Exterior cloaking with active sources in two dimensional acoustics

We cloak a region from a known incident wave by surrounding the region with three or more devices that cancel out the field in the cloaked region without significantly radiating waves. Since very little waves reach scatterers within the cloaked region, the scattered field is small and the scatterers are for all practical purposes undetectable. The devices are multipolar point sources that can be determined from Green's formula and an addition theorem for Hankel functions. The cloaking devices are exterior to the cloaked region.     

Design and analysis of nonlinear-transformation-based broadband cloaking for acoustic wave propagation

A coordinate-transformation method can be used to design invisibility cloaks for many types of waves, including acoustic waves. The traditional method for designing a cloak depends on a transformation from a virtual space to a physical space. Previous acoustic cloaks that are mainly designed with linear-transformation-based acoustics have drawbacks that acoustic wave trajectories in the cloaks cannot be controlled and tuned. This work uses a nonlinear mapping from a ray trajectory perspective to construct acoustic cloaks with tunable non-singular material properties. Use of a ray trajectory equation is a straightforward and alternate way to study propagation characteristics of different types of waves, which allows more flexibility in controlling the waves. A broadband cylindrical cloak for acoustic waves in an inviscid fluid is realized with layered non-singular, homogeneous, and isotropic materials based on a nonlinear transformation. Some advantages and improvements of the invisibility nonlinear-transformation cloak over a traditional linear-transformation cloak are analyzed. The invisibility capability of the nonlinear-transformation cloak can be tuned by adjusting a design parameter that is shown to have influence on the acoustic wave energy flowing into the region inside the cloak. Numerical examples show that the nonlinear-transformation cloak is more effective for making a domain undetectable by acoustic waves in an inviscid fluid and shielding acoustic waves from outside the cloak than the linear-transformation cloak in a broad frequency range. The methodology developed here can be used to design nonlinear-transformation cloaks for other types of waves.     

Transformation elastodynamics and cloaking for flexural waves

The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general form of the partial differential equation is not invariant with respect to the cloaking transformation. The significant result of this paper is the analysis of the transformed equation and its interpretation in the framework of the linear theory of pre-stressed plates. The paper provides a formal framework for transformation elastodynamics as applied to elastic plates. Furthermore, an algorithm is proposed for designing a broadband square cloak for flexural waves, which employs a regularised push-out transformation. Illustrative numerical examples show high accuracy and efficiency of the proposed cloaking algorithm. In particular, a physical configuration involving a perturbation of an interference pattern generated by two coherent sources is presented. It is demonstrated that the perturbation produced by a cloaked defect is negligibly small even for such a delicate interference pattern.     

Transformational cloaking from seismic surface waves by micropolar metamaterials with finite couple stiffness

Transformational elastodynamics can be used to protect sensitive structures from harmful waves and vibrations. By designing the material properties in a region around the sensitive structure, a cloak, the incident waves can be redirected as to cause minimal or no harmful response on the pertinent structure. In this paper, we consider such transformational cloaking built up by a suitably designed metamaterial exhibiting micropolar properties. First, a theoretically perfect cloak is obtained by designing the properties of an (unphysical) restricted micropolar material within the surrounding medium. Secondly, we investigate the performance of the cloak under more feasible design criteria, relating to finite elastic parameters. In particular, the behavior of a physically realizable cloak built up by unrestricted micropolar elastic media is investigated. Numerical studies are conducted for the case of buried as well as surface breaking structures in 2D subjected to incident Rayleigh waves pertinent to seismic loading. The studies show how the developed cloaking procedure can be utilized to substantially reduce the response of the structure. In particular, the results indicate the performance of the cloak in relation to constraints on the elastic parameters.     

