大规模边界元模态分析的高效数值方法

发布时间：2018-03-03 04:10

本文选题：边界元法　切入点：非线性特征值问题　出处：《力学学报》2017年05期 　论文类型：期刊论文

【摘要】：随着大规模快速边界元计算技术的发展,在复杂结构的动态设计、振动与噪声分析中愈来愈多地采用边界元法,因此求解大规模边界元特征值问题、进行复杂结构和声场模态分析,成为工程应用中一个十分重要,但却极具挑战性的课题,目前国际上还没有十分有效的数值方法.本文针对边界元法中典型的非线性特征值问题,提出了一种通用、高效的数值解法,称为基于预解矩阵采样的Rayleigh-Ritz投影法,记为RSRR.首先,通过求解一系列频域边界元问题来构造特征向量搜索空间,进而可以采用Rayleigh-Ritz投影,将原问题转化为一个可以采用现有方法求解的小规模缩减特征值问题;其次,为了降低Rayleigh-Ritz投影过程的计算量,基于解析函数的Cauchy积分公式,构造了边界元系数矩阵的插值近似方法,以及缩减特征值问题系数矩阵的快速计算方法,给出了插值项数的估计策略;最后,将RSRR与声学快速边界元法结合,应用于大规模吸声结构的复模态分析.数值算例表明,RSRR方法能够可靠地求出给定频段内的全部特征值和特征向量,具有计算效率高、精度高、通用等优点.
[Abstract]:With the development of large-scale and fast boundary element computing technology, the boundary element method is used more and more in the dynamic design, vibration and noise analysis of complex structures, so the eigenvalue problem of large-scale boundary element is solved. Modal analysis of complex structures and sound fields has become a very important but challenging subject in engineering applications. At present, there is no very effective numerical method in the world. In this paper, a general and efficient numerical method is proposed to solve the typical nonlinear eigenvalue problems in BEM, which is called Rayleigh-Ritz projection method based on the sampling of resolvent matrix. By solving a series of frequency-domain boundary element problems, the eigenvector search space can be constructed, and then the Rayleigh-Ritz projection can be used to transform the original problem into a small-scale reduced eigenvalue problem that can be solved by the existing methods. In order to reduce the computation of Rayleigh-Ritz projection process, based on the Cauchy integral formula of analytic function, the interpolation approximation method of boundary element coefficient matrix and the fast calculation method of reducing eigenvalue problem coefficient matrix are constructed. The estimation strategy of interpolation term number is given. Finally, RSRR is combined with acoustical fast boundary element method. A numerical example shows that the RSRR method can reliably obtain all eigenvalues and Eigenvectors in a given frequency band, and has the advantages of high computational efficiency, high accuracy and generality.
【作者单位】：西北工业大学航天学院;
【基金】：国家自然科学基金(11102154,11472217) 中央高校基本科研业务费专项资金资助项目
【分类号】：O241;O42

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