Wave mixing in coupled phononic crystals via a variable stiffness mechanism

We investigate wave mixing effects in a phononic crystal that couples the wave dynamics of two channels – primary and control ones – via a variable stiffness mechanism. We demonstrate analytically and numerically that the wave transmission in the primary channel can be manipulated by the control channel's signal. We show that the application of control waves allows the selection of a specific mode through the primary channel. We also demonstrate that the mixing of two wave modes is possible whereby a modulation effect is observed. A detailed study of the design parameters is also carried out to optimize the switching capabilities of the proposed system. Finally, we verify that the system can fulfill both switching and amplification functionalities, potentially enabling the realization of an acoustic transistor.     

The band gap and transmission characteristics investigation of local resonant quaternary phononic crystals with periodic coating

In this article, the investigation of the Lamb wave propagation in two-dimensional phononic crystals (PCs) composed of an array of periodic coating on a thin plate is presented. Compared with the traditional PCs usually consist of cylindrical scatters with uniform coatings in their exterior structure, the newly exterior coating structures with periodic alternant arrangement of two different materials are proposed. The band structures are calculated using finite element method. We discover that a complete band gap can be exhibited at low frequency. Furthermore, for a finite PCs plate, the computed transmission and resonance spectra shown an evident resonance nature which can be directly related to formation of the low-frequency gaps. The effects of different material parameters and arrangement mode of coating on the acoustic energy transmission and attenuation are also studied. Finally, the experimental transmission spectrum of the periodic coating PCs are also presented and compared with the numerical results. This study will provide useful support to the design of tuning band gaps and isolators in the low-frequency range.     

Negative refraction and imaging of acoustic waves in a two-dimensional square chiral lattice structure

The negative refraction behavior and imaging effect for acoustic waves in a kind of two-dimensional square chiral lattice structure are studied in this paper. The unit cell of the proposed structure consists of four zigzag arms connected through a thin circular ring at the central part. The relation of the symmetry of the unit cell and the negative refraction phenomenon is investigated. Using the finite element method, we calculate the band structures and the equi-frequency surfaces of the system, and confirm the frequency range where the negative refraction is present. Due to the rotational symmetry of the unit cell, a phase difference is induced to the waves propagating from a point source through the structure to the other side. The phase difference is related to the width of the structure and the frequency of the source, so we can get a tunable deviated imaging. This kind of phenomenon is also demonstrated by the numerical simulation of two Gaussian beams that are symmetrical about the interface normal with the same incident angle, and the different negative refractive indexes are presented. Based on this special performance, a double-functional mirror-symmetrical slab is proposed for realizing acoustic focusing and beam separation.     

Harvesting vibrations via 3D phononic isolators

We report on the existence of unidirectional phononic band gaps that may span over extended regions of the Brillouin zone and can find application in trapping elastic (acoustic) waves in properly designed multilayered 3D structures. Phononic isolators operate as a result of asymmetrical wave transmission through a slab of a crystallographic phononic structure with broken mirror symmetry. Due to the use of lossless materials in the crystal, the absorption rate is dramatically enhanced when the proposed isolator is placed next to a vibrational harvesting cell.     

Elastic properties of finite three-dimensional solid phononic-crystal slabs

We study theoretically, by means of layer-multiple scattering techniques, the propagation of elastic waves through finite slabs of phononic crystals consisting of metallic spheres in polyester matrix, embedded in air. We focus on the study of modes localized on the surfaces of the structure, investigating the physical parameters which influence and determine their appearance. Our results reveal the existence of absolute phononic frequency gaps in these finite structures, and point out the possibility, under an appropriate choice of the parameters, of tunable regions of frequency free of propagating and/or surface-localized modes. This could be very useful in the design of devices related to frequency filtering, waveguiding, etc.     

Effect of defect configuration on the localization of phonons in two-dimensional phononic crystals

Effects of defect location on the defect frequency and the localization of phonons are investigated in two novel kinds of model, created by moving the location of the native cylinder and inserting an ad-cylinder in the central cellular respectively. The results show that the defect frequency in Model 1 is only related to the distance, while in Model 2, is related not only to the distance, but also to the moving direction. From the pressure distribution, obvious localization phenomenon is found. The position and shape of the localized energy are varied with the position of the defect.     

Frequency-dependent acoustic energy focusing in hexagonal ceramic micro-scaffolds

Acoustic properties of an additive-manufactured SiC scaffold with hexagonal symmetry fabricated by the robocasting method are studied both numerically and experimentally. The numerical analysis is based on the finite element method (FEM) using Bloch boundary conditions. The calculations show both angular and frequency dispersion of the acoustic waves with wavelengths comparable to the spacing between the rods, i.e., on a millimeter scale, indicating interesting acoustic properties in the MHz range. The dispersion character leads to focusing of the energy propagation into the directions of the rods of the hexagonal structure. This is illustrated by modal-based calculations of the propagation of longitudinal and out-of-plane shear wave packets with a dominant wavelength. The experimental analysis consists of two steps, the measurement of the resonant spectrum and shear wave propagation character. The measured resonant spectrum is in good agreement with the one calculated using numerically obtained low-frequency properties of the structure, also showing the quality of the overall manufactured structure. The time-domain measurement shows significant changes in the energy propagation between low and high frequencies, as predicted by FEM calculations.     

Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers

We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach for finding the dispersion curves associated with Floquet–Bloch waves through an infinite array of scatterers. The approach lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on topical examples from topological wave physics.     

Band gap structures for viscoelastic phononic crystals based on numerical and experimental investigation

Many materials used as phononic crystals (PCs) are viscoelastic one. It is believed that viscosity results in damping to attenuate wave propagation, which may help to tune the defect modes or band gaps of viscoelastic phononic crystals. To investigate above phenomenon, firstly, we have extended the application of boundary element method (BEM) to the study of viscoelastic phononic crystals with and without a point defect. A new developed BEM within the framework of Bloch theory can easily deal with viscoelastic phononic crystals with arbitrary shapes of the scatterers. Experimental methods have been put forward based on the self-made viscoelastic phononic crystals. Verified by the experimental results, systematic comprehensive parametric studies on the band structure of viscoelastic phononic crystals with varying factors (final–initial value ratio, relaxation time, volume fraction of scatterers, shapes of scatterers) have been discussed by the numerical simulation. To further address the possibility to change the defect modes, the band structure of viscoelastic phononic crystals with a point defect has been studied based on the numerical and experimental methods. From present research work, it can be found that by adjusting the two viscous parameters combined with considering the effect of volume fraction and shapes, a wider and lower initial forbidden frequency or lower and higher quality factor resonant frequency can be obtained.     

局域共振单元与薄膜复合声子晶体板结构的低频降噪

提出了一种局域共振单元复合声子晶体板结构,并结合有限元对晶体板结构的带隙特性、隔声性能进行了分析.结果表明,共振带隙的产生是由共振单元与板中传播的弹性波相互耦合造成的,耦合强度直接影响共振频率和带隙宽度,隔声效果与薄膜的厚度直接相关.通过改变薄膜的厚度可以将隔声效果调节到满足机舱飞行员正常驾驶的要求.该结构在200dB以下具有良好的隔振效果,最大隔声量达到150dB.该研究为获得良好的隔声效果提供了理论支持,在航空发动机减振降噪方面具有潜在的应用前景.