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。     

舰船低频水下辐射噪声的声固耦合数值计算方法

针对舰船低频域水下辐射噪声计算问题,指出采用严格遵循声固耦合动力学方程的耦合声学有限元与远场自动匹配层(FEM/AML)方法以及耦合声学间接边界元(IBEM)方法是计算精度较高的策略。以某小水线面双体船(SWATH)为研究对象,使用声功率作为评价指标,探讨了声场区域特征尺度选取对计算精度的影响,比较了上述两种方法与常规基于流固耦合的两种方法在计算特性方面的差异。研究表明,声固耦合模式较流固耦合模式声学响应计算结果偏小,对于SWATH船的合成总声功率级两者偏差达到1dB~3dB,前者计算结果更为精确,基于声固耦合模式的耦合声学IBEM方法是舰船水下辐射噪声预报的首选算法。     

声学数值计算的分区光滑径向点插值无网格法

针对标准的有限元法分析声学问题时由于数值色散导致高波数计算结果不可靠问题,将分区光滑径向点插值法(cell-based smoothed radial point interpolation method, CS-RPIM)应用到二维声学分析中,推导了分区光滑径向点插值法分析二维声学问题的原理公式。该方法将问题域划分为三角形背景单元,每个单元进一步分成若干个光滑域,对每个光滑域进行声压梯度光滑处理,运用光滑Galerkin弱形式构造系统方程,并按有限元中方法施加必要的边界条件。CS-RPIM提供了合适的模型硬度,能有效降低色散效应,提高计算精度。对管道和二维轿车声学问题的数值分析结果表明,与标准有限元法相比,CS-RPIM具有更高的精度和准确度,在高波数计算时这种优势特别明显。     

辐板型式和轮轨接触点位置对车轮声辐射特性的影响

为了分析不同车轮辐板型式和轮轨接触点位置对车轮声辐射特性的影响,建立了车轮有限元-边界元混合振动声辐射模型。首先,根据车轮实际拓扑结构建立三维实体有限元模型,采用分块Lanzos法求解结构的特征值问题,然后采用模态叠加法计算车轮结构在法向单位力激励下的动态响应,将车轮外表面的速度处理成声学边界元的输入,计算车轮的辐射噪声。数值计算中,考虑了S型、直型和波浪型三种辐板型式和轮缘、名义滚动圆处和车轮外侧三个轮轨接触点位置。结果表明,辐板型式和轮轨接触点位置对车轮声辐射具有较明显的影响。而且,不同辐板型式车轮在不同轮轨接触点位置下的声辐射特性也不尽相同。数值分析可以为低噪声车轮的选型提供一定的参考。     

大展弦比机翼气动颤振的有限元分析

摘要：在Theodorsen二元气动力的基础上,建立非定常气动力时域内积分形式的表达式或者等价的频域表达式,利用粘弹性结构振动分析中对积分方程的等价变换将其写成与结构动力学方程一致的二阶常微分方程,将气动力的影响作为对结构有限元模型质量阵、刚度阵和阻尼阵的补充,保留了结构原有的所有动力学特性,并且能够直接用计算结构动力学的通用有限元软件进行空气-结构耦合的整体动力学分析,适合应用于具有复杂结构的气弹问题。气动力模型的建立可以利用各种试验及数值方法得到的气动力数据,适用性强。算例给出了大展弦比机翼的颤振边界计算结果。     

水中结构振动时声学相似性的数值验证

摘 要：以声学相似性原理为基础,用因次理论得到了在相似准数相等条件下的无因次系数,给出了模型和原型声学相似的条件。采用结构有限元耦合流体边界元方法计算水下相似加肋圆柱壳模型的流固耦合振动和声辐射。数值计算表明在相似条件下几何相似模型的壳体振动声学传递函数及其谱峰频率满足相似性,水下的模态、流固耦合振动响应以及声辐射均满足相似关系,并且与理论结果能够符合。     

