有限元/边界积分方法在海面及其上方弹体目标电磁散射中的应用

本文将有限元/边界积分方法(FE/BIM)结合区域分解方法引入到粗糙海面及其上方目标 的电磁散射问题的研究中. 由于积分边界可以以任意形状设置在距模型表面任意远的距离处, 故本文采用共形人工边界结合区域分解建模方法截断模型的开放计算区域以减少求解未知量, 在截断区域内部采用有限元方法求解, 而计算区域的边界条件通过边界积分方程方法得到. 通过与矩量法获得的数值计算结果进行比较, 证明了该混合算法及模型处理方法的正确性, 进而研究了海面上方弹体目标的电磁散射特性, 并讨论了其双站散射系数随电磁波入射角度、目标高度、海面风速以及弹体尺寸的电磁散射特性变化情况. 本文结果可用于反演复杂背景下的目标信息及目标探测等领域. 关键词： 电磁散射 粗糙海面 目标 有限元/边界积分方法     

气溶胶凝聚粒子散射特性的数值计算

利用Cluster-cluster aggregation (CCA)模型,模拟了由相同数目球形原始微粒凝聚而成的四种随机取向气溶胶凝聚粒子.根据物质的电结构,将气溶胶凝聚粒子离散为一系列偶极子,结合离散偶极子近似方法,在获得每一个偶极子的电偶极矩之后,数值计算了气溶胶凝聚粒子散射强度的角分布,并分析了散射强度随入射光入射角度和气溶胶凝聚粒子尺寸参数变化的规律.结果显示:当散射角较小时,气溶胶凝聚粒子取向和入射光的入射角度对散射强度影响不大,当散射角增大时,散射强度则明显依赖于气溶胶凝聚粒子取向和入射光的入射角度;对于不同尺寸参数的气溶胶凝聚粒子,在同一角度入射情况下,随尺寸参数的增加,气溶胶凝聚粒子的散射主要集中于前向散射.     

气溶胶凝聚粒子散射特性的数值计算

利用Cluster-cluster aggregation (CCA)模型,模拟了由相同数目球形原始微粒凝聚而成的四种随机取向气溶胶凝聚粒子．根据物质的电结构,将气溶胶凝聚粒子离散为一系列偶极子,结合离散偶极子近似方法,在获得每一个偶极子的电偶极矩之后,数值计算了气溶胶凝聚粒子散射强度的角分布,并分析了散射强度随入射光入射角度和气溶胶凝聚粒子尺寸参数变化的规律．结果显示：当散射角较小时,气溶胶凝聚粒子取向和入射光的入射角度对散射强度影响不大,当散射角增大时,散射强度则明显依赖于气溶胶凝聚粒子取向和入射光的入射角度;对于不同尺寸参数的气溶胶凝聚粒子,在同一角度入射情况下,随尺寸参数的增加,气溶胶凝聚粒子的散射主要集中于前向散射．     

非球形粒子散射光的去偏振特性研究

目标对入射偏振光的散射特性反映了目标的属性信息。在Rayleigh散射理论的基础上，通过单层非球形粒子对入射偏振光的散射数学模型，应用矢量传输方程来计算非球形粒子散射的Mueller矩阵元，求解散射介质的偏振度，讨论在不同介质层厚度、粒子半径和探测角的条件下，非球形粒子散射光去偏振度的变化特性，给出了模拟仿真结果。该方法为研究目标的内部结构、厚度和粗糙度等特征以及目标的探测和识别提供了一种新的途径。     

均匀椭球粒子对拉盖尔-高斯光束的散射特性研究

基于广义Mie理论, 研究了椭球粒子对在轴入射的拉盖尔-高斯光束的散射特性. 通过局域近似法求解椭球坐标系中的波束因子, 计算得到了波束因子之间满足的普遍关系. 对散射强度随椭球粒子不同尺寸参数和扁圆程度的变化特性进行了数值计算, 并针对不同拓扑荷时的散射强度进行了对比分析. 结果表明: 当椭球粒子尺寸在与入射光波长可比拟的范围内变化时, 散射强度随尺寸参数的增大而增大, 随椭球长短轴之比和拓扑荷的增大而减小. 本文的理论研究能够为拉盖尔-高斯光束在粒径测量、大气激光通信、 大气遥感等领域的应用提供更准确的粒子模型和参考价值. 关键词： 椭球粒子 拉盖尔-高斯光束 波束因子 散射强度     