Cloaking of a circular cylindrical elastic inclusion from antiplane elastic waves and resonance effects

Cloaking of a circular cylindrical elastic inclusion embedded in a homogeneous linear isotropic elastic medium from antiplane elastic waves is studied. The transformation or change-of-variables method is used to determine the material properties of the cloak and the homogenization theory of composites is used to construct a multilayered cloak consisting of many bi-material cells. The large system of algebraic equations associated with this problem is solved by using the concept of multiple scattering with wave expansion coefficient matrices. Numerical results for cloaking of an elastic inclusion and a rigid inclusion are compared with the case of a cavity. It is found that while the cloaking patterns for the three cases are similar, the major difference is that standing waves are generated in the elastic inclusion and the multilayered cloak cannot prevent the motion inside the elastic inclusion, even though the cloak seems nearly perfect. Waves can penetrate into and cause vibrations inside the elastic inclusion, where the amplitude of standing waves depend on the material properties of the inclusion but are very much reduced when compared to the case when there is no cloak. For a prescribed mass density, the displacements inside the elastic cylinder decrease as the shear modulus increases. Moreover, the cloaking of the elastic inclusion over a range of wavenumbers is also investigated. There is significant low frequency scattering even if the cloak consists of a large number of layers. When the wavenumber increases, the multilayered cloak is not effective if the cloak consists of an insufficient number of layers. Resonance effects that occur in cloaking of elastic inclusions are also discussed.     

用各向同性材料实现宽带声波功能器件设计

利用坐标变换的方法并结合保角映射技术,论文介绍了一种利用常规的各向同性材料来设计声波器件的方法.基于此理论,设计了二维声波隐身斗篷,并进行有限元模拟,证明了该器件的有效性.另外由于设计中没有利用材料共振的性质,所以器件是宽带有效的.该方法将有助于拓宽声波功能器件的设计,并为实验验证声波器件提供了可能.     

Assembling hydrodynamic cloaks to conceal complex objects from drag

Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces.     

条形平板中裂纹识别的遗传算法

研究条形平板中平行于上下边界的单一裂纹的识别问题。给出了当一声波入射这一条形平板时，裂纹参数与反射、透射系数之间的关系式，并应用遗传算法对裂纹进行了定量识别。计算结果表明本文给出的方法具有较好的识别精度。     

Antiplane elastic wave cloaking using metamaterials,homogenization and hyperelasticity

We consider the problem of how to cloak objects from antiplane elastic waves using two alternative techniques. The first is the use of a layered metamaterial in the spirit of the work of Torrent and Sanchez-Dehesa (2008) who considered acoustic cloaks, motivated by homogenization theories, whilst the second is the use of a hyperelastic cloak in the spirit of the work of Parnell et al. (2012). We extend the hyperelastic cloaking theory to the case of a Mooney–Rivlin material since this is often considered to be a more realistic constitutive model of rubber-like media than the neo-Hookean case studied by Parnell et al. (2012), certainly at the deformations required to produce a significant cloaking effect. Although not perfect, the Mooney–Rivlin material appears to be a reasonable hyperelastic cloak. This is clearly encouraging for applications. We quantify the effectiveness of the various cloaks considered by plotting the scattering cross section as a function of frequency, noting that this would be zero for a perfect cloak.     

Acoustic scattering from baffled membranes that are backed by elastic cavities

An elastic membrane backed by a fluid-filled cavity in an elastic body is set into an infinite plane baffle. A time harmonic wave propagating in the acoustic fluid in the upper half-space is incident on the plane. It is assumed that the densities of this fluid and the fluid inside the cavity are small compared with the densities of the membrane and of the elastic walls of the cavity, thus defining a small parameter . Asymptotic expansions of the solution of this scattering problem as →0, that are uniform in the wave number k of the incident wave, are obtained using the method of matched asymptotic expansions. When the frequency of the incident wave is bounded away from the resonant frequencies of the membrane, the cavity fluid, and the elastic body, the resultant wave is a small perturbation (the “outer expansion”) of the specularly reflected wave from a completely rigid plane. However, when the incident wave frequency is near a resonant frequency (the “inner expansion”) then the scattered wave results from the interaction of the acoustic fluid with the membrane, the membrane with the cavity fluid, and finally the cavity fluid with the elastic body, and the resulting scattered field may be “large”. The cavity backed membrane (CBM) was previously analyzed for a rigid cavity wall. In this paper, we study the effects of the elastic cavity walls on modifying the response of the CBM. For incident frequencies near the membrane resonant frequencies, the elasticity of the cavity gives only a higher order (in ) correction to the scattered field. However, near a cavity fluid resonant frequency, and, of course, near an elastic body resonant frequency the elasticity contributes to the scattered field. The method is applied to the two dimensional problem of an infinite strip membrane backed by an infinitely long rectangular cavity. The cavity is formed by two infinitely long rectangular elastic solids. We speculate on the possible significance of the results with respect to viscoelastic membranes and viscoelastic instead of elastic cavity walls for surface sound absorbers.     

