Solid-fluid Phononic Crystal Research Articles

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.

Acoustic invisibility cloak based on two-dimensional solid-fluid phononic crystals

In this paper, we present a cloaking structure based on two-dimensional phononic crystals and show the ability to hiding the object with any size and shape, which fit in the invisibility area, from the acoustic wave, that the operating frequency can be easily changed by changing dimensions of the unit cell and filling factor. The cooperation of two important features of phononic crystals including negative refraction and self-collimation enabled us to design the phononic structure for invisibility purposes. We will show that scattering from the object with the proposed cloak is minimized and the wave will be reconstructed behind the structure, so the shadow effect will also be reduced. In this article, we were able to hide an object from the detector by reducing the scattering, whether the detector is on the source side or on the opposite side.

Phononic Eco-Sensor for Detection of Heavy Metals Pollutions in Water With Spectrum Analyzer

In this research, the numerical analyzing procedure for a two-dimensional (2D) solid-fluid phononic crystal (PnC) demultiplexer is presented. The demultiplexer acts as a selective sensor that could separate three dangerous heavy metals (CuSO4, MgSO4 and MnSO4) with a very low concentration of 1% added in water. The platform consists of a T-model waveguide with three hollow cylinder branches. The PnC demultiplexer is designed with a square arrangement of infinite rods of Stainless steel embedded in the distilled water substrate. To determine the band structure and transmission spectrum, the finite element method has been evaluated. The main waveguides aremade by eliminating one row or one column of scatterers. For each branch, the radius of inclusions is changed to have three different defect branches. Hence, the intended demultiplexer can classify three frequencies in the range of kHz. The demultiplexer showed higher performance parameters for all mixtures. Where, the highest transmission intensity is about 95% for MgSO4-water mixture. The highest sensitivity (66000 Hz.cm3/g) was obtained for theMgSO4-watermixturewhile the highest quality factor (10694) and FOM(2437 cm3/g)were obtained for the CuSO4-water mixture. Themaximum crosstalk (The worst value) among the three channels equals the value of −25.22 dB. The proposed demultiplexer can act as an eco-sensor for detecting water pollutions with higher performance and selectivity.

Phononic crystals for sensing FAMEs with demultiplexed frequencies

A numerical investigation on a solid-fluid phononic crystal as a sensor-demultiplexer is presented in order to detect MeCs, including Fatty Acid Methyl Esters group materials - a kind of vegetable oil and basically similar to the fossil fuels. The proposed sensor includes a Mach-Zehnder waveguide with two cavities in which the MeCs are embedded. The cavities contain the target sample and act as frequency resonator. The PnC sensor consists of a square periodic inclusions of Water embedded in stainless steel substrate. Water and stainless steel have a good contrast in physical properties. Therefore, it is possible to have a wide bandgap. To evaluate the band structure and transmission spectrum, the finite element method (FEM) is utilized. Also, the section of demultiplexer acts as a frequency separator for the target sample and finally each of MeCs including MeC 10:0, 12:0 and 14:0 can be sensed based on the relevant frequency extracted from different outputs. The final waveguides are made by changing the radius of scatterers. For each branch, the radii of inclusions are designed to achieve various defect modes. Finally, the Mach-Zehnder sensor-demultiplexer has ability to divide 83.354, 83.361 and 83.367 KHz for MeCs 10:0, 12:0 and 14:0, respectively. To the best of our knowledge, this study is the first to propose a phononic sensor with different outputs for the respective frequencies of various sample combinations.

