多个椭圆柱波浪力的一种解析解

波浪在大尺寸结构表面产生不可忽略的散射波, 该散射波在多柱体体系中继续传播, 并在同体系中的其他柱体上产生高次散射波. 本文基于椭圆坐标系和绕射波理论首先推导了波浪作用下椭圆单柱体产生的散射波压力公式, 随后考虑该散射波在多柱体系中的传播, 将其视为第二次入射波, 推导出柱体上第二次散射波压力公式, 同理可以推导出高次散射波压力公式, 最后得到椭圆多柱体波浪力解析解, 并用数值解验证了本文解析方法的正确性. 本文以双柱体和四柱体体系为例, 分析了不同参数(波数、净距、波浪入射角度等)下, 高次散射波对柱体上波浪作用的影响. 结果表明: 波数较大的情况下, 高次散射波引起柱体上的波浪力不能忽略; 结构间距较大的情况下, 虽然高次波的作用有减小的趋势但仍然明显; 高次散射波来自多个柱体对入射波的散射, 柱体数目的增加后, 高次波的影响会增加, 结构所受的高次波作用因参数变化而起的波动会变剧烈; 高次波对上游柱体波浪力的贡献较对下游柱体的贡献大.      

Scattering of sound waves by smooth convex elastic cylindrical shells

A plane acoustic wave travelling through an infinite inviscid fluid is scattered by an empty thin shell. A simple approximate but explicit formula is proposed to describe the behaviour of the acoustic pressure scattered by the shell, at an observation point situated in the far field, for backscattering. Only the contributions to the scattered field of specularly reflected, refracted and re-radiated wave are taken into account. The domain of validity of the proposed approximation is given. An example of the frequency dependent calculation is presented for the case of an Armco iron shell with elliptical cross shape immersed in water.     

Sound scattering and its cancellation by an elastic spherical shell in free space and near a free surface

Sound scattering by an elastic spherical shell is analysed using linear acoustics and linear structural dynamics. It is suggested to utilize the shell’s structural dynamics to reduce or even eliminate the scattered sound field, thus making it practically acoustically invisible. This can be achieved using a prescribed external pressure distribution acting on the shell’s wall. Exact analytical solutions are found for that external pressure distribution, eliminating the scattered wave when the sphere is in free space or near a free surface and is subject to an incoming planar monochromatic sound wave. The latter is assumed to propagate in a direction perpendicular to the free surface (if it exists). The case of a few pressure-actuators acting on the shell’s wall is also modelled and an optimal solution which reduces the sound scattering by these actuators is found. An aluminium shell of 1 m radius and 5 mm thickness, situated in fresh water is analysed for sound frequencies of up to 10 kHz. The scattered wave fields are presented as well as the external pressure distributions that eliminate these scattered sound field, i.e. achieving acoustic cloaking. Significant reduction in the scattered wave energy and the target strength of more than 10 dB are also realized using a few pressure-actuators as long as the distance between the actuators is no more than three times the incident wave length for the investigated cases.     

层状介质中双硬币形裂纹对扭转波的散射──远场解

本文在[1]的基础上,研究了多层介质中由于双硬币形裂纹引起的对弹性扭转波散射的远场特性.文中应用Hankel积分变换和Abel变换,将问题最后归结为求解一组第二类Fredholm积分方程,并导出了用积分形式给出的散射位移场表达式.最后运用围道积分技术和渐近分析的方法,对散射位移场在远离裂纹时的主要性态进行了分析讨论.     

Characteristic relations of flow birefringence

The general problems of the flow-induced birefringence in liquids have been presented and discussed in Part 1 of this paper, in which some particular responses of an aqueous solution of NGS 1828 were presented, namely, the pertinent mechanical responses and the birefringence responses in transmitted radiation. This paper presents the optical responses of NGS 1828 observed in the scattered radiation. It is shown that the scattered-light techniques can become a powerful and indispensable tool of flow-birefringence techniques, if the actual patterns of light scattering are taken into account. Proof is given that the light scattering and the related birefringence cannot be described by Rayleigh's mathematical model of scattering (Part 1, Ref. 51). The optical effects of the modulation of the primary beam and the scattered beam, called scattered primary isochromatics and scattered secondary isochromatics, are described in terms of the parameters of the system. A practical example is presented. Samples of typical recordings of light-intensity modulation by typical flow patterns are given in the form of scattered primary and secondary isochromatics and integrated isochromatics. One type of intensity modulation enables the determination of shear-strain rate at an interior point in the flow field. Using the determined shear-strain rates at the interior points, a velocity profile along the axis of symmetry of a rectangular-conduit flow was obtained. The results so obtained were satisfactory when compared with the results of direct volumetric measurement. The other type of intensity modulation reveals the nonuniform distribution of birefringence along the path of the transmitted light in the rectangular-conduit flow. The results presented in Part 1 of this paper, are complementary to the results presented below.     

