预报振动噪声的径向基点插值无网格与无限元耦合方法

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (10) : 32-43.

论文

吴绍维1，向阳2，黄庭瑞3

作者信息 +

A meshless radial point interpolation coupled with improved infinite element method for predicting sound radiation

WU Shaowei1，XIANG Yang2，HUANG Tingrui3

Author information +

文章历史 +

摘要

为克服传统的有限元耦合无限元方法中的单元匹配问题，研究了径向基点插值法和无限元法的耦合规律，提出了一种预报无限域结构振动噪声的径向基点插值无网格与可变阶无限声波包络单元耦合方法，推导了预报声压的计算公式。为提高声场预报精度和满足声波在无限域的自由衰减，结构外部无限声场分为使用无网格表示的近场和可变阶声波包络单元离散的远场。在该耦合方法中，通过在近场与远场之间的交界面上配置虚拟网格来构造具有连续性的声压形函数，确保了声压的连续与一致性。采用数值仿真和试验对该耦合方法进行了验证，结果表明该耦合方法拥有无网格法的高精度和可变阶声波包络单元法满足声波自由衰减的特点，具有良好的精度和收敛性，可用于实际噪声预报。

Abstract

To eliminate the element matching in traditional method based on finite and infinite elements, the coupling of the radial point interpolation method (RPIM) and the variable order infinite acoustic wave envelope element (WEE)was studied.A RPIM coupled with improved WEE method was proposed for exterior sound problems in infinite domain.The coupling formula of this method was theoretically derived.To improve accuracy and properly imitate the amplitude decay of the outgoing travelling wave, the infinite acoustic field was divided into near and far acoustic fields, which were discretized by arbitrarily distributed nodes and WEEs respectively.The continuity and compatibility of the acoustic pressure were maintained by constructing hybrid acoustic pressure shape function on the fictitious meshin the near field along the interface between the two fields.Simulations and experiments were performed to test the method.The results show that the method can take full advantage of both the RPIM and WEE methods and is a valuable approach.

导出引用

吴绍维1，向阳2，黄庭瑞3. 预报振动噪声的径向基点插值无网格与无限元耦合方法[J]. 振动与冲击, 2020, 39(10): 32-43

WU Shaowei1，XIANG Yang2，HUANG Tingrui3. A meshless radial point interpolation coupled with improved infinite element method for predicting sound radiation[J]. Journal of Vibration and Shock, 2020, 39(10): 32-43

参考文献

[1] Thompson L L. A review of finite-element methods for time-harmonic acoustics[J]. Journal of the Acoustical Society of America, 2006, 119(3)：1315-1330.

[2] Marburg S. A pollution effect in the boundary element method for acoustic problems[J]. Journal of Theoretical and Computational Acoustics, 2018, 26(2)：1850018.

[3] Visser R. A boundary element approach to acoustic radiation and source identification[D]. Enschede：University of Twente, 2006.

[4] 缪宇跃，李天匀，朱翔，等. 声学边界元拟奇异积分计算的自适应方法[J]. 振动与冲击，2017, 36(2)：23-31.

MIAO Yu-yue, LI Tian-yun, ZHU Xiang. Adaptive method for calculating nearly singular integrals in acoustic boundary elements[J]. Journal of vibration and shock, 2017, 36(2)：23-31.

[5] 龚家元，安俊英，马力，等. 边界元奇异与近奇异数值积分方法及其应用于大规模声学问题[J]. 声学学报，2016, 41(5)：768-775.

GONG Jia-yuan, AN Jun-ying, MA Li, et al. Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems[J]. Acta Acustica, 2016, 41(5)：768-775.

[6] Chai Y B, Li W, Gong Z X, et al. Hybrid smoothed finite element method for two-dimensional under water acoustic scattering problems [J]. Ocean Engineering, 2016, 116：129-141.

[7] Gonzalez J D, Lavia F F, Blanc S. A Computational Method to Calculate the Exact Solution for Acoustic Scattering by Fluid Spheroids[J]. Acta Acustica United with Acustica, 2016, 102(6)：1061-1071.

[8] Liu G R, Zhang G Y. Smoothed point interpolation methods: G space theory and weakened weak forms[M]. Singapore：World Scientific, 2013.

[9] Liu G R, Zhang G Y, Zong Z, et al. Meshfree cell-based smoothed alpha radial point interpolation method (CS-α RPIM) for solid mechanics problems[J]. International Journal of Computational Methods, 2013, 10(4)：1350020.

[10] Chai Y B, Li W, Gong Z X, et al. Hybrid smoothed finite element method for two dimensional acoustic radiation problems[J]. Applied Acoustics, 2016, 103：90-101.

[11] Chai Y B, Li W, Li T Y, et al. Analysis of underwater acoustic scattering problems using stable node-based smoothed finite element method[J]. Engineering Analysis with Boundary Elements, 2016, 72：27-41.

[12] Li W, Chai Y B, Lei M, et al. Numerical investigation of the edge-based gradient smoothing technique for exterior Helmholtz equation in two dimensions[J]. Computers &Structures, 2017, 182：149-164.