基于FEM和BEM法的大型立式齿轮箱振动噪声计算及测试分析

根据某大型立式行星传动齿轮箱的结构和安装特点,基于FEM法建立了该齿轮箱的和有限元模型,对其进行了振动模态分析,计算了其模态频率和稳态不平衡响应;基于BEM法建立了该齿轮箱的外声场边界元模型,导入了齿轮箱振动稳态不平衡响应结果作为声学边界条件,对辐射声场进行了数值计算和仿真分析。通过对齿轮箱进行现场振动和噪声测试分析,得到的测试结果与理论计算结果较为一致,表明了理论计算的可行性和准确性     

双吸离心泵正反转工况流致振动噪声研究

为深入了解双吸离心泵运行的振动噪声规律,以某一双吸式离心泵为研究对象,基于声学间接边界元法(IBEM),采用LMS Virtual-Lab分析计算平台,进行基于泵壳模态的强迫振动响应计算。然后根据泵壳模态强迫振动响应计算与声学间接边界元的声学波动方程求解耦合方程,得到双吸泵在液力透平工况和泵工况下外辐射声场的声压级指向分布和声压级分布。结果表明:偶极子声源是流体噪声的主要声源;在蜗壳隔舌处非定常脉动力是主要的噪声源;叶频及其倍频是双吸泵外辐射声场噪声的主要诱导频率;泵壳发生了共振,所以声振耦合的作用不可忽略。研究揭示了双吸泵作液力透平及泵工况内部流动诱发的外辐射声场的声振耦合计算规律,为后续减振降噪研究提供了理论基础。     

声学-结构设计灵敏度分析

声学 -结构设计灵敏度分析揭示了结构振动引起的辐射声压与结构设计变量之间的关系。分别用有限元法和边界元法计算结构设计灵敏度和声学灵敏度。将两个灵敏度结合得到最终的声学 -结构设计灵敏度。在边界元计算中 ,采用退化元处理奇异积分问题 ,对特征频率不唯一问题采用CHIEF方法处理。以脉动球和箱体为例 ,验证了算法的可行性和精确性。     

快速多极子边界元法在吸声材料声场计算中的应用

对快速多极子边界元法中多极子展开式的数值计算进行了研究,建立四点单级传递关系与多极传递关系模型。通过与格林函数及其法向导数理论值的比较,考察两种传递情况下,多极子展开式在吸声材料介质及空气介质中的计算精度。结果表明,复波数展开式的求解精度与截断项数的大小相关,而且当复波数虚部值与展开点间距离乘积过大时,展开式值开始与真值相背离。最后提出了解决此问题的两种方法。此外,以膨胀腔阻性消声器传递损失计算为例,验证了本文方法的有效性与可行性。     

Boundary element formulation for the coupled stretching-bending analysis of thin laminated plates

The boundary integral equations for the coupled stretching-bending analysis of thin laminated plates involve an integral which will be singular when the field point approaches the source point. To avoid the singular problem occurring in the numerical programming, the boundary integral equations are modified in which the integrals of singular part are integrated analytically. The analytical solutions for the free term coefficients and singular integrals are obtained in explicit closed-form. By dividing the boundary into elements and using suitable interpolation polynomials for basic functions, the set of equations necessary for boundary element programming are written explicitly for regular nodes and corner nodes. The equations for the determination of displacements and stresses at internal points are also presented in this paper.     