Analytical study of spherical cloak/anti-cloak interactions

The intriguing concept of “anti-cloaking” has been recently introduced within the framework of transformation optics (TO), first as a “countermeasure” to invisibility-cloaking (i.e., to restore the scattering response of a cloaked target), and more recently in connection with “sensor invisibility” (i.e., to strongly reduce the scattering response while maintaining the field-sensing capabilities). In this paper, we extend our previous studies, which were limited to a two-dimensional cylindrical scenario, to the three-dimensional spherical case. More specifically, via a generalized (coordinate-mapped) Mie-series approach, we derive a general analytical full-wave solution pertaining to plane-wave-excited configurations featuring a spherical object surrounded by a TO-based invisibility cloak coupled via a vacuum layer to an anti-cloak, and explore the various interactions of interest. With a number of selected examples, we illustrate the cloaking and field-restoring capabilities of various configurations, highlighting similarities and differences with respect to the cylindrical case, with special emphasis on sensor-cloaking scenarios and ideas for approximate implementations that require the use of double-positive media only.     

Design of elliptical underwater acoustic cloak with truss-latticed pentamode materials

Pentamode acoustic cloak is promising for underwater sound control due to its solid nature and broadband efficiency, however its realization is only limited to simple cylindrical shape. In this work, we established a set of techniques for the microstructure design of elliptical pentamode acoustic cloak based on truss lattice model, including the inverse design of unit cell and algorithms for latticed cloak assembly. The designed cloak was numerically validated by the well wave concealing performance. The work proves that more general pentamode acoustic wave devices beyond simple cylindrical geometry are theoretically feasible, and sheds light on more practical design for waterborne sound manipulation.     

Plasmonic cloaking and scattering cancelation for electromagnetic and acoustic waves

One popular approach to cloaking objects from electromagnetic waves at moderately long wavelengths is the scattering cancelation technique. This mechanism is based on the use of a single homogeneous thin layer to cover an object of interest in order to provide scattering suppression in a given frequency band. This approach has also been recently extended to acoustic waves. This paper provides an investigation of the physical nature of scattering cancelation by a uniform thin layer for both electromagnetic and acoustic waves in inviscid fluids. Two distinct scattering cancelation regions are obtained within the available parameter space: a non-resonant plasmonic cloaking region and an anti-resonant cloaking region, which are identified and compared in both the electromagnetic and acoustic domains. Although both types of operations allow for the suppression of the dominant scattering orders, the resulting internal fields and physical functionality of the cloaks present distinct differences between the two domains. We discuss analogies and differences between these functionalities and their implications in electromagnetic and acoustic cloaking problems, with an insight into their practical implementation.     

基于贴体网格的VOF方法数模流场研究

提出了一种基于VOF方法的模拟具有复杂边界形状结构物附近流场的新算法,BFC—SIMPLE—VOF算法。采用坐标变换方法实现了任意复杂区域的结构化网格划分,在贴体网格下对二维不可压缩粘性流体的控制方程进行了离散。提出了基于交错网格的修正SIMPLE算法来迭代求解压力一速度场,修正了贴体坐标下的界面跟踪方法（VOF方法）...     

水下声波传播过程的时域间断Galerkin有限元方法

本文构建了声压波动方程的改进时域间断Galerkin有限元方法.传统时域连续有限元方法在计算高梯度、强间断特征水中声波传播问题时往往会出现虚假数值振荡现象,这些数值振荡会影响正常波动的计算精度.为了解决这一问题,本文通过引入人工阻尼的方式构建了改进的时域间断Galerkin有限元方法,并针对具有高梯度、强间断特征的多障...     

