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Wang Junpeng, Xiao Jinyou, Wen Lihua. AN EFFICIENT NUMERICAL METHOD FOR LARGE-SCALE MODAL ANALYSIS USING BOUNDARY ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1070-1080. doi: 10.6052/0459-1879-17-040
Citation: Wang Junpeng, Xiao Jinyou, Wen Lihua. AN EFFICIENT NUMERICAL METHOD FOR LARGE-SCALE MODAL ANALYSIS USING BOUNDARY ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1070-1080. doi: 10.6052/0459-1879-17-040

AN EFFICIENT NUMERICAL METHOD FOR LARGE-SCALE MODAL ANALYSIS USING BOUNDARY ELEMENT METHOD

doi: 10.6052/0459-1879-17-040
  • Received Date: 2017-02-15
    Available Online: 2017-07-20
  • Publish Date: 2017-09-18
  • Thanks to the great advances in fast boundary element method (BEM) achieved in the last two decades, the BEM has been increasingly used in the dynamic design of engineering structures, the analysis of noise and vibration. Consequently, solving large-scale eigenvalue problems and performing modal analysis for complicated structures and acoustic fields using the BEM becomes an very important but challenging task; so far there are no effective numerical methods for this purpose. This paper aims to extend the application of the newly-developed resolvent sampling based Rayleigh-Ritz projection method (RSRR) to the solution of the general nonlinear eigenvalue problems (NEP) in BEM. First, in order to generate reliable eigenvector search spaces, a series of BEM linear systerms in frequency domain are solved. Then the original NEP can be transformed to a reduced NEP based the classical Rayleigh-Ritz procedure, and the reduced NEP could be solved by those exiting NEP solvers easily. Second, to reduce the prohibitive computational burden involved in solving the projected NEP by the Rayleigh-Ritz procedure, a BEM matrix interpolation technique and a fast computation method for reduced NEP systerm matrix are proposed based on the discretized Cauchy integral formula of analytic functions. Then a simple rule for estimating the number of terms in the interpolation is proposed as well. Finally, the RSRR method is used to solve large-scale practical acoustic modal analysis problems using fast BEM with complicated sound absorbing boundary conditions. Numerical results indicate that the method can robustly dig out all the interested eigenvalues and the corresponding eigenvectors with good accuracy and high computational efficiency.

     

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  • [1]
    姚振汉, 王海涛.边界元法.北京:高等教育出版社, 2010

    Yao Zhenghan, Wang Haitao. Boundary Element Method. Beijing:Higher Education Press, 2010 (in Chinese)
    [2]
    高效伟, 刘健, 彭海峰.集成单元边界元法及其在主动冷却热防护系统分析中的应用.力学学报, 2016, 48(4):994-1003 http://lxxb.cstam.org.cn/CN/abstract/abstract145937.shtml

    Gao Xiaowei, Liu Jian, Peng Haifeng. Integrated unit BEM and its application in analysis of actively cooling TPS. Chinese Journal of Theoretical and Applied Mechnics, 2016, 48(4):994-1003 (in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract145937.shtml
    [3]
    申建伟, 孙中奎, 詹世革等.第9届全国动力学与控制青年学者学术研讨会报告综述.力学学报, 2015, 47(6):1079-1083 doi: 10.6052/0459-1879-15-366

    Shen Jianwei, Sun Zhongkui, Zhan Shige, et al. Review of the ninth national symposium on dynamics and control for young scholars. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6):1079-1083 (in Chinese) doi: 10.6052/0459-1879-15-366
    [4]
    荣俊杰, 校金友, 文立华.弹性动力学高阶核无关快速多极边界元法.力学学报, 2014, 46(5):776-785 http://lxxb.cstam.org.cn/CN/abstract/abstract144819.shtml