抛物方程基于自然边界归化的耦合法

将冯康和余德浩提出的自然边界归化方法^[1~4]应用于求解抛物方程初边值外区域问题,提出一种自然边界元与有限元耦合算法。先将控制方程对时间进行离散化,得到关于时间步长的离散化格式,给出圆外域上的自然积分方程,基于此研究抛物方程无界区域问题的自然边界元与有限元耦合法,最后给出相应的数值例子。     

利用T矩阵模型计算水体中非球形悬浮颗粒物光散射特性

水体中悬浮颗粒物的光散射特性是影响基于直接光谱法水质检测结果准确性的一个重要参数。依据T矩阵模型,研究了紫外-可见光照射下水体中非球形悬浮颗粒物的光散射强度特性。以藻类和泥沙类颗粒物为例,构造了椭球、圆柱和广义Chebyshev三种非球形粒子光散射模型,分析了入射光波长、悬浮颗粒物形状、复折射率与相对散射光强之间的关系,计算了不同悬浮颗粒物相对散射光强随波长、颗粒物尺寸以及旋转角变化的情况。数值仿真结果表明,不同种类非球形悬浮颗粒物的散射光强度均呈现出显著的变化。在200~800nm波长范围内,随入射波长的增大,粒子几何尺寸所带来影响逐渐减小,散射特性主要由复折射率决定。当粒子尺寸小于0.2μm或接近1μm时,在入射光波长位于紫外或红外的条件下,散射光强度较大且呈现强烈振荡;而当粒子尺寸r=0.3~0.9μm,散射强度较稳定,接近于0且受到入射光波长的干扰较小。这可为提高紫外-可见吸收光谱法的检测精度、抑制散射干扰提供一定依据。     

聚合物充填过程中裹气现象的数值模拟

针对聚合物充填过程中的裹气现象,采用一种有限元（FEM）-间断有限元（DG）耦合算法对其进行数值模拟。对于自由运动界面,采用水平集（Level Set）方法进行捕捉;用XPP（eXtended Pom-Pom）本构模型来描述黏弹性流体的流变行为。采用有限元-间断有限元耦合算法求解统一的流场方程,并采用隐式间断有限元求解XPP本构方程、Level Set及其重新初始化方程。数值结果与文献中的实验结果及模拟结果吻合较好,验证了数值方法的稳定性及准确性。分析带有非规则嵌件型腔内,注射速度及浇口尺寸对裹气现象的影响,裹气容易出现在较高注射速度及较小浇口的情形。     

鳀鱼(Engraulis japonicus)目标强度的模型法研究

采用声散射理论和目标强度近似模型评估法对黄海鲤鱼（Engraulis japonicus）的声散射特征和目标强度进行了数值计算与评估研究。散射模型由鱼鳔模型和鱼体模型两个部分构成，其中鱼鳔采用充满气体的椭球体模型，鳔除外的鱼体采用充满液体的椭球体模型。理论数值计算所需参数取自全长12．6cm的鲤鱼个体，其鱼鳔尺寸利用X光照片测得。平均目标强度利用模型算得的不同角度下的声散射强度与鲲鱼倾角分布函数的卷积计算，其中倾角（度）的分布函数设为N（-3．9，12．8^2）。结果显示，鲲鱼对声波的散射具有明显指向性；在38kHz和120kHz工作频率下，鲲鱼的最大背向目标强度分别为-41．2dB和-39．5dB，有效平均目标强度分别为-48．0dB和-51．5dB，与实测结果吻合较好。另外还对鲲鱼的反向散射指向性特征、目标强度的频率特征以及鱼鳔对鲲鱼整体目标强度的贡献等进行了分析与讨论。以上研究表明，模型法作为现场测定研究方法的重要补充和认知鱼类声学散射特性的有效途径，可在我国鱼类目标强度的研究中发挥重要作用。     