A dual-observation method for determining photoelastic parameters in scattered light

A dual-observation method is developed for determining photoelastic parameters in scattered light. Using this method, the intensities of scattered light along two directions of observation, making an angle of 45 deg in a plane normal to the beam, are recorded simultaneously without rotation of either the beam or the model. Photoelastic parameters are evaluated from these records. The theory of the method, the apparatus and techniques, as well as an illustrative experiment, are reported.     

The scattered energy around a circular hole by SH wave in anisotropic media

A new approach based on complex function for solving the SH-wave scattering problem around a circular hole in an anisotropic media is desribed in this paper. It is found that the scattered energy depends on the incident wave number and the hole radius. Finally, some numerical results of scattered energy of a circular hole in an anisotropic media are given.The project has been supported by National Natural Science Foundation of China.     

An inversion integral for crack-scattering data

The inverse problem of determining the size, shape and orientation of a flat crack from high-frequency far-field elastic waves scattered by the crack is investigated. The results show that desired information on a crack can be obtained from the first arriving scattered longitudinal waves only. It is shown that an approximate high-frequency solution to the direct problem, based on physical elastodynamics, yields an expression for the scattered far-field of longitudinal motion which suggests a solution to the inverse problem by application of Fourier-type inversion integrals to scattering data. Two kinds of inversion integrals are examined. The inversion problem becomes relatively simple if some a-priori information is available, either on the orientation of the plane of the crack or on a plane of symmetry. The method of inversion is verified for a flat crack of elliptical shape. Some computational technicalities are discussed, and the method is also applied to experimental scattering data.     

On the plane-wave extinction cross-section of an obstacle

Summary A time-harmonic plane electromagnetic wave is incident upon an obstacle of finite dimensions. The properties of the obstacle are such that electromagnetic power is both absorbed and scattered. A close relation exists between the extinction cross-section of the obstacle and the amplitude and phase of the scattered wave in the direction of propagation of the incident wave. The exact form of this relation, the cross-section theorem, is proved by making use of an explicit representation of the scattered field. The result is valid for a plane wave with arbitrary elliptic polarization. Finally, a similar relation for the scattering of sound waves is given.     

A new fundamental diagram theory with the individual difference of the driver’s perception ability

Based on the driver’s individual difference of the driver’s perception ability, we in this paper develop a new fundamental diagram with the driver’s perceived error and speed deviation difference. The analytical and numerical results show that the speed-density and flow-density data are divided into three prominent regions. In the first region, the speed-density and flow-density data are scattered around the equilibrium speed-density and flow-density curves of the classical fundamental diagram theory, where the widths of these scattered data are very narrow and slightly increase with the real density (i.e., the scattered data appear as two thicker lines); the running speed is approximately equal to the free flow speed and the real flow approximately linearly increases with the real density. In the second region, the speed-density and flow-density data are scattered widely in a two-dimensional region, but the shapes of these widely scattered data are related to the properties of the driver’s perceived error and speed deviation difference. In the third region, the scattered speed-density and flow-density data appear but these scattered data will quickly degenerate into the equilibrium speed-density and flow-density curves with the increase of the real density. Finally, the numerical results illustrate that the new fundamental diagram theory also produces the F-line, U-line, and L-line. The shapes of the scattered data, F-line, U-line, and L-line are relevant to the properties of the driver’s perceived error and speed deviation difference. These results are qualitatively accordant with the real traffic, which shows that the new fundamental diagram theory can better describe some complex traffic phenomena in the real traffic system. In addition, the above results can help us to further explain why the widely scattered speed-density and flow-density data appear in the real traffic system and better understand the effects of the driver’s individual difference on traffic flow.     

Reciprocity and power-flow theorems for the scattering of plane elastic waves in a half space

In this paper we present six field-reciprocity relations, and an additional six power-reciprocity relations for the far-zone scattered field if time-harmonic plane elastic waves are incident upon an obstacle in a half space. The incident waves are successively selected as to be either a P-wave, a SV-wave or a Rayleigh surface wave, each propagating in a prescribed direction. In the derivations we employ an explicit integral representation for the far-zone scattered field amplitude. The latter is obtained by expanding the half-space Green's displacement tensor in the far-zone region. Then, starting with the general Betti-Rayleigh theorem, the reciprocity identities are systematically inferred by inspection. We also present energy-conservation relations due to a single incident P-, SV- or Rayleigh wave.     

Study of basic patterns of light scattering in aqueous solution of milling yellow

Basic characteristics of light scattering in an aqueous solution of milling yellow are presented in a form of relations between the scattered radiant power, states of polarization of primary radiation and scattered radiation, observation angle and azimuthal angle.It is found that the state of polarization of the scattered light in milling-yellow solution can be utilized as a foundation of reliable photoelastic scattered-light techniques for flow analysis. However, Rayleight's model of scattering is nnt directly applicable.Paper contains data on major parameters of light scattering, knowledge of which is necessary to correctly design flowbirefringence experiments. In particular, these data can be used to develop a set of conditions and constraints for designing of particular scattered-light flow-birefringence experiments, and of corresponding transfer functions.     

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.     