    Rong Junjie, Xiao Jinyou, Wen Lihua. A high order kernel independent fast multipole boundary element method for elastodynamics. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5):776-785 (in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract144819.shtml
    [5]
    Liu YJ, Mukherjee S, Nishimura N, et al. Recent advances and emerging applications of the boundary element method. Applied Mechanics Reviews, 2011, 64(3):030802 http://appliedmechanicsreviews.asmedigitalcollection.asme.org/article.aspx?articleid=1678921
    [6]
    Tisseur F, Meerbergen K. The quadratic eigenvalue problem. SIAM Review, 2001, 43(2):235-286 doi: 10.1137/S0036144500381988
    [7]
    Mehrmann V, Schröder C. Nonlinear eigenvalue and frequency response problems in industrial practice. Journal of Mathematics in Industry, 2011, 1(1):7 doi: 10.1186/2190-5983-1-7
    [8]
    Effenberger C. Robust solution methods for nonlinear eigenvalue problems.[PhD Thesis]. École polytechnique fédérale de Lausanne, 2013 doi: 10.5075/epfl-thesis-5920
    [9]
    Van Beeumen, Rational Krylov methods for nonlinear eigenvalue problems[PhD Thesis], KU Leuven, 2015 http://lirias.kuleuven.be/handle/123456789/487915
    [10]
    Ali A, Rajakumar C, Yunus SM. Advances in acoustic eigenvalue analysis using boundary element method. Computers & Structures, 1995, 56(5):837-847 http://www.sciencedirect.com/science/article/pii/0045794995000126
    [11]
    Bezine G. A mixed boundary integral-finite element approach to plate vibration problems. Mechanics Research Communications, 1980, 7(3):141-150 doi: 10.1016/0093-6413(80)90003-8
    [12]
    Nardini D, Brebbia CA. A new approach to free vibration analysis using boundary elements. Applied Mathematical Modelling, 1983, 7(3):157-162 doi: 10.1016/0307-904X(83)90003-3
    [13]
    Ali A, Rajakumar C, Yunus SM. On the formulation of the acoustic boundary element eigenvalue problems. International Journal for Numerical Methods in Engineering, 1991, 31(7):1271-1282 doi: 10.1002/(ISSN)1097-0207
    [14]
    Kamiya N, Andoh E. Standard eigenvalue analysis by boundaryelement method. International Journal for Numerical Methods in Biomedical Engineering, 1993, 9(6):489-495 doi: 10.1002/cnm.1640090606/pdf
    [15]
    Asakura J, Sakurai T, Tadano H, et al. A numerical method for nonlinear eigenvalue problems using contour integrals. JSIAM Letters, 2009, 1:52-55 doi: 10.14495/jsiaml.1.52
    [16]
    Beyn WJ. An integral method for solving nonlinear eigenvalue problems. Linear Algebra and Its Applications, 2012, 436(10):3839-3863 doi: 10.1016/j.laa.2011.03.030
    [17]
    Sakurai T, Asakura J, Tadano H, et al. Error analysis for a matrix pencil of Hankel matrices with perturbed complex moments. JSIAM Letters, 2009, 1:76-79 doi: 10.14495/jsiaml.1.76
    [18]
    Yokota S, Sakurai T. A projection method for nonlinear eigenvalue problems using contour integrals. JSIAM Letters, 2013, 5:41-44 doi: 10.14495/jsiaml.5.41
    [19]
    Zheng CJ, Chen HB, Gao HF, et al. Is the Burton-Miller formulation really free of fictitious eigenfrequencies? Engineering Analysis with Boundary Elements, 2015, 59:43-51 doi: 10.1016/j.enganabound.2015.04.014
    [20]
    Gao HF, Matsumoto T, Takahashi T, et al. Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai-Sugiura method. Engineering Analysis with Boundary Elements, 2013, 37(6):914-923 doi: 10.1016/j.enganabound.2013.03.015
    [21]
    Leblanc A, Lavie A. Solving acoustic nonlinear eigenvalue problems with a contour integral method. Engineering Analysis with Boundary Elements, 2013, 37(1):162-166 doi: 10.1016/j.enganabound.2012.09.007
    [22]
    Xiao JY, Meng SS, Zhang CZ, et al. Resolvent sampling based Rayleigh-Ritz method for large-scale nonlinear eigenvalue problems. Computer Methods in Applied Mechanics and Engineering, 2016, 310:33-57 doi: 10.1016/j.cma.2016.06.018
    [23]
    Xiao JY, Zhou H, Zhang CZ, et al. Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method. Computational Mechanics, 2016:1-18 http://dl.acm.org/citation.cfm?id=3054532
    [24]
    Mehrmann V, Voss H. Nonlinear eigenvalue problems:A challenge for modern eigenvalue methods. GAMM-Mitteilungen, 2004, 27(2):121-152 doi: 10.1002/gamm.v27.2
    [25]
    Leblanc A, Lavie A. Numerical analysis of eigenproblem for cavities by a particular integral method with a low frequency approximation of surface admittance. The Journal of the Acoustical Society of America, 2012, 131(5):3876-3882 doi: 10.1121/1.3699270
    [26]
    Du JT, Li WL, Liu ZG, et al. Acoustic analysis of a rectangular cavity with general impedance boundary conditions. The Journal of the Acoustical Society of America, 2011, 130(2):807-817 doi: 10.1121/1.3605534
    [27]
    屈伸, 陈浩然.敷设多孔吸声材料声腔特征值分析的径向积分边界元法.计算力学学报, 2015, 32(1):123-128 doi: 10.7511/jslx201501021

    Qu Shen, Chen Haoran. Eigenvalue analysis for acoustical cavity covered with porous materials by using the radial integration boundary element method. Chinese Journal of Computational Mechanics, 2015, 32(1):123-128 (in Chinese) doi: 10.7511/jslx201501021
    [28]
    陈文炯, 刘书田.周期性吸声多孔材料微结构优化设计.计算力学学报, 2013, 30(1):45-50 doi: 10.7511/jslx201301008

    Chen Wenjiong, Liu Shutian. Optimizing design of micro-structural configurations of periodic porous soundabsorbing materials. Chinese Journal of Computational Mechanics, 2013, 30(1):45-50(in Chinese) doi: 10.7511/jslx201301008
    [29]
    Cao YC, Wen LH, Xiao JY, et al. A fast directional BEM for largescale acoustic problems based on the Burton-Miller formulation. Engineering Analysis with Boundary Elements, 2015, 50:47-58 doi: 10.1016/j.enganabound.2014.07.006
    [30]
    Engquist B, Ying Lexing. Fast directional multilevel algorithms for oscillatory kernels. SIAM Journal on Scientific Computing, 2007, 29(4):1710-1737 doi: 10.1137/07068583X
    [31]
    Rong J, Wen L, Xiao J. Efficiency improvement of the polar coordinate transformation for evaluating BEM singular integrals on curved elements. Engineering Analysis with Boundary Elements, 2014, 38:83-93 doi: 10.1016/j.enganabound.2013.10.014
    [32]
    Gohberg I, Rodman L. Analytic matrix functions with prescribed local data. Journal d'Analyse Mathématique, 1981, 40(1):90-128 doi: 10.1007/BF02790157
    [33]
    Austin AP, Kravanja P, Trefethen LN. Numerical algorithms based on analytic function values at roots of unity. SIAM Journal on Numerical Analysis, 2014, 52(4):1795-1821 doi: 10.1137/130931035
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