based SAW Magnetic-Field Sensors

In this theoretical study, we explore the enhancement of sensing capabilities in surface acoustic wave (SAW)-based magnetic field sensors through the integration of engineered phononic crystals (PnCs). We particularly focus on amplifying the interaction between the SAW and magnetostrictive materials within the PnC structure. Through comprehensive simulations, we demonstrate the synchronization between the SAWs generated by IDTs and the resonant modes of PnCs, thereby leading to an enhancement in sensitivity. Furthermore, we investigate the ΔE effect, highlighting the sensor's responsiveness to changes in external magnetic fields, and quantify its magnetic sensitivity through observable changes in the SAW phase velocity leading to phase shifts at the end of the delay line. Notably, our approach yields a magnetic field sensitivity of approximately S~138 °mT for a delay line length of only 77 µm in homogeneous magnetic fields. Our findings underline the potential of PnCs to advance magnetic field sensing. This research offers insights into the integration of engineered materials for improved sensor performance, paving the way for more effective and accurate magnetic field detection solutions.

Reem-Shape Phononic Crystal for Q Anchor Enhancement of Thin-Film-Piezoelectric-on-Si MEMS Resonator

This paper proposes a reem-shaped phononic crystal for the performance enhancement of TPoS resonators. The proposed phononic crystal offers an ultra-wide acoustic band gap that prevents energy leakage through the supporting substrate upon its placement at the anchoring boundary, resulting in significant improvements in the resonator quality factor. Simulated results show reem-shape phononic crystals generate a band gap up to 175 MHz with a BG of 90% and enhance the anchor quality factor from 180,000 to 6,000,000 and the unloaded quality factor from 133,000 to 160,000, representing 33.3-fold and 1.2-fold improvements, respectively.

Deep-Learning-Based Acoustic Metamaterial Design for Attenuating Structure-Borne Noise in Auditory Frequency Bands

In engineering acoustics, the propagation of elastic flexural waves in plate and shell structures is a common transmission path of vibrations and structure-borne noises. Phononic metamaterials with a frequency band gap can effectively block elastic waves in certain frequency ranges, but often require a tedious trial-and-error design process. In recent years, deep neural networks (DNNs) have shown competence in solving various inverse problems. This study proposes a deep-learning-based workflow for phononic plate metamaterial design. The Mindlin plate formulation was used to expedite the forward calculations, and the neural network was trained for inverse design. We showed that, with only 360 sets of data for training and testing, the neural network attained a 2% error in achieving the target band gap, by optimizing five design parameters. The designed metamaterial plate showed a -1 dB/mm omnidirectional attenuation for flexural waves around 3 kHz.

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.

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.

Tunable Graphene Phononic Crystal

In the field of phononics, periodic patterning controls vibrations and thereby the flow of heat and sound in matter. Bandgaps arising in such phononic crystals (PnCs) realize low-dissipation vibrational modes and enable applications toward mechanical qubits, efficient waveguides, and state-of-the-art sensing. Here, we combine phononics and two-dimensional materials and explore tuning of PnCs via applied mechanical pressure. To this end, we fabricate the thinnest possible PnC from monolayer graphene and simulate its vibrational properties. We find a bandgap in the megahertz regime within which we localize a defect mode with a small effective mass of 0.72 ag = 0.002 m_physical. We exploit graphene's flexibility and simulate mechanical tuning of a finite size PnC. Under electrostatic pressure up to 30 kPa, we observe an upshift in frequency of the entire phononic system by ∼350%. At the same time, the defect mode stays within the bandgap and remains localized, suggesting a high-quality, dynamically tunable mechanical system.

