用高频近似计算结构体辐射声场

本文对高频段结构体辐射场场用高频近似即所谓平面波近似方法来计算。该方法不但避免了通常所用的边界元法计算结构体辐射声场出现的３个问题：１．不光滑点Ｃ（Ｐ）因子计算，（２）奇异积分，（３）特征频率处理的非唯一性，而且该方法精度较高，计算量小，于微机计算。     

半无限域中结构体辐射声场计算

本文从无限域Ｈｅｌｍｈｏｌｔｚ积分方程入手，用边界元法（ＢＥＭ）计算任意形状结构体辐射声场，对用ＢＥＭ计算声场出现的奇异积分，特征频率，边角点处向不连续，高频段计算误差较大等问题进行了有效，简便的处理，并用理论算例验证了这些方法有较精度。     

共聚物组成曲线的数学分析

用数学分析的方法对共聚物组成曲线进行了处理；首次得到了交替共聚的恒比点为Ｆ１＝ｆ１＝１／（２－ｒ）（０〈ｒ１〈１，ｒ２＝０）或Ｆ１＝ｆ１＝（１－ｒ２）／（２－ｒ２）（ｒ１＝０，０〈ｒ２〈１）。     

一种无奇异积分的边界单元法

处理基本解的奇异性是边界单元法的难题之一。本文避开奇异基本解,用非奇异基本解建立边界积分方程。非奇异基本解取自齐次微分方程的一般解和完备系,使求解边界积分方程容易。文中对边界未知量采用样条插值函数,计算精度良好。     

声学边界元拟奇异积分计算的自适应方法

提出一种自适应方法计算声学边界元中的拟奇异积分,通过单元分级细分将总积分转移到子单元上以消除拟奇异性。在此方法基础上深入研究拟奇异性,进一步提出接近度的概念,其中临界接近度可作为拟奇异积分计算的理论依据,并可用于预估拟奇异性是否存在。此方法的积分精度可调控,且不受场点位置限制,相比于已有方法更加灵活高效。数值分析表明拟奇异性强弱由场点与单元的相对位置决定,单元上远离场点的区域拟奇异性很弱,无需处理。研究结果为处理边界元法中的拟奇异性问题提供了新的选择和参考。     

Helmholtz声学边界积分方程中奇异积分的计算

提出了一种非等参单元的四边形坐标变换,它将积分的曲面单元映射为另一四边形单元,通过两次坐标变换引入的雅可比行列式可以消除Helmholtz声学边界积分方程中的弱奇异型O(1／r))积分．而且利用δr／δn以及坐标变换可以同时消除坐标变换无法消除的Cauchy型(O(1／r^2))奇异积分,并给出了消除奇异性的详细证明．该方法给Helmholtz声学边界积分方程中的弱奇异积分与Cauchy奇异积分的计算以及编程提供了极大便利。     

用高频近似计算结构体辐射声场

本文对高频段（ｋａ≥５）结构体辐射声场用高频近似即所谓平面波近似方法来计算。该方法不但避免了通常所用的边界元法（ＢｏｕｎｄａｒｙＥｌｅｍｅｎｔＭｅｔｈｏｄ，简称ＢＥＭ法）计算结构体辐射声场出现的３个问题：（１）不光滑点处的Ｃ（Ｐ）因子计算，（２）奇异积分，（３）特征频率处解的非唯一性，而且该方法精度较高，计算量小，便于微机计算     

模拟转子不平衡响应数值分析及实验研究

对模拟转子进行了不平衡响应的有限元计算，并进行了相应的实验研究。在转速为９６０ｒ／ｍｉｎ和１５６８ｒ／ｍｉｎ时，不平衡响应的计算结果与实验结果的误差近似为１．７％和２．１％，计算结果与实验结果相符。     