含腔电大尺寸导体目标电磁散射的一体化数值模拟

应用等效原理，通过引入口面上等效磁流将含腔导电目标电磁散射简化为腔内、外两个等效 问题. 腔内问题分段求解并应用级联法获得口面等效导纳矩阵；腔内外的耦合关系应用近似 边界元方法描述并由此获得口面等效磁流；最后，这一具有混合源的腔体内外一体化散射问 题则应用所提出的广义混合场积分方程方法建立电磁模型，并用多层快速多极子方法实现高 效数值求解. 实例计算结果与测试结果具有很好的一致性. 关键词： 含腔目标 电磁散射 混合场积分方程 数值分析     

Superspheroidal modeling of resonance scattering from elongated air bubbles and fish swim bladders

The extended boundary condition technique of Waterman [J. Acoust. Soc. Am. 45, 1417-1429 (1969)] has been used to make accurate studies of the frequency and azimuthal scattering distributions from extended axisymmetric acoustic objects. These objects are formed using the mathematical function for a "superellipse" [i.e., (x/a)(s) + z/b)(s) = 1, where s = 2n, n = 1,2,[ellipsis (horizontal)]], and revolving around the z-axis. For s = 2, the object is a spheroid with aspect ratio α = b/a. As s increases, the shape of the object approaches a right circular cylinder of diameter 2a and length 2b. The method is applied to the case of prolate (i.e., α > 1) air-filled objects in water, which has importance for the interpretation of acoustic scattering from oceanic objects such as air-bubbles, the swim bladders of some fish, and zooplankton. It is found that the resonance frequency increases with α, essentially as predicted using a different method by Weston, and increases in a relatively minor way with s. The resonance peak amplitude, and Q, are also more sensitive to changes in α, than s. The method shows that the monopole resonance continues to dominate low frequency scattering, leading to an almost spherically symmetric azimuthal scattering distribution, even for elongated, cylindrical, air-filled, objects with an aspect ratio up to α = 20, and s = 32.     

收发分置目标强度的计算及前向散射信号的分离

研究时域有限差分(FDTD)法计算收发分置弹性目标散射声场的有效性,和实验测量中从直达与散射干涉信号中分离目标前向散射信号的方法。将FDTD法应用于三维声场计算,分别计算了平顶圆柱、球顶圆柱、球锥顶圆柱和扁长回转椭球等几种不同形状的弹性体散射近场空间分布,再用近远场变换方法获取远场目标强度空间分布。模拟结果表明:目标强度的空间指向性是受声波入射方向、无量纲波数kL(k-波数,L-目标特征尺度)、目标形状、材料等影响;在本文所计算的几种不同形状目标的尺度和kL取值范围内,计算得到的收发分置目标强度空间分布均有显著的前向散射与镜反射特征。计算结果得到解析解和实验结果的印证,从而表明了FDTD法计算收发分置目标散射场的有效性。对接收信号采用相关处理方法,能有效地分离出目标前向散射信号,表明对于收发分置目标散射声强的测量,这是一种简单有效的分离目标前向散射信号的方法。      

Orientation dependence of broadband acoustic backscattering from live squid

A controlled laboratory experiment of broadband acoustic backscattering from live squid (Loligo pealeii) was conducted using linear chirp signals (60-103 kHz) with data collected over the full 360° of orientation in the lateral plane, in <1° increments. The acoustic measurements were compared with an analytical prolate spheroid model and a three-dimensional numerical model with randomized squid shape, both based on the distorted-wave Born approximation formulation. The data were consistent with the hypothesized fluid-like scattering properties of squid. The contributions from the front and back interfaces of the squid were found to dominate the scattering at normal incidence, while the arms had a significant effect at other angles. The three-dimensional numerical model predictions out-performed the prolate spheroid model over a wide range of orientations. The predictions were found to be sensitive to the shape parameters, including the arms and the fins. Accurate predictions require setting these shape parameters to best describe the most probable squid shape for different applications. The understanding developed here serves as a basis for the accurate interpretation of in situ acoustic scattering measurements of squid.     