A sinh transformation for evaluating nearly singular boundary element integrals

An implementation of the boundary element method requires the accurate evaluation of many integrals. When the source point is far from the boundary element under consideration, a straightforward application of Gaussian quadrature suffices to evaluate such integrals. When the source point is on the element, the integrand becomes singular and accurate evaluation can be obtained using the same Gaussian points transformed under a polynomial transformation which has zero Jacobian at the singular point. A class of integrals which lies between these two extremes is that of ‘nearly singular’ integrals. Here, the source point is close to, but not on, the element and the integrand remains finite at all points. However, instead of remaining flat, the integrand develops a sharp peak as the source point moves closer to the element, thus rendering accurate evaluation of the integral difficult. This paper presents a transformation, based on the sinh function, which automatically takes into account the position of the projection of the source point onto the element, which we call the ‘nearly singular point’, and the distance from the source point to the element. The transformation again clusters the points towards the nearly singular point, but does not have a zero Jacobian. Implementation of the transformation is straightforward and could easily be included in existing boundary element method software. It is shown that, for the two‐dimensional boundary element method, several orders of magnitude improvement in relative error can be obtained using this transformation compared to a conventional implementation of Gaussian quadrature. Asymptotic estimates for the truncation errors are also quoted. Copyright © 2004 John Wiley & Sons, Ltd.     

An efficient method to evaluate hypersingular and supersingular integrals in boundary integral equations analysis

An efficient algorithm is employed to evaluated hyper and super singular integral equations encountered in boundary integral equations analysis of engineering problems. The algorithm is based on multiple subtractions and additions to separate singular and regular integral terms in the polar transformation domain, primarily established in Refs. (Guiggiani M, Krishnasamy G, Rudolphi TJ, Rizzo FJ. A general algorithm for the numerical solution of hypersingular boundary integral equations. Trans ASME 1992;59:604–614; Guiggiani M, Casalini P. Direct computation of Cauchy principal value integral in advanced boundary element. Int J Numer Meth Engng 1987;24:1711–1720. Guiggiani M, Gigante A. A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method. J Appl Mech Trans ASME 1990;57:906–915). It can be proved that the regular terms have finite analytical solutions in the range of integration, and the singular terms will be replaced by special periodic kernels in the integral equations. The subtractions involve to multiple derivatives of analytical kernels and the additions require some manipulation to separate the remaining regular terms from singular ones. The regular terms are computed numerically. Three examples on numerical evaluation of singular boundary integrals are presented to show the efficiency and accuracy of the algorithm. In this respect, strongly singular and hypersingular integrals of potential flow problems are considered, followed by a supersingular integral which is extracted from the partial differentiation of a hypersingular integral with respect to the source point.     

Regularization of nearly hypersingular integrals in the boundary element method

A critical aspect in all implementations of the boundary element method is an accurate computation of the kernels' integration. These kernels are singular or hypersingular when the collocation point belongs to the integration element, and different techniques have been devised to tackle this problem. Another important issue is the integration of the kernels when the collocation point is close to but not in the integration element. The ensuing integrals although regular are termed quasi-singular or nearly singular, and quasi-hypersingular or nearly hypersingular since the integrand varies rapidly within the integration interval, and cannot be accurately computed by standard procedures. A kernels' complex regularization procedure is presented in this paper, which leads to a decomposition of the quasi-singular and quasi-hypersingular integrals in a series of simpler terms. The method is applied to the stress boundary integral equation for two-dimensional bodies, and it is tested in both curved and straight elements. For straight elements, the method leads to closed-form formulas, which are included in the paper.     

Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies

A frequency domain boundary element methodology of solving three dimensional electromagnetic wave scattering problems by dielectric particles is reported. The method utilizes a computationally attractive surface integral equation containing only weakly and strongly singular integrals in the contrast to most formulations involving not only strongly singular but hypersingular integrals as well. The main advantage of this integral equation is the fact that its strongly singular part is similar to the one appearing in the corresponding integral equation of dynamic elasticity. Thus, well known advanced integration techniques used successfully in elastic scattering problems can be directly applied to the present analysis. Both continuous and discontinuous quadratic elements are employed in order to accurately treat dielectric scatterers with smooth and piecewise smooth boundaries. Numerical examples dealing with three dimensional electromagnetic wave scattering problems demonstrate the accuracy and efficiency of the proposed boundary element formulation.     