Nonlinear acoustic metamaterial for efficient frequency down-conversion

Frequency conversion is one of the most important nonlinear wave phenomena that has been widely used in the field of electromagnetic waves for changing signal frequencies. Recently, studies on frequency conversion have been actively performed in the field of acoustics owing to its importance in nonlinear ultrasonic nondestructive evaluation and directional speakers. However, acoustic frequency conversion presents relatively poor efficiency owing to the small amplitudes of the converted frequencies and undesired intermodulation. Herein, we propose an acoustic metamaterial to achieve an efficient frequency down-conversion of acoustic waves. Based on background theory, we discovered that the amplitudes of the converted frequencies are inversely proportional to the cube of the speed of sound. Accordingly, we amplify the converted frequency components by reducing the effective speed of sound by coiling up space while suppressing undesired intermodulation by the Bragg gap. Numerical simulation and analytical results show that efficient frequency down-conversion is possible using the corresponding metamaterial. Additionally, dissipation due to viscosity and boundary layer effects is considered. We expect our study results to facilitate research regarding acoustic frequency conversion.

Continuum constitutive laws to describe acoustic attenuation in glasses

Nowadays metamaterials are at the focus of an intense research as promising for thermal and acoustic engineering. However, the computational cost associated to the large system size required for correctly simulating them imposes the use of finite-elements simulations, developing continuum models, able to grasp the physics at play without entering in the atomistic details. Still, a correct description should be able to reproduce not only the extrinsic scattering sources on waves propagation, as introduced by the metamaterial microstructure, but also the intrinsic wave attenuation of the material itself. This becomes dramatically important when the metamaterial is made out of a glass, which is intrinsically highly dissipative and with a wave attenuation strongly dependent on frequency. Here we propose a continuum mechanical model for a viscoelastic medium, able to bridge atomic and macroscopic scale in amorphous materials and describe phonon attenuation due to atomistic mechanisms, characterized by a defined frequency dependence. This represents a first decisive step for investigating the effect of a complex nano- or microstructure on acoustic attenuation, while including the atomistic contribution as well.

Narrow Band Solid-Liquid Composite Arrangements: Alternative Solutions for Phononic Crystal-Based Liquid Sensors

Periodic elastic composite structures attract great attention. They offer the ability to design artificial properties to advance the control over the propagation of elastic/acoustic waves. In previous work, we drew attention to composite periodic structures comprising liquids. It was shown that the transmission spectrum of the structure, specifically a well-isolated peak, follows the material properties of liquid constituent in a distinct manner. This idea was realized in several liquid sensor concepts that launched the field of phononic crystal liquid sensors. In this work we introduce a novel concept—narrow band solid-liquid composite arrangements. We demonstrate two different concepts to design narrow band structures, and show the results of theoretical studies and results of experimental investigations that confirm the theoretical predictions. This work extends prior studies in the field of phononic crystal liquid sensors with novel concepts and results that have a high potential in a field of volumetric liquid properties evaluation.

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.

Attenuation Zones of Two-Dimensional Periodic Foundations Including the Effect of Vertical Loads

Periodic foundations for seismic isolation are getting increasing attention in the field of civil engineering. Initial stresses due to the vertical loads from the upper structures exist in periodic foundations. In the present paper, attenuation zones of two-dimensional periodic foundations including the effect of vertical loads are studied by the weak form quadrature element method. Comparisons with existing results in special cases without the effect of vertical loads are conducted to validate the proposed method, and good agreement is found. A comprehensive parametric study is conducted to investigate the effects of vertical loads on the attenuation zones. Moreover, frequency-domain and time-domain response analyses of a two-dimensional periodic foundation with finite unit cells are conducted to verify the theoretical results. The results show that bound frequencies of the attenuation zones, corresponding to the vibration mode of the core, are affected by vertical loads. It is also found that vertical loads shift the complete attenuation zones to lower frequencies and reduce the attenuation coefficients in the attenuation zones.