Resonant reflection of a surface acoustic wave from strip waveguides

A numerical study is performed of the oblique reflection of a surface acoustic wave from a strip of finite width deposited on the surface of a half-infinite substrate. The finite element method is used. If the strip–substrate contact supports waveguide modes with the velocity exceeding the surface wave velocity on the free surface of the substrate, then an interval of angles of incidence exists where the surface wave efficiently excites a waveguide mode. The excitation of the waveguide mode is accompanied by a singular behavior of the reflection and the transmission coefficients. The dependence of the magnitude and the phase of the coefficients on the angle of incidence, the frequency, the width and the thickness of the strip is examined. In particular, it is found that the magnitude of the reflection coefficient abruptly almost vanishes and abruptly increases almost to unity within the resonance interval of angles of incidence.     

Gas-dynamic approach in the nonlinear theory of ion acoustic waves in a plasma: An exact solution

An exact solution of the problem of the acoustic wave structure in a plasma is obtained. Both plasma component are treated as gases with specified initial temperatures and adiabatic exponents. The system of equations describing the wave profile is solved using an original method consisting of reducing the system to the Bernoulli equation. A numerical example of the obtained general solution of the problem of the wave profile for arbitrary parameters is given. Curves are constructed that bound the region of existence of a stationary solitary ion acoustic wave in the parameter space. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 3–11, September–October, 2007.     

Analysis of comb transducers with sliding teeth

Ultrasonic comb transducer generates surface acoustic waves on an elastic substrate by periodic traction exerted by its vibrating periodic teeth on the substrate surface. In this paper, the comb teeth are actually sliding elastic spacers between an acoustic buffer and the substrate. The incident wave in acoustic buffer scatters on periodic spacers producing interface waves in the system which transform into Rayleigh waves at the transducer edges. The full-wave theory of interface wave generation is presented, concluded by efficiency estimation of transformation of the incident wave into the surface wave in the substrate and of the surface waves back to bulk waves in the acoustic buffer. Numerical examples presented for all aluminum substrate, buffer and teeth show the 11-teeth comb combined efficiency for generation and detection on the level of ?40 dB for optimized teeth height.     

纤维增强复合材料热隐身斗篷设计

基于变换热动力学原理可获得具有热隐身性能的隐身结构(隐身斗篷)所需要的材料性质的空间分布。但这种材料性质的复杂分布形式以及局部热传导性能无限大等极值性质需求,使得隐身斗篷设计的实现非常困难,需要研究基于常规材料的隐身斗篷设计。本文基于常规材料的热隐身结构实现问题,提出了基于纤维增强复合材料圆环结构的实现热隐身的结构形式。首先,基于变换热动力学原理获得热隐身所需的热传导系数沿半径方向的变化规律;进而,通过设计复合材料不同位置的纤维铺设方式(含量和铺设方向)实现热隐身对材料性能的需求。选择金属银作为纤维,空气作为基体,设计出了具有热隐身性能的复合材料圆环结构纤维含量和铺设方向沿径向的分布方案。对该设计方案进行数值仿真,结果显示所设计的隐身结构具有良好的热隐身性能。由于设计方案基于常规材料,因此具有容易实现的优点。     

二维激波与剪切层相互作用的直接数值模拟研究

采用五阶weighed esseritially non-oscillatory (WENO) 格式和三阶total variation diminishing (TVD) Runge-Kutta 格式, 通过求解二维非定常Navier-Stokes 方程, 直接数值模拟了激波与剪切层相互作用, 目的在于揭示激波与剪切层相互作用过程中噪声产生的机理. 研究发现:(1) 当入射激波穿过剪切层时, 剪切层中心位置向下层区域偏移;(2) 入射激波穿过剪切层产生小激波, 在小激波与剪切层接触点处产生声波并向外辐射;(3) 反射激波穿过剪切层后形成了分段弧状激波;(4) 当反射激波穿过剪切层时, 激波在鞍点处泄漏并向外辐射声波, 这是一种激波泄漏机制.