New variable transformations for evaluating nearly singular integrals in 2D boundary element method

This work presents a further development of the distance transformation technique for accurate evaluation of the nearly singular integrals arising in the 2D boundary element method (BEM). The traditional technique separates the nearly hypersingular integral into two parts: a near strong singular part and a nearly hypersingular part. The near strong singular part with the one-ordered distance transformation is evaluated by the standard Gaussian quadrature and the nearly hypersingular part still needs to be transformed into an analytical form. In this paper, the distance transformation is performed by four steps in case the source point coincides with the projection point or five steps otherwise. For each step, new transformation is proposed based on the approximate distance function, so that all steps can finally be unified into a uniform formation. With the new formulation, the nearly hypersingular integral can be dealt with directly and the near singularity separation and the cumbersome analytical deductions related to a specific fundamental solution are avoided. Numerical examples and comparisons with the existing methods on straight line elements and curved elements demonstrate that our method is accurate and effective.     

Design of a new scheme to indicate the domain of applicability of near singular approach in 2D BEM

The Gauss–Legendre integration is not appropriate for singular and nearly singular integrations in BEM. In this study, some criteria are introduced for recognizing the nearly singular integrals in integral form of Laplace equation. At first, a criterion is obtained for constant element and consequently higher order elements are investigated. To indicate this near singular approach, there are different formulations amongst which the Romberg method was selected due to its compatibility with analytical integration. The singular integrals were carried out by composing the Romberg method and midpoint rule. The potential functions over geometrically linear BEM elements can be defined in the form of constant, linear or other types of interpolation functions. In those elements, the Gauss–Legendre integration will be accurate, if the source point is placed out of the circle with a diameter equal to element length and its center matched to midpoint of the element. Also, some criteria are obtained for parabolic function of geometry over an element.     

Semi‐sigmoidal transformations for evaluating weakly singular boundary element integrals

Accurate numerical integration of line integrals is of fundamental importance to reliable implementation of the boundary element method. Usually, the regular integrals arising from a boundary element method implementation are evaluated using standard Gaussian quadrature. However, the singular integrals which arise are often evaluated in another way, sometimes using a different integration method with different nodes and weights. Here, a co‐ordinate transformation technique is introduced for evaluating weakly singular integrals which, after some initial manipulation of the integral, uses the same integration nodes and weights as those of the regular integrals. The transformation technique is based on newly defined semi‐sigmoidal transformations, which cluster integration nodes only near the singular point. The semi‐sigmoidal transformations are defined in terms of existing sigmoidal transformations and have the benefit of evaluating integrals more accurately than full sigmoidal transformations as the clustering is restricted to one end point of the interval. Comparison of this new method with existing coordinate transformation techniques shows that more accurate evaluation of weakly singular integrals can be obtained. Based on observation of several integrals considered, guidelines are suggested for the type of semi‐sigmoidal transformation to use and the degree to which nodes should be clustered at the singular points. Copyright © 2000 John Wiley & Sons, Ltd.     

Analytic formulations for calculating nearly singular integrals in two-dimensional BEM

There exist the nearly singular integrals in the boundary integral equations when a source point is close to an integration element but not on the element, such as the field problems with thin domains. In this paper, the analytic formulations are achieved to calculate the nearly weakly singular, strongly singular and hyper-singular integrals on the straight elements for the two-dimensional (2D) boundary element methods (BEM). The algorithm is performed after the BIE are discretized by a set of boundary elements. The singular factor, which is expressed by the minimum relative distance from the source point to the closer element, is separated from the nearly singular integrands by the use of integration by parts. Thus, it results in exact integrations of the nearly singular integrals for the straight elements, instead of the numerical integration. The analytic algorithm is also used to calculate nearly singular integrals on the curved element by subdividing it into several linear or sub-parametric elements only when the nearly singular integrals need to be determined. The approach can achieve high accuracy in cases of the curved elements without increasing other computational efforts. As an application, the technique is employed to analyze the 2D elasticity problems, including the thin-walled structures. Some numerical results demonstrate the accuracy and effectiveness of the algorithm.