边界元中近奇异积分的一种解析方法

准确求解边界元方法中的近奇异积分是一个非常重要的问题。一般情况下,分析中涉及到的常规积分采用高斯方法即可获得较高的精度。但当源点位于边界附近时,采用高斯积分就会使计算结果精度大大降低,甚至得出错误的结果。对于平面问题,以源点作为原点,以所积分单元的切向和法向为坐标轴建立局部坐标系,对于线性单元可以得到所有积分的解析解。基于除角点外的所有边界点的场变量在边界上连续且有界的特点,所有在边界上引起场变量奇异的项之和必为零,故对于边界上的点可以直接在解析解中删除这些奇异项即可。算例表明,该方法可大大提高边界元的计算精度和效率。     

运动介质中奇异边界元积分式的精确求解

采用边界元方法求解与运动介质相关声学问题时,难点之一是如何精确计算场点与源点重合所导致的奇异积分式。论文提出一种将具有奇性的单元面积分式拆分为奇性和非奇性积分部分分别进行计算的新方法。对奇性积分部分,经过严格的数学推导给出解析解;而对非奇性积分部分则通过高斯积分法处理。新方法可有效地提高边界元计算精度和效率,对运动介质中的有关声学问题的边界元数值计算具有重要意义。     

Numerical evaluation of arbitrary singular domain integrals based on radial integration method

In this paper, a new approach is presented for the numerical evaluation of arbitrary singular domain integrals based on the radial integration method. The transformation from domain integrals to boundary integrals and the analytical elimination of singularities can be accomplished by expressing the non-singular part of the integration kernels as polynomials of the distance r and using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. Some numerical examples are provided to verify the correctness and robustness of the presented method.     

Method for efficient computation of stress intensity factors from weight functions by singular point elimination

Mode I stress intensity factor K_I can be computed by integration of a function representing a stress profile (e.g., variation of stress with depth), modified by an appropriate weight function. Usually, numerical integration is required. However, widely used weight functions cause the end (s) of integration intervals to be singular points, complicating numerical integration. Approaches for computing K_I that deal with singularities by approximating stress profiles by a linear function near a singular point, or transforming a weight function to a form that enables Gauss–Chebyshev integration, are reviewed. As an alternative to those approaches, this study presents a different method for numerical integration involving weight functions. First, a general, variable transformation method to eliminate singularities is introduced. Elimination of singular point enables elementary integration approaches such as Simpson’s rule, as well more involved methods, such as adaptive-Lobatto integration, to be applied. Benchmark tests using a variety of numerical integration formulas show the singular point elimination method to provide accurate, robust and computationally efficient integrations.     

Self-inductance of air-core circular coils with rectangular cross section

Using analytic integration, accurate self-inductance expressions (requiring only single numerical integration) for air-core circular coils with rectangular cross sections (and two special cases, namely thin-wall solenoids and disk (pancake) coils) are derived from the basic mutual-energy formula of two coaxial circular current loops. Based upon these expressions, with integration singularities analytically treated, the self-inductance of any air-core coil can be precisely calculated by use of a microcomputer. Values so computed agreed, to one part in 10⁴, with those reported in the literature.     

小波极大模方法在旋转机械故障诊断中的应用研究

通过小波变换奇异性检测理论,利用连续小波变换提取极大模值线并求取Lipschitz指数,提取转子每转中Lipschitz指数的平均个数和全部Lipschitz指数的平均值作为转子故障振动信号的奇异性特征。通过BP神经网络对转子不平衡、不对中、油膜涡动、摩碰和无故障5种状态进行分类识别,取得了较好的效果。     

求解水下非圆弹性环声散射问题的一种半解析方法

基于传递矩阵法、齐次扩容精细积分法和复数矢径虚拟边界谱方法 ,提出了一种求解水下非圆弹性环声散射问题的半解析方法。该方法具有以下几个优点 :(1)采用复数矢径虚拟边界谱方法 ,不仅能保证在全波数域内Helmholtz外问题解的唯一性 ,而且由于虚拟源强密度函数采用 Fourier级数展开 ,克服了用单元离散解法不能用于较高频率范围的缺点 ;(2 )采用齐次扩容精细积分法求解非圆弹性环的状态微分方程 ,其计算结果具有很高的精度 ;(3)耦合方程不需要交错迭代求解 ,提高了计算效率。文中给出了两个典型非圆弹性环在平面声波激励下的声散射算例 ,计算结果表明本文方法是一种求解二维非圆弹性环声散射问题非常有效的半解析法。     