Eight-channel acoustic demultiplexer based on solid-fluid phononic crystals with hollow cylinders

We design a novel eight-channel demultiplexer in a solid-fluid phononic crystal structure. The basic structure has been formed by square arrangement of holes filled by water in tungsten background. These holes are embedded in background with filling fraction of 46 %. Generally, the proposed structure consists of nine type line defects for input and output channels. These line defects consist of two types of hollow cylinders. One of them is used in input channel and the other creates output channels. Input waveguide contains an L-branch waveguide which has been made by a row of hollow cylinders of water which is internally filled with tungsten. Each of output channels contains a row of hollow cylinders of Methyl Nonafluorobutyl Ether filled with tungsten. Hollow cylinders have different inner radii in each output waveguides. Hence, each output channels can transmit diverse narrow frequency passbands. We use the finite element method to determine the eigenfrequencies of structure. This structure can separate eight acoustic waves in frequency range between 166.6 kHz and 168.1 kHz. Separation of frequencies is accomplished with high quality factor and the width of frequency spectra between outputs are about 200 Hz. Crosstalk values of the proposed structure show that the eight-channel demultiplexer has efficient performance so that, the worst case of crosstalk value is equal to -26.68 dB.

Band gaps of a fan-like solid-fluid phononic crystal

The vibration problem has a serious impact on modern life. The phononic crystal (PHC) is a periodically arranged composite material, which has good vibration attenuation capability because of its band gap (BG) characteristics. Most of available PHCs are limited to solid structures and the application ranges are limited. In this paper, a new fan-like solid-fluid PHC structure is proposed to supress vibration in special environment. Firstly, the unit cell of fan-like PHC is built and the corresponding band structure is further calulauted by finite element method (FEM). The band structures reveal that this fan-like PHC structure has four BGs below 10000 Hz. In order to illustrate the functionality of the fan-like PHC structure for vibration attenuation, the frequency response function (FRF) of a finite fan-like PHC structure is calculated. The FRF shows that there are strong attenuations in the ranges of BGs. Finally by adjusting the side length of the square inclusion, the influence of the filling rate of the scatterer on BGs is studied. This new PHC provides new ideas for the vibration attenuation of builds at the riverside.

Acoustic Tamm states of three-dimensional solid-fluid phononic crystals

In this work, the existence and propagation of acoustic Tamm states at the interface of air and a face-centered cubic solid-fluid phononic crystal composed of spherical air voids interconnected by cylindrical air channels are demonstrated. Supercell band structure computations via the finite element method reveal surface bands for Tamm states on (100), (110), and (111) surfaces of the phononic crystal. The states decay sharply into the phononic crystal so that only a two-row slab is sufficient to guide them over the respective surfaces without leakage, as confirmed by finite element simulations. In addition, surface wave propagation along the [10] direction of the (100) surface is experimentally demonstrated. Ability to confine the Tamm states in all three dimensions is a key aspect in designing few-layer-thick acoustic circuits. Low material filling fraction of the phononic crystal could be leveraged to realize lightweight all-acoustic systems where either bulk or surface states can be incorporated.

Trapped-mode-induced Fano resonance and acoustical transparency in a one-dimensional solid-fluid phononic crystal

We investigate theoretically and numerically the possibility of existence of Fano and acoustic-induced transparency (AIT) resonances in a simple though realistic one-dimensional acoustic structure made of solid-fluid layers inserted between two fluids. These resonances are obtained by combining appropriately the zeros of transmission (antiresonance) induced by the solid layers and the local resonances induced by the solid or combined solid-fluid layers with surface free boundary conditions. In particular, we show the possibility of trapped modes, also called bound states in continuum, which have recently found a high renewal interest. These modes appear as resonances with zero width in the transmission spectra as well as in the density of states (DOS). We consider three different structures: (i) a single solid layer inserted between two fluids. This simple structure shows the possibility of existence of trapped modes, which are discrete modes of the solid layer that lie in the continuum modes of the surrounding fluids. We give explicit analytical expressions of the dispersion relation of these eigenmodes of the solid layer which are found independent of the nature of the surrounding fluids. By slightly detuning the angle of incidence from that associated to the trapped mode, we get a well-defined Fano resonance characterized by an asymmetric Fano profile in the transmission spectra. (ii) The second structure consists of a solid-fluid-solid triple layer embedded between two fluids. This structure is found more appropriate to show both Fano and acoustic-induced transparency resonances. We provide detailed analytical expressions for the transmission and reflection coefficients that enable us to deduce a closed-form expression of the dispersion relation giving the trapped modes. Two situations can be distinguished in the triple-layer system: in the case of a symmetric structure (i.e., the same solid layers) we show, by detuning the incidence angle $\ensuremath{\theta}$, the possibility of existence of Fano resonances that can be fitted following a Fano-type expression. The variation of the Fano parameter that describes the asymmetry of such resonances as well as their width versus $\ensuremath{\theta}$ is studied in detail. In the case of an asymmetric structure (i.e., different solid layers), we show the existence of an incidence angle that enables to squeeze a resonance between two transmission zeros induced by the two solid layers. This resonance behaves like an AIT resonance, its position and width depend on the nature of the fluid and solid layers as well as on the difference between the thicknesses of the solid layers. (iii) In the case of a periodic structure (phononic crystal), we show that trapped modes and Fano resonances give rise, respectively, to dispersionless flat bands with zero group velocity and nearly flat bands with negative or positive group velocities. The analytical results presented here are obtained by means of the Green's function method which enables to deduce in closed form: dispersion curves, transmission and reflection coefficients, DOS, as well as the displacement fields. The proposed solid-fluid layered structures should have important applications for designing acoustic mirrors and acoustic filters as well as supersonic and subsonic materials.