Phononic Crystal Waveguide Transducers for Nonlinear Elastic Wave Sensing

Second harmonic generation is one of the most sensitive and reliable nonlinear elastic signatures for micro-damage assessment. However, its detection requires powerful amplification systems generating fictitious harmonics that are difficult to discern from pure nonlinear elastic effects. Current state-of-the-art nonlinear ultrasonic methods still involve impractical solutions such as cumbersome signal calibration processes and substantial modifications of the test component in order to create material-based tunable harmonic filters. Here we propose and demonstrate a valid and sensible alternative strategy involving the development of an ultrasonic phononic crystal waveguide transducer that exhibits both single and multiple frequency stop-bands filtering out fictitious second harmonic frequencies. Remarkably, such a sensing device can be easily fabricated and integrated on the surface of the test structure without altering its mechanical and geometrical properties. The design of the phononic crystal structure is supported by a perturbative theoretical model predicting the frequency band-gaps of periodic plates with sinusoidal corrugation. We find our theoretical findings in excellent agreement with experimental testing revealing that the proposed phononic crystal waveguide transducer successfully attenuates second harmonics caused by the ultrasonic equipment, thus demonstrating its wide range of potential applications for acousto/ultrasonic material damage inspection.

Band structure analysis of phononic crystals based on the Chebyshev interval method

Due to environmental changes and manufacturing errors, uncertainties inherently exist in phononic crystals, especially in the material properties and geometric parameters. To handle the uncertainties with limited information, two different methods are proposed for band structure analysis of phononic crystals with uncertainties. One is the Monte Carlo method (MCM). The main shortcoming of it is the high computational cost. The other is the simplex Chebyshev polynomial expansion (SPCE) method. In addition, the computational efficiency of the SPCE method is much higher. In the SPCE method, the simplex Chebyshev is employed to estimate the band structures of phononic crystals. Meanwhile, the simplified incremental sampling strategy is introduced for the simplex Chebyshev to retain calculation accuracy and improve computational efficiency simultaneously. In the Chebyshev surrogate model, the samples yielded with the MCM are used to calculate the interval ranges of the band structures in phononic crystals. Three numerical examples, including a two-dimensional (2D) Helmholtz resonator phononic crystal, a 2D solid-solid phononic crystal, and a three-dimensional phononic crystal, are introduced to verify the effectiveness and efficiency of the proposed method.

Approaching the intrinsic quality factor limit for micromechanical bulk acoustic resonators using phononic crystal tethers

We systematically demonstrate that one-dimensional phononic crystal (1-D PnC) tethers can significantly reduce tether loss in micromechanical resonators to a point where the total energy loss is dominated by intrinsic mechanisms, particularly phonon damping. Multiple silicon resonators are designed, fabricated, and tested to provide comparisons in terms of the number of periods in the PnC and the resonance frequency, as well as a comparison with conventional straight-beam tethers. The product of resonance frequency and measured quality factor (f×Q) is the critical figure of merit, as it is inversely related to the total energy dissipation in a resonator. For a wide range of frequencies, devices with PnC tethers consistently demonstrate higher f×Q values than the best conventional straight-beam tether designs. The f×Q product improves with increasing number of PnC periods, and at a maximum value of 1.2 × 10¹³ Hz, approaches limiting values set by intrinsic material loss mechanisms.

Propagation of thickness shear waves in a periodically corrugated quartz crystal plate and its application exploration in acoustic wave filters

The propagation of thickness shear waves in a periodically corrugated quartz crystal plate is investigated in the present paper using a power series expansion technique. In the proposed simulation model, an equivalent continuity of shear stress moment is introduced as an approximation to handle sectional interfaces with abrupt thickness changes. The Bloch theory is applied to simulate the band structures for three different thickness variation patterns. It is shown that the power series expansion method exhibits good convergence and accuracy, in agreement with results by finite element method (FEM). A broad stop band can be obtained in the power transmission spectra owing to the trapped thickness shear modes excited by the thickness variation, whose physical mechanism is totally different from the well-known Bragg scattering effect and is insensitive to the structural periodicity. Based on the observed energy trapping phenomenon, an acoustic wave filter is proposed in a quartz plate with sectional decreasing thickness, which inhibits wave propagation in different regions.