The scattering of a scalar beam from isotropic and anisotropic two-dimensional randomly rough Dirichlet or Neumann surfaces: The full angular intensity distributions

By the use of Green’s second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral equations for the scattering amplitudes are solved nonperturbatively by a rigorous computer simulation approach. The results of these calculations are used to calculate the full angular distribution of the mean differential reflection coefficient. For isotropic surfaces, the results of the present calculations for in-plane scattering are compared with those of earlier studies of this problem. The reflectivities of Dirichlet and Neumann surfaces are calculated as functions of the polar angle of incidence, and the reflectivities for the two kinds of surfaces of similar roughness parameters are found to be different. For an increasing level of surface anisotropy, we study how the angular intensity distributions of the scattered waves are affected by this level. We find that even small to moderate levels of surface anisotropy can significantly alter the symmetry, shape, and amplitude of the scattered intensity distributions when Gaussian beams are incident on the anisotropic surfaces from different azimuthal angles of incidence.     

Scattering of an incident wave from an interface separating two fluids

We consider the scattering of an incident pulse from an interface separating two fluids. The interface can be either an elastic membrane or a two-fluid interface with surface tension. By considering the limit where the ratio of acoustic wavelength to the surface wavelength is small, we systematically derived a boundary condition relating the scattered wave and the surface deformation. This condition is local and can be used to derive a partial differential equation for the deformation of the interface. This equation includes the contribution of the acoustic waves induced by the motion of the interface and once it is solved it can be used to determine the scattered field. At leading order in our analysis we find the plane wave approximation. The addition of the next order terms results in an on surface condition equivalent to that of Kriegsmann and Scandrett. We present numerical calculations to show that our results are in good agreement with the exact numerical solution as well as that of Kriegsmann and Scandrett. Physical situations where the conditions of our analysis are valid are presented.     

Removal of guided waves from seismic data in laterally varying media

A major source of unwanted signals in seismic data recorded for geophysical exploration is the presence of guided waves which are scattered near the surface of the earth. These waves do not contain information on the structure of the deeper subsurface and should therefore be removed. In this paper we derive a method for removing this type of waves based on a modal expansion. The problem of finding an appropriate scatterer distribution is formulated as a minimization problem. We apply the method to simulated data and watertank data, and find that the scattered guided waves are strongly attenuated and that the reflections of interest (from deeper layers) are not affected.     

THE MEAN MOTION RESONANCE OF THE KUIPER BELT OBJECTS

研究柯伊伯带小行星对理解太阳系的起源和演化有着重要的意义。由于距离海王星较近,柯伊伯带小行星受其影响较大。这其中,又以共振小行星和离散小行星两族受影响最为明显。本文主要讨论了这两族小行星与海王星的共振现象。共振小行星处在共振轨道中,可以避免与海王星的近距离接触,轨道相对稳定,可以长时间保持。离散小行星的演化过程是共振黏滞与引力离散共同作用的结果。本文除了综述共振小行星和离散小行星的研究进展,还进一步分析了相应共振比下共振在大偏心率时的宽度,解释了离散小行星在离散盘大量分布的原因。     

Time-resolved spectral-line-filtered velocimetry

Measurements were obtained with a velocimeter that simultaneously illuminates the particulate in a flow with argon and He–Ne lasers and the scattered light is passed through a carefully controlled iodine filter. The iodine cell absorbs the argon emission at a rate proportional to the velocity of the scattering particle, while the absorption of scattered He–Ne light is independent of velocity. A tunable acousto-optic filter is used to multiplex the argon and He–Ne signals collected from a single photodetector. The problem of detector alignment in conventional Doppler global velocimetry is thus avoided. Experimental results on a scattering disk and an axisymmetric jet are presented and compared with laser Doppler anemometry measurements. Received: 7 March 2000/Accepted: 5 January 2001     

A mathematical and numerical framework for gradient meta-surfaces built upon periodically repeating arrays of Helmholtz resonators

In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a finite number of Helmholtz resonators in a unit cell and that unit cell is repeated periodically. To solve the scattering problem, the mathematical framework elaborated in Ammari et al. (2019) is used. The main result is an approximate formula for the scattered wave in terms of the lengths of the openings. Our framework provides analytic expressions for the scattering wave vector and angle and the phase-shift. It justifies the apparent absorption. Moreover, it shows that at specific lengths for the openings and a specific frequency there is an abrupt shift of the phase of the scattered wave due to the subwavelength resonances of the Helmholtz resonators. A numerically fast implementation is given to identify a region of those specific values of the openings and the frequencies.     

折线型裂纹对SH波的动力响应

利用Fourier积分变换方法,得出了无限平面中用裂纹位错密度函数表示的单裂纹散射场．根据无穷积分的性质,把单裂纹的散射场分解为奇异部分和有界部分．利用单裂纹的散射场建立了折线裂纹在SH波作用下的Cauchy型奇异积分方程．根据折线裂纹散射场和所得的积分方程讨论了裂纹在折点处的奇性应力及折点处的奇性应力指数．利用所得的奇性应力定义了折点处的应力强度因子．对所得Cauchy型奇积分方程的数值求解,可得裂纹端点和折点处的动应力强度因子。