[13] Chai Y B, Li W, Liu G R, et al. A superconvergent alpha finite element method (SαFEM) for static and free vibration analysis of shell structures[J]. Computers &Structures, 2017, 179：22-47.

[14] Cremers L, Fyfe K R. A variable order infinite acoustic wave envelope element[J]. Journal of Sound and Vibration, 1994, 171(4)：483-508.

[15] Cremers L, Fyfe K R. On the use of variable order infinite wave envelope elements for acoustic radiation and scattering[J]. Journal of the Acoustical Society of America, 1994, 97(4)：2028-2040.

[16] Moheit L, Marburg S. Infinite elements and their influence on normal and radiation modes in exterior acoustics[J]. Journal of Computational Acoustics, 2017, 25(4)：1650020.

[17] Baghbani A, Gregory-Smith D. A new infinite element for unbounded water wave problems[J]. Applied Ocean Research, 2003, 25(4)：213-223.

[18] Autrique J C, Magoules F. Studies of an infinite element method for acoustical radiation[J]. Applied Mathematical Modelling, 2006, 30(7)：641-655.

[19] Liu G R, Gu Y T. An introduction to meshfree methods and their programming[M]. The Netherlands：Springer Verlag, 2006.

[20] Zhang Z, Hao S Y, Liew K M, et al. The improved element-free Galerkin method for two-dimensional elastodynamics problems[J]. Engineering Analysis with Boundary Elements, 2013, 37(12)：1576-1584.

[21] Abbasbandy S, Ghehsareh H R, Hashim I. Numerical analysis of a mathematical model for capillary formation in tumor angiogenesis using a meshfree method based on the radial basis function[J]. Engineering Analysis with Boundary Elements, 2012, 36(12)：1811-1818.

[22] Gu Y T, Liu G R. A meshfree weak-strong (MWS) form method for time dependent problems[J]. Computational Mechanics, 2005, 35(2：134-145.

[23] Liu G R, Gu Y T. A point interpolation method for two-dimensional solids[J]. International Journal for Numerical Methods in Engineering, 2001, 50(4)：937-951.

[24] Liu G R, Gu Y T. A matrix triangularization algorithm for the polynomial point interpolation method[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(19)：2269-2295.

[25] Biancolini M E, Chiappa A, Giorgetti F, et al. A balanced load mapping method based on radial basis functions and fuzzy sets[J]. International Journal for Numerical Methods in Engineering, 2018, 115(12)：1411-1429.

[26] Wang J G, Liu G R. A point interpolation meshless method based on radial basis functions[J]. International Journal for Numerical Methods in Engineering, 2002, 54(11)：1623-1648.

[27] Wang J G, Liu G R, Lin P. Numerical analysis of Biot’s consolidation process by radial point interpolation method[J]. International Journal of Solids & Structures, 2002, 39(6)：1557-1573.

[28] Liu G R, Dai K Y, Lim K M, et al. A radial point interpolation method for simulation of two-dimensional piezoelectric structures[J]. Smart Material Structures, 2003, 12(2)：171-180.

[29] Wenterodt C, Estorff O V. Optimized meshfree methods for acoustics[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(25)：2223-2236.

[30] 陈宁，于德介，吕辉，等. 板结构-声场耦合分析的FE-LSPIM/FE-LSPIM法[J]. 振动与冲击，2014,33(15)：131-137.

CHEN Ning, YU De-jie, LV Hui, et al. A finite element-least square point interpolation method for simulation analysis of plate structural-acoustic coupled systems[J]. Journal of vibration and shock, 2014, 33(15)：131-137.

[31] 杜功焕，朱哲民，龚秀芬. 声学基础[M]. 南京：南京大学出版社，2012.

DU Gong-huan, ZHU Zhe-min, GONG Xiu-fen. Fundamentals of acoustics[M]. Nanjing: Nanjing University Press, 2012.

[32] 吴绍维，向阳，张波. 自由场声辐射预报的可变阶波包络单元与有限元耦合方法[J]. 机械工程学报，2018, 54(7)：74-86.

WU Shao-wei, XIANG Yang, ZHANG Bo. A coupled variable order acoustic wave envelope element-finite element method for sound radiation in Infinite domain[J]. Journal of Mechanical Engineering, 2018, 54(7)：74-86.

[33] Wu S W, Xiang Y, Yao J C. A Meshfree Radial Point Interpolation Coupled with Infinite Acoustic Wave Envelope Element Method for Computing Acoustic Fields[J]. Acta Acustica United with Acustica, 2018, 104(1)：64-78.

[34] 陈鸿洋，商德江，李琪，等. 声场匹配波叠加法的水下结构声辐射预报[J]. 声学学报，2013, 38(2)：137-146.

CHEN Hong-yang, SHANG De-jiang, LI Qi, et al. Sound radiation prediction for underwater structure by field-matching wave superposition method[J]. Acta Acustica, 2013, 38(2)：137-146.