High-efficiency acousto-optic coupling in phoxonic resonator based on silicon fishbone nanobeam cavity

We investigate the acousto-optic coupling rates between different acoustic resonance modes and a specified optical resonance mode in a one-dimensional phoxonic crystal fishbone nanobeam formed by periodically arranging semi-cylinders of air on both sides of a suspended silicon waveguide. The gradually tapered unit cells form optical and acoustic resonators. In acousto-optic coupling rate calculation, the acoustic fields and optical fields are obtained by steady state monochromatic analysis and eigen-mode computation, respectively. Results showed that the acoustic polarizations and symmetries of the acoustic resonance modes are dominant factors in the acousto-optic coupling efficiency, and appropriate selection of these parameters can prevent cancellation of acousto-optic interactions, thereby enhancing acousto-optic coupling rates. This study provides important insights that can be applied to acousto-optic device designs.

Two-Dimensional Phononic Crystals: Disorder Matters

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

Tunable Lamb wave band gaps in two-dimensional magnetoelastic phononic crystal slabs by an applied external magnetostatic field

This paper theoretically investigates the band gaps of Lamb mode waves in two-dimensional magnetoelastic phononic crystal slabs by an applied external magnetostatic field. With the assumption of uniformly oriented magnetization, an equivalent piezomagnetic material model is used. The effects of magnetostatic field on phononic crystals are considered carefully in this model. The numerical results indicate that the width of the first band gap is significantly changed by applying the external magnetic field with different amplitude, and the ratio between the maximum and minimum gap widths reaches 228%. Further calculations demonstrate that the orientation of the magnetic field obviously affects the width and location of the first band gap. The contactless tunability of the proposed phononic crystal slabs shows many potential applications of vibration isolation in engineering.

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.

Experimental Ultrasound Transmission through Fluid-Solid and Air-Solid Phononic Plates

Underwater ultrasonic transmissions for fluid-solid and air-solid phononic brass plates are reported in this work. Although the structure is roughly the same, experimental results show very different behaviour between fluid-solid and air-solid phononic plates, due to most of the properties of the fluid-solid perforated plates rely on Fabry-Perot resonances, Wood anomalies and Lamb modes. In air-solid phononic plates Fabry-Perot resonance is highly attenuated due to impedances difference between air and water, and therefore some transmission modes are now distinguishable due to surface modes coupling.

Investigation of complete bandgaps in a piezoelectric slab covered with periodically structured coatings

The propagation of elastic waves in a piezoelectric slab covered with periodically structured coatings or the so-called stubbed phononic crystal slab is investigated. Four different models are selected and the effects of distribution forms and geometrical parameters of the structured coatings on complete bandgaps are discussed. The phononic crystal slab with symmetric coatings can generate wider complete bandgaps while that with asymmetric coatings is favorable for the generation of multi-bandgaps. The complete bandgaps, which are induced by locally resonant effects, change significantly as the geometry of the coatings changes. Moreover, the piezoelectric effects benefit the opening of the complete bandgaps.

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.

Control of coherent information via on-chip photonic-phononic emitter-receivers

Rapid progress in integrated photonics has fostered numerous chip-scale sensing, computing and signal processing technologies. However, many crucial filtering and signal delay operations are difficult to perform with all-optical devices. Unlike photons propagating at luminal speeds, GHz-acoustic phonons moving at slower velocities allow information to be stored, filtered and delayed over comparatively smaller length-scales with remarkable fidelity. Hence, controllable and efficient coupling between coherent photons and phonons enables new signal processing technologies that greatly enhance the performance and potential impact of integrated photonics. Here we demonstrate a mechanism for coherent information processing based on travelling-wave photon-phonon transduction, which achieves a phonon emit-and-receive process between distinct nanophotonic waveguides. Using this device, physics--which supports GHz frequencies--we create wavelength-insensitive radiofrequency photonic filters with frequency selectivity, narrow-linewidth and high power-handling in silicon. More generally, this emit-receive concept is the impetus for enabling new signal processing schemes.