Excitation of surface waves on one-dimensional solid–fluid phononic crystals and the beam displacement effect

The possibility of surface wave generation by diffraction of pressure waves on deeply corrugated one-dimensional phononic crystal gratings is studied both theoretically and experimentally. Generation of leaky surface waves, indeed, is generally invoked in the explanation of the beam displacement effect that can be observed upon reflection on a shallow grating of an acoustic beam of finite width. True surface waves of the grating, however, have a dispersion that lies below the sound cone in water. They thus cannot satisfy the phase-matching condition for diffraction from plane waves of infinite extent incident from water. Diffraction measurements indicate that deeply corrugated one-dimensional phononic crystal gratings defined in a silicon wafer are very efficient diffraction gratings. They also confirm that all propagating waves detected in water follow the grating law. Numerical simulations however reveal that in the sub-diffraction regime, acoustic energy of a beam of finite extent can be transferred to elastic waves guided at the surface of the grating. Their leakage to the specular direction along the grating surface explains the apparent beam displacement effect.

Tuning the acoustic directional radiation by rotating square rods in two-dimensional phononic crystals

Analysis is given to acoustic directional radiation tuned by rotating square rods in two-dimensional (2D) solid–fluid phononic crystals (PC). The contour line method is introduced which predicts how the acoustic waves propagate at different frequency. As a specific example, for the systems of steel rods with square cross-section in a water host, we employ this approach to the analysis of the directivity successfully. The directional radiation frequency of two lowest bands are studied in this paper. The results show that the directional radiation frequency can be turned in a wide range by rotating the square rods. While the directivity of acoustic propagation keeps unchanged when the acoustic directional radiation frequency is located in the same band. Moreover, PCs exhibit excellent characteristic of single radiation branch as a corner cut off in a finite structure. Our approach may supply a new way to tune the directional radiation frequency.

Guided wave propagation along the surface of a one-dimensional solid–fluid phononic crystal

We consider an arbitrary periodic corrugated surface of a semi-infinite elastic solid that is immersed in a fluid, forming a one-dimensional phononic crystal. We study the existence and the polarization of guided waves that propagate along the interface. A coupled elastic-acoustic variational model is devised to obtain the dispersion of guided waves, which is implemented with a finite element method. It is found that the deeply corrugated interface supports a family of interface waves whose phase velocity decreases as the corrugation depth increases. Among these interface waves, some display an evanescent decay in the fluid that is reminiscent of the Scholte–Stoneley wave, while others propagate in the solid without causing significant pressure variation in the fluid, or cause localized pressure variations only inside the corrugation openings. The obtained results open the way for the study of conversions between bulk and surface waves in solid–fluid phononic crystals, and their use for wave confinement at the surface.