利用近前向散射图样识别单粒子形状的理论研究

近前向光学散射图样可以用来表征颗粒物的形状.基于球形芽孢杆菌、枯草芽孢杆菌、类鼻疽伯克氏菌的回转长椭球模型, 采用离散偶极子近似方法, 通过模拟3个不同方位探测器接收的散射光强响应信号, 讨论了非球形生物气溶胶颗粒的形状对前向角分辨光强的影响.结合球形指数反演算法, 在一定取向条件下, 前向5°–20° 内角分辨散射光强具有识别长形颗粒物和非长形颗粒物的能力.该研究可以为颗粒物形态测量仪器设计以及快速检测有害生物气溶胶提供依据.     

Acoustic backscattering by Hawaiian lutjanid snappers. 1. Target strength and swimbladder characteristics

The target strengths and swimbladder morphology of six snapper species were investigated using broadband sonar, x rays, and swimbladder casts. Backscatter data were obtained using a frequency-modulated sweep (60-200 kHz) and a broadband, dolphinlike click (peak frequency 120 kHz) from live fish, mounted and rotated around each of their three axes. X rays revealed species-specific differences in the shape, size, and orientation of the swimbladders. The angle between the fish's dorsal aspect and the major axis of its swimbladder ranged from 3 degrees to 12 degrees and was consistent between individuals within a species. This angle had a one-to-one relationship with the angle at which the maximum dorsal aspect target strength was measured (r2 = 0.93), regardless of species. Maximum dorsal aspect target strength was correlated with length within species. However, the swimbladder modeled as an air-filled prolate spheroid with axes measured from the x rays of the swimbladder predicted maximum target strength significantly better than models based on fish length or swimbladder volume. For both the dorsal and lateral aspects, the prolate spheroid model's predictions were not significantly different from the measured target strengths (observed power >0.75) and were within 3 dB of the measured values. This model predicts the target strengths of all species equally well, unlike those based on length.     

Study of the scattering of nonlinearly interacting plane acoustic waves by an elongated spheroid

The scattering of nonlinearly interacting plane acoustic waves on a rigid elongated spheroid is considered. The foci of the spheroid coincide with foci of the spheroidal coordinate system. The method of successive approximations is used to obtain the solutions to the inhomogeneous wave equation in the first and second approximations. Asymptotic expressions are offered for the components of the total acoustic pressure of the difference frequency wave, and the scattering diagrams for these components are presented.     

Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton

Scattering models that correctly incorporate organism size and shape are a critical component for the remote detection and classification of many marine organisms. In this work, an acoustic scattering model has been developed for fluid-like zooplankton that is based on the distorted wave Born approximation (DWBA) and that makes use of high-resolution three-dimensional measurements of the animal's outer boundary shape. High-resolution computerized tomography (CT) was used to determine the three-dimensional digitizations of animal shape. This study focuses on developing the methodology for incorporating high-resolution CT scans into a scattering model that is generally valid for any body with fluid-like material properties. The model predictions are compared to controlled laboratory measurements of the acoustic backscattering from live individual decapod shrimp. The frequency range used was 50 kHz to 1 MHz and the angular characteristics of the backscattering were investigated with up to a 1 degree angular resolution. The practical conditions under which it is necessary to make use of high-resolution digitizations of shape are assessed.     

Coupled FEM/BEM for control of noise radiation and sound transmission using piezoelectric shunt damping

In this paper, we present a coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by passive piezoelectric techniques. The system consists of an elastic structure (with surface mounted piezoelectric patches) coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low frequency range. The originality of the present paper lies in evaluating the classically used FEM/BEM methods for structural–acoustics problems when taking account smart systems at the fluid–structure interfaces.     

Near-field calculations for a rigid spheroid with an arbitrary incident acoustic field

A general spheroidal coordinate separation-of-variables solution is developed for the determination of the acoustic pressure distribution near the surface of a rigid spheroid for a monofrequency incident acoustic field of arbitrary character. Calculations are presented, for both the prolate and oblate geometries, demonstrating the effects of incident field orientation and character (plane-wave, spherical wave, cylindrical wave, and focused beam) on the resultant acoustic pressure distribution.