Numerical study and topology optimization of 1D periodic bimaterial phononic crystal plates for bandgaps of low order Lamb waves

The optimum topology of bimaterial phononic crystal (PhCr) plates with one-dimensional (1D) periodicity to attain maximum relative bandgap width of low order Lamb waves is computationally investigated. The evolution of optimized topology with respect to filling fraction of constituents, alternatively stiff scattering inclusion, is explored. The underlying idea is to develop PhCr plate structures with high specific bandgap efficiency at particular filling fraction, or further with multiscale functionality through gradient of optimized PhCr unitcell all over the lattice array. Multiobjective genetic algorithm (GA) is employed in this research in conjunction with finite element method (FEM) for topology optimization of silicon-tungsten PhCr plate unitcells. A specialized FEM model is developed and verified for dispersion analysis of plate waves and calculation of modal response. Modal band structure of regular PhCr plate unitcells with centric scattering layer is studied as a function of aspect ratio and filling fraction. Topology optimization is then carried out for a few aspect ratios, with and without prescribed symmetry, over various filling fractions. The efficiency of obtained solutions is verified as compared to corresponding regular centric PhCr plate unitcells. Moreover, being inspired by the obtained optimum topologies, definite and easy to produce topologies are proposed with enhanced bandgap efficiency as compared to centric unitcells. Finally a few cases are introduced to evaluate the frequency response of finite PhCr plate structures produced by achieved topologies and also to confirm the reliability of calculated modal band structures. Cases made by consecutive unitcells of different filling fraction are examined in order to attest the bandgap efficiency and multiscale functionality of such graded PhCr plate structures.

Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanics

Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how their frame is clamped to the sample mount, which in practice usually necessitates delicate, and difficult-to-reproduce mounting solutions. Here, we demonstrate that a phononic bandgap shield integrated in the membrane's silicon frame eliminates this dependence, by suppressing dissipation through phonon tunneling. We dry-etch the membrane's frame so that it assumes the form of a cm-sized bridge featuring a 1-dimensional periodic pattern, whose phononic density of states is tailored to exhibit one, or several, full band gaps around the membrane's high-Q modes in the MHz-range. We quantify the effectiveness of this phononic bandgap shield by optical interferometry measuring both the suppressed transmission of vibrations, as well as the influence of frame clamping conditions on the membrane modes. We find suppressions up to 40 dB and, for three different realized phononic structures, consistently observe significant suppression of the dependence of the membrane's modes on sample clamping-if the mode's frequency lies in the bandgap. As a result, we achieve membrane mode quality factors of 5 × 10(6) with samples that are tightly bolted to the 8 K-cold finger of a cryostat. Q × f -products of 6 × 10(12) Hz at 300 K and 14 × 10(12) Hz at 8 K are observed, satisfying one of the main requirements for optical cooling of mechanical vibrations to their quantum ground-state.

Engineering thermal conductance using a two-dimensional phononic crystal

Controlling thermal transport has become relevant in recent years. Traditionally, this control has been achieved by tuning the scattering of phonons by including various types of scattering centres in the material (nanoparticles, impurities, etc). Here we take another approach and demonstrate that one can also use coherent band structure effects to control phonon thermal conductance, with the help of periodically nanostructured phononic crystals. We perform the experiments at low temperatures below 1 K, which not only leads to negligible bulk phonon scattering, but also increases the wavelength of the dominant thermal phonons by more than two orders of magnitude compared to room temperature. Thus, phononic crystals with lattice constants ≥1 μm are shown to strongly reduce the thermal conduction. The observed effect is in quantitative agreement with the theoretical calculation presented, which accurately determined the ballistic thermal conductance in a phononic crystal device.

Controlling thermal transport is commonly achieved by introducing scattering centres. Here, the authors demonstrate that coherent band structure effects can also be used to control phonon transport, via the use of periodically nanostructured phononic crystals.