Application of the Jk integral to mixed mode crack problems for anisotropic composite laminates

The J_k integral method for determining mixed mode stress intensity factors separately in the cracked anisotropic plate is developed. Stress intensity factors are indirectly determined from the value of J₁ and J₂. The J₂ integral can be evaluated efficiently from a finite element solution, neglecting the contribution from the portion of the integration contour along the crack faces, by selecting the integration contour in the vicinity of the crack tip. Using functions of a complex variable, the complete relations between J₁, J₂ and K_I, K_II for anisotropic materials are derived conveniently by selecting narrow rectangular contours shrinking to the crack tip. Compared to the existing path independent integral methods, the present method does not involve calculating the auxiliary solution and hence numerical procedures become quite simple. Numerical results to various propblems are given and demonstrate the accuracy, stability and versatility of the method.     

SINS/GPS组合导航的扩展Kalman滤波算法

针对捷联惯性导航系统(SINS)无法长时间单独工作和GPS卫星信号易失锁而无法定位的问题,分析了两种导航系统的优缺点,提出了SINS/GPS组合导航的方法.建立了陀螺和加速度计的误差模型,采用松耦合方式,设计了扩展Kalman滤波器.以姿态、速度、位置的误差以及陀螺、加速度计的误差作为状态变量,对姿态、速度、位置进行校正.运用Matlab对组合导航系统进行了仿真.结果表明,该算法简单,容易实现,能满足导航精度要求.     

On the computation of nearly singular integrals in 3D BEM collocation

In this paper, we propose an efficient strategy to compute nearly singular integrals over planar triangles in R ³ arising in boundary element method collocation. The strategy is based on a proper use of various non‐linear transformations, which smooth or move away or quite eliminate all the singularities close to the domain of integration. We will deal with near singularities of the form 1/r, 1/r² and 1/r³, r=∥ x ? y ∥ being the distance between a fixed near observation point x and a generic point y of a triangular element. Extensive numerical tests and comparisons with some already existing methods show that the approach proposed here is highly efficient and competitive. Copyright © 2007 John Wiley & Sons, Ltd.     

On non‐linear transformations for accurate numerical evaluation of weakly singular boundary integrals

This paper presents a study of the performance of the non‐linear co‐ordinate transformations in the numerical integration of weakly singular boundary integrals. A comparison of the smoothing property, numerical convergence and accuracy of the available non‐linear polynomial transformations is presented for two‐dimensional problems. Effectiveness of generalized transformations valid for any type and location of singularity has been investigated. It is found that weakly singular integrals are more efficiently handled with transformations valid for end‐point singularities by partitioning the element at the singular point. Further, transformations which are excellent for CPV integrals are not as accurate for weakly singular integrals. Connection between the maximum permissible order of polynomial transformations and precision of computations has also been investigated; cubic transformation is seen to be the optimum choice for single precision, and quartic or quintic one, for double precision computations. A new approach which combines the method of singularity subtraction with non‐linear transformation has been proposed. This composite approach is found to be more accurate, efficient and robust than the singularity subtraction method and the non‐linear transformation methods. Copyright © 2001 John Wiley & Sons, Ltd.     

Effective schema for the rigorous modeling of grating diffraction with focused beams

Most modal diffraction methods are formulated for incident plane waves. In practical applications, the probing beam is focused. Usually, this is simulated by means of numerical integration where Gaussian quadrature formulas are most effective. These formulas require smooth integrands, which is not fulfilled for gratings due to Rayleigh singularities and physical resonances. The violation of this condition entails inaccurate integration results, such as kinks and other artifacts. In this paper, a methodology for the efficient treatment of the numerical integration with improved accuracy is presented. It is based on the subdivision of the aperture along the lines of Rayleigh singularities, mapping of these subapertures into unit squares, and separate application of the Gaussian cubature formulas for each subarea.