在可变阶波包络单元法和声有限元法的基础上，研究了预报无限域自由场结构声辐射的可变阶波包络单元与有限元耦合方法，推导了预报声压的耦合计算公式。在该方法中，结构外区域自由场空间分为使用有限元单元离散的内区域和可变阶波包络单元离散的外区域，根据外区域波包络单元构成的刚度矩阵的组成特性，对其进行分解，并对总系统耦合矩阵方程进行了重组，使得刚度矩阵的计算独立于频率，提高了频段上声压预报的效率。质量、刚度及载荷矩阵的元素需通过积分运算获取，积分精度对最终声场预报的精度具有很大的影响，为确保积分精度，提出了一种混合自适应高斯积分来计算相关矩阵的元素。具有解析解的无限长圆柱和脉动球源算例表明，对可变阶波包络单元组成的刚度矩阵进行分解后，计算效率得以显著提高；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具有较好的精度和收敛性。
A coupled variable order acoustic wave envelope element-finite element method for sound radiation in infinite domain is studied based on wave envelope element method and finite element method. The coupling formula for predicting sound pressure is theoretically derived. In this method, the infinite domain exterior to structure is divided into inner region meshed with finite element and outer region discretized with wave envelope element. To improve computational efficiency in frequency range, the stiffness matrix corresponding to outer region is decomposed according to its characteristics to make the stiffness matrix in total coupled equation independent on the frequency. A hybrid adaptive Gauss integral is devised to calculate the matrix elements which have great effect on the prediction accuracy of the pressure. Examples of acoustic radiations from a uniformly pulsating sphere and an infinitely long cylinder indicate that the computational efficiency is improved significantly based on the decomposition. Simulations and experiments are performed to test the coupled method. The results show that the method has good accuracy and convergence.
[1] VISSER R. A boundary element approach to acoustic radiation and source identification[D]. Enschede:University of Twente, 2004.
[2] DAVEY K, FAROOQ A. Evaluation of free terms in hypersingular boundary integral equations[J]. Engineering Analysis with Boundary Elements, 2011, 35(9):1060-1074.
[3] D'AMICO R, NEHER J, WENDER B, et al. On the improvement of the solution accuracy for exterior acoustic problems with BEM and FMBEM[J]. Engineering Analysis with Boundary Elements, 2012, 36(7):1104-1115.
[4] SEYBERT A F, RENGARAJAN T K. The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations[J]. Journal of the Acoustical Society of America, 1987, 81(5):1299-1306.
[5] BURTON A, MILLER G. The application of the integral equation methods to the numerical solution of some exterior boundary-value problems[J]. Preceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 1971, 323:201-210.
[6] 赵志高. 结构声辐射的机理与数值方法研究[D]. 武汉:华中科技大学, 2005. ZHAO Zhigao. Research on principle and numerical method of sound radiation for structure[D]. Wuhan:Huazhong University of Science&Technology, 2005.
[7] KOOPMANN G H, SONG L, FAHNLINE J B. A method for computing acoustic fields based on the principle of wave superposition[J]. Journal of the Acoustical Society of America, 1989, 86(6):2433-2438.
[8] GOUNT Y J R, MUSAFIR R E. Simulation of scattered fied:Some guidelines for the equivalent source method[J]. Journal of Sound and Vibration, 2011, 330(5):3698-3709.
[9] BAI M R, CHEN Chingcheng, LIN Jiahong. On optimal retreat distance for the equivalent source method based nearfield acoustical holohraphy[J]. Journal of the Acoustical Society of America, 2011, 129(3):1407-1416.
[10] 吴绍维,向阳,李胜杨. 体积速度匹配分布源边界点法的特解源位置优化方法研究[J]. 声学学报,2015,40(3):381-390. WU Shaowei, XIANG Yang, LI Shengyang. Research on position optimization of particular sources for distributed source boundary point method by volume velocitymatching[J]. Acta Acustica, 2015, 40(3):381-390.
[11] 毕传心,袁艳,贺春东,等. 基于分布源边界点法的局部近场声全息技术[J]. 物理学报, 2010, 59(12):8646-8654. BI Chuanxin, YUAN Yan, HE Chundong, et al. Patch nearfield acoustic holography based on the distributed source boundary point method[J]. Acta Physica Sinica, 2010, 59(12):8646-8654.
[12] 陈心昭,毕传心. 近场声全息技术及其应用[M]. 北京:科学出版社, 2013. CHEN Xinzhao, BI Chuanxin. Near field acoustic holography and applications[M]. Beijing:Science Press, 2013.
[13] 夏百战,于德介,姚凌云. 二维声学数值计算的径向插值有限元法[J]. 机械工程学报, 2012, 48(11):159-165. XIA Baizhan, YU Dejie, YAO Lingyun. Radial interpolation finite element method for two dimension acoustic numerical computation[J]. Journal of Mechanical Engineering, 2012, 48(11):159-165.
[14] 催向阳,胡鑫,王刚,等. 二维声学数值计算的梯度最小二乘加权[J]. 机械工程学报, 2016, 52(15):52-58. CUI Xiangyang, HU Xin, WANG Gang, et al. Gradient weighted by moving least-squares for two dimension acoustic numerical computation[J]. Journal of Mechanical Engineering, 2016, 52(15):52-58.
[15] HUANG Jun, ZHANG Jianhui, SHI Weidong, et al. 3D FEM analyses on flow field characteristics of the valveless piezoelectric pump[J]. Chinese Journal of Mechanical Engineering, 2016, 29(4):825-831.
[16] ASTLEY R J, MACAULAY G J. Mapped wave envelope element for acoustical radiation and scattering[J]. Journal of Sound and Vibration, 1994, 170(1):97-118.
[17] ASTLEY R J, MACAULAY G J. Three-dimensional wave-envelope elements of variable order for acoustic radiation and scattering. Part I. Formulation in the frequency domain[J]. Journal of the Acoustical Society of America, 2007, 103(1):49-83.
[18] CREMERS L, FYFE K R. A variable order infinite acoustic wave envelope element[J]. Journal of Sound and Vibration, 1994, 171(4):483-508.
[19] ASTLEY R J, COYETTE J P. The performance of spheroidal infinite elements[J]. International Journal for Numerical Methods in Engineering, 2001, 52(12):1379-1396.
[20] DREYER D, PRETERSEN S, ESTORFF O V. Effectiveness and robustness of improved infinite elements for exterior acoustics[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(29):3591-3607
[21] BAGHBANI A, GREGORY-SMITH D. A new infinite element for unbounded water wave problems[J]. Applied Ocean Research, 2003, 25(4):213-223.
[22] 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.
[23] 魏应三, 王永生. 基于声场精细积分算法的潜艇流噪声预报[J]. 计算力学学报, 2014, 29(4):574-581. WEI Yingsan, WANG Yongsheng. Flow-excited submarine structure acoustic prediction based on a refined integral algorithm[J]. Chinese Journal of Computational Mechanics, 2014, 29(4):574-581.
[24] 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 Gonghuan, ZHU Zhemin, GONG Xiufen. Fundamentals of acoustics[M]. Nanjing:Nanjing University Press, 2012.