Increasing the modal density in plates for mono-element focusing in air

Acoustic focusing experiments usually require large arrays of transducers. It has been shown by Etaix et al. [J. Acoust. Soc. Am. 131, 395-399 (2012)] that the use of a cavity allows reducing this number of transducers. This paper presents experiments with Duralumin plates (the cavities) containing scatterers to improve the contrast of focusing. The use of a scatterer array in the plate allows increasing the modal density at given frequencies. The scatterers used are membranes and buttons that are manufactured in Duralumin plates. Their resonances are studied both experimentally and numerically. Such scatterers present the advantage of having a tunable frequency resonance, which allows controlling the frequencies at which the modal density increases. The dispersion relations of plates with scatterer array show high modal density at given frequencies. Finally acoustic focusing experiments in air, using these plates, are compared to the ones of simple duralumin plates demonstrating the improvement of contrast. Acoustic source localization is also realized using these plates.

Sonic crystal acoustic switch device

This study reports a wave-controlled sonic crystal switch device that exhibits a destructive interference-based wave to wave reverse switching effect. By applying control waves, this acoustic device, composed of a two-dimensional square lattice sonic crystal block, reduces acoustic wave transmission from input to output. The finite difference time domain simulation and experimental results confirm the wave-to-wave reverse switching effect at the peak frequencies of the second band. The proposed sonic crystal switch prototype provides a contrast rate of 86% at 11.3 kHz frequency. This wave-to-wave switching effect is useful for controlling wave propagation for smart structure applications.

The slow zero order antisymmetric Lamb mode in phononic crystal plates

In this paper, the group velocities of the zero order antisymmetric (A0) Lamb modes in a phononic crystal plate with single layer cylindrical holes parallel to the surface of the plate were investigated theoretically. The results show that by increasing the filling fraction, the A0 mode can be efficiently slowed down and the group velocity of the A0 modes can be tuned from the positive to the negative referring to the phase velocity. Moreover, the zero group velocity of the A0 modes can be obtained with a given filling fraction. These results may be useful in designing acoustic devices.

Effects of shapes and symmetries of scatterers on acoustic dual-negative refraction

The potential operating conditions of acoustic dual-negative refraction (ADNR) are investigated by band structure theory for scatterers with different shapes and symmetries. Specifically, two types of lattices (triangular and honeycomb) and four different shapes of scatterers (circle, hexagon, square and triangle) are considered. Based on the generation mechanism of the ADNR effect, which is dependent on the frequency of the incident wave at the overlapping second and third Bloch bands, the optimum operating frequencies of ADNR with different crystal structures are given. The calculations demonstrate that the ADNR effect can be generated at the normalized frequency from 0.8 to 1.05.

Complete band gaps of phononic crystal plates with square rods

Much of previous work has been devoted in studying complete band gaps for bulk phononic crystal (PC). In this paper, we theoretically investigate the existence and widths of these gaps for PC plates. We focus our attention on steel rods of square cross sectional area embedded in epoxy matrix. The equations for calculating the dispersion relation for square rods in a square or a triangular lattice have been derived. Our analysis is based on super cell plane wave expansion (SC-PWE) method. The influence of inclusions filling factor and plate thickness on the existence and width of the phononic band gaps has been discussed. Our calculations show that there is a certain filling factor (f=0.55) below which arrangement of square rods in a triangular lattice is superior to the arrangement in a square lattice. A comparison between square and circular cross sectional rods reveals that the former has superior normalized gap width than the latter in case of a square lattice. This situation is switched in case of a triangular lattice. Moreover, a maximum normalized gap width of 0.7 can be achieved for PC plate of square rods embedded in a square lattice and having height 90% of the lattice constant.

Band structures of phononic-crystal plates in the form of a sandwich-layered structure

This study investigates the propagation of Lamb waves in phononic-crystal plates in the form of a sandwich-layered structure. The composite plates are composed of periodic layers bilaterally deposited on both sides of the homogeneous core layer. Using the analyses of the band structures and the transmission spectra, it is revealed that the core layer may induce significant modulations to the lower-order Lamb modes. The modulations are ascribed to the reshaped particle displacement fields of the eigenmodes. Prominently, the core layer made of soft material (rubber) combines the identical eigenmodes of the periodic layers into a pair of asymmetric and symmetric modes in which case the periodic layers vibrate independently. However, the core layer made of hard material (tungsten) or medium hardness material (silicon) couples the periodic layers tightly, in which case the composites vibrate as a whole. In addition, it is found that the phononic band gaps are very sensitive to the thickness of the core layer; this could be indispensable to practical applications such as bandgap tuning.