Bandgap calculations of two-dimensional solid–fluid phononic crystals with the boundary element method

A boundary element method (BEM) is presented to compute the bandgaps of two-dimensional (2D) solid–fluid phononic crystals which are composed of square or triangular lattices with arbitrarily shaped scatterers. The system may be either an array of solid scatterers embedded in the fluid matrix or an array of fluid scatterers embedded in a solid matrix. The boundary integral equations of both matrix and scatterer are established for a periodic unit cell. Substituting the quasi-periodic boundary condition (i.e. Bloch–Floquet condition) and the interface conditions, an eigenvalue equation dependent on the Bloch wave vector is derived. The present method takes into account the solid–fluid interface conditions and the transverse wave mode in the solid component which has been proved to be significant. Some typical examples are illustrated to discuss the accuracy of the presented method and analyze the localization mode of the fluid scatterers.

Bandgap calculation of two-dimensional mixed solid–fluid phononic crystals by Dirichlet-to-Neumann maps

A numerical method based on the Dirichlet-to-Neumann (DtN) map is presented to compute the bandgaps of two-dimensional phononic crystals, which are composed of square or triangular lattices of circular solid cylinders in a fluid matrix. The DtN map is constructed using the cylindrical wave expansion in a unit cell. A linear eigenvalue problem, which depends on the Bloch wave vector and involves relatively small matrices, is formulated. Numerical calculations are performed for typical systems with various acoustic impedance ratios of the solid inclusions and the fluid matrix. The results indicate that the DtN-map based method can provide accurate results for various systems efficiently. In particular it takes into account the fluid–solid interface conditions and the transverse wave mode in the solid component, which has been proven to be significant when the acoustic impedance of the solid inclusions is close to or smaller than that of the fluid matrix. For systems with an acoustic impedance of the inclusion much less than that of the matrix, physical flat bands appear in the band structures, which will be missed if the transverse wave mode in the solid inclusions is neglected.

Studies on Band Structures and Wave Localization Phenomenon of the Randomly Disordered Two-Dimensional Solid-Fluid Phononic Crystals

The supercell based plane wave expansion method is used to study the effects of random disorders on the band structures of a two-dimensional (2D) solid-fluid phononic crystal. Phononic systems with steel scatterers embedded in a water matrix are calculated in detail. The radius disorder and location disorder are concerned. The influences of the disorder degree on the first band gap are investigated. The localization phenomenon is discussed by computing the displacement fields in the supercell.

Surface and confined acoustic waves in finite size 1D solid-fluid phononic crystals

Using a Green's function method, we investigate theoretically the eigenmodes of a finite one-dimensional phononic crystal (superlattice) composed of N alternating layers of an elastic solid and an ideal fluid. If the finite superlattice is free of stress on both sides, we show that there are always N-1 modes in the allowed bands whereas there is one and only one mode corresponding to each band gap. This mode is either a surface mode in the band gap or a constant-frequency confined band-edge mode. If the finite superlattice is bounded from one side by a homogeneous fluid whereas the other surface is kept free, then an incident phonon from the fluid is perfectly reflected, however this reflection takes place with a large delay time if the frequency of the incident phonon coincides with the eigenfrequency of a surface mode

Wavelet-based method for calculating elastic band gaps of two-dimensional phononic crystals

A wavelet-based method is developed to calculate elastic band gaps of two-dimensional phononic crystals. The wave field is expanded in the wavelet basis and an equivalent eigenvalue problem is derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method is applied to a binary system. We first compute the band gaps of Au cylinders in an epoxy host. The advantages of the wavelet-based method are discussed in regard with the well-known plane-wave expansion method. Then the method is used to compute the band gaps of Au cylinders in a soft rubber with elastic constant ${10}^{6}$ times lower than that of Au. The convergence tests show that the wavelet-based method can reduce the Gibbs effect to a certain extent. These advantages make it possible for easy calculations of band structures of mixed solid-fluid phononic crystals where the traditional plane wave method encounters difficulties. In addition, the adaptability of wavelets makes the method possible for efficient band gap computations of more complex phononic structures.