Phononic plate waves

In the past two decades, phononic crystals (PCs) which consist of periodically arranged media have attracted considerable interest because of the existence of complete frequency band gaps and maneuverable band structures. Recently, Lamb waves in thin plates with PC structures have started to receive increasing attention for their potential applications in filters, resonators, and waveguides. This paper presents a review of recent works related to phononic plate waves which have recently been published by the authors and coworkers. Theoretical and experimental studies of Lamb waves in 2-D PC plate structures are covered. On the theoretical side, analyses of Lamb waves in 2-D PC plates using the plane wave expansion (PWE) method, finite-difference time-domain (FDTD) method, and finite-element (FE) method are addressed. These methods were applied to study the complete band gaps of Lamb waves, characteristics of the propagating and localized wave modes, and behavior of anomalous refraction, called negative refraction, in the PC plates. The theoretical analyses demonstrated the effects of PC-based negative refraction, lens, waveguides, and resonant cavities. We also discuss the influences of geometrical parameters on the guiding and resonance efficiency and on the frequencies of waveguide and cavity modes. On the experimental side, the design and fabrication of a silicon-based Lamb wave resonator which utilizes PC plates as reflective gratings to form the resonant cavity are discussed. The measured results showed significant improvement of the insertion losses and quality factors of the resonators when the PCs were applied.

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.

Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs

We demonstrate theoretically that photons and acoustic phonons can be simultaneously guided and slowed down in specially designed nanostructures. Phoxonic crystal waveguides presenting simultaneous phononic and photonic band gaps were designed in perforated silicon membranes that can be conveniently obtained using silicon-on-insulator technology. Geometrical parameters for simultaneous photonic and phononic band gaps were first chosen for optical wavelengths around 1550 nm, based on the finite element analysis of a perfect phoxonic crystal of circular holes. A plain core waveguide was then defined, and simultaneous slow light and elastic guided modes were identified for some waveguide width. Joint guidance of light and elastic waves is predicted with group velocities as low as c/25 and 180 m/s, respectively.

Temperature effects on the band gaps of Lamb waves in a one-dimensional phononic-crystal plate (L)

This study investigates the temperature-tuned band gaps of Lamb waves in a one-dimensional phononic-crystal plate, which is formed by alternating strips of ferroelectric ceramic Ba(0.7)Sr(0.3)TiO(3) and epoxy. The sensitive and continuous temperature-tunability of Lamb wave band gaps is demonstrated using the analyses of the band structures and the transmission spectra. The width and position of Lamb wave band gaps shift prominently with variation of temperature in the range of 26 °C-50 °C. For example, the width of the second band gap increases from 0.066 to 0.111 MHz as the temperature is increased from 26 °C to 50 °C. The strong shift promises that the structure could be suitable for temperature-tuned multi-frequency Lamb wave filters.

Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs

We discuss the simultaneous existence of phononic and photonic band gaps in a periodic array of holes drilled in a Si membrane. We investigate in detail both the centered square lattice and the boron nitride (BN) lattice with two atoms per unit cell which include the simple square, triangular and honeycomb lattices as particular cases. We show that complete phononic and photonic band gaps can be obtained from the honeycomb lattice as well as BN lattices close to honeycomb. Otherwise, all investigated structures present the possibility of a complete phononic gap together with a photonic band gap of a given symmetry, odd or even, depending on the geometrical parameters.

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.

A Lamb wave source based on the resonant cavity of phononic-crystal plates

In this paper, we propose a Lamb wave source that is based on the resonant cavity of a phononic-crystal plate. The phononic-crystal plate is composed of tungsten cylinders that form square lattices in a silicon plate, and the resonant cavity is created by arranging defects inside the periodic structure. The dispersion, transmission, and displacement of Lamb waves are analyzed by the finite-difference time-domain (FDTD) method. The eigenmodes inside the cavities of the phononic-crystal plate are identified as resonant modes. The fundamental and higher order resonant modes, which vary with the length of cavities, are calculated. By exciting the specific resonant mode in an asymmetric cavity, the 232.40 MHz flexural Lamb wave has a magnified amplitude of 78 times larger than the normal one. Thus, the cavity on the tungsten/silicon phononic-crystal plate may serve as a source element in a microscale acoustic wave device.

Plate-mode waves in phononic crystal thin slabs: mode conversion

We have computed the dispersion curves of plate-mode waves propagating in periodic composite structures composed of isotropic aluminum cylinders embedded in an isotropic nickel background. The phononic crystal has a square symmetry and the calculation is based on the plane-wave expansion method. Along GammaX or GammaM directions, shear-horizontal modes do not couple to the Lamb wave modes which are polarized in the sagittal plane. Whatever the direction of propagation in between GammaX and GammaM, shear-horizontal modes convert to Lamb waves and couple with the flexural and dilatational modes. This phenomenon is demonstrated both through the mode splitting in the lower-order symmetric band structure and through the calculation of all three components of the particle displacements. The phononic case is different from the pure isotropic plate case where shear-horizontal waves decouple from Lamb waves whatever the direction of propagation.

Calculations of Lamb wave band gaps and dispersions for piezoelectric phononic plates using mindlin's theory-based plane wave expansion method

Based on Mindlin's piezoelectric plate theory and the plane wave expansion method, a formulation is proposed to study the frequency band gaps and dispersion relations of the lower-order Lamb waves in two-dimensional piezoelectric phononic plates. The method is applied to analyze the phononic plates composed of solid-solid and airsolid constituents with square and triangular lattices, respectively. Factors that influence the opening and width of the complete Lamb wave gaps are identified and discussed. For solid/solid phononic plates, it is suggested that the filling material be chosen with larger mass density, proper stiffness, and weak anisotropic factor embedded in a soft matrix in order to obtain wider complete band gaps of the lower-order Lamb waves. By comparing to the calculated results without considering the piezoelectricity, the influences of piezoelectric effect on Lamb waves are analyzed as well. On the other hand, for air/solid phononic plates, a background material itself with proper anisotropy and a high filling fraction of air may favor the opening of the complete Lamb wave gaps.

Waveguiding inside the complete band gap of a phononic crystal slab

The propagation of acoustic waves in a square-lattice phononic crystal slab consisting of a single layer of spherical steel beads in a solid epoxy matrix is studied experimentally. Waves are excited by an ultrasonic transducer and fully characterized on the slab surface by laser interferometry. A complete band gap is found to extend around 300 kHz, in good agreement with theoretical predictions. The transmission attenuation caused by absorption and band gap effects is obtained as a function of frequency and propagation distance. Well confined acoustic wave propagation inside a line-defect waveguide is further observed experimentally.

The band gaps of plate-mode waves in one-dimensional piezoelectric composite plates: polarizations and boundary conditions

Theoretical studies are presented for the band structures of plate-mode waves in a one-dimensional (1-D) phononic crystal plate consisting of piezoelectric ceramics placed periodically in an epoxy substrate. The dependences of the widths and starting frequencies of first band gaps (FBG) on the filling fraction and the thickness to lattice pitch ratio are calculated for different polarizations of piezoelectric ceramics under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). We found that the FBG always is broadened by polarizing piezoelectric ceramics, and the FBG widths with SC always are larger than that with OC for the same polarization. Our research shows that there are three critical parameters which determine the FBG: the polarized directions, the filling fraction, and the ratio of the plate thickness to the lattice pitch, respectively. Therefore, we can control the width and starting frequency of the FBG in the engineering according to need by choosing these parameters of the system.