轴对称结构声辐射预报的等效面声源与点声源联合算法

doi:10.12382/bgxb.2024.0317

摘要/Abstract

摘要：

轴对称结构作为工程中的常见结构,其声学仿真计算受到工程界广泛关注。对轴对称结构的声辐射问题,提出一种综合利用等效面声源与点声源的方法。针对传统等效点声源在对应结构内部Dirichlet特征频率处解非唯一和对于声学参数灵敏度较大问题,在结构内部布置面声源进行结构外声场的匹配运算,点声源则位于面声源内部以保证解的唯一性。根据结构的对称性,将表面声压与振速按旋转角度展成Fourier级数形式,利用级数之间正交性建立各项待定系数表达形式。基于波叠加原理,建立等效源强度与Fourier级数待定系数之间的关系方程,并把虚拟面积分方程转变为轴对称结构外侧边界积分和旋转角度积分的乘积形式;进一步利用形函数对结构外侧边界进行插值处理,以此获取轴对称结构表面声压与振速之间的传递函数。采用新方法与传统等效点声源法、面声源法与解析法等结果作对比,结果表明了新方法的精确性。

关键词: 等效声源, 轴对称结构, 波叠加, 特征频率, 声辐射

Abstract:

As a common structure in engineering, axisymmetric structures have attracted widespread attention in the engineering community for their acoustic simulation calculations. A method to comprehensively utilize the equivalent surface sound source and point sound source for predicting the acoustic radiation from axisymmetric structure is proposed. In response to the non-uniqueness of solutions for the traditional equivalent point sound sources at the corresponding Dirichlet characteristic frequency inside the structure and the high sensitivity to acoustic parameters, a surface sound source is arranged inside the structure for the matching operations of external sound field, while the point sound source is located inside the surface sound source to ensure the uniqueness of the solution. Based on the symmetry of the structure, the surface sound pressure and vibration velocity are expanded into Fourier series form according to the rotation angle, and the orthogonality between the series is utilized to establish the expression of various undetermined coefficients. An equation for the relationship between the equivalent source strength and the undetermined coefficients of Fourier series is established based on the principle of wave superposition, and the virtual area integral equation is transformed into a product form of the outer boundary integral and rotation angle integral of axisymmetric structure. The shape function is utilized to interpolate the outer boundary of the structure in order to obtain the transfer function between the surface sound pressure and vibration velocity of axisymmetric structure. The accuracy of the proposed method is demonstrated by comparing the results of the proposed method with those of traditional equivalent point sound source method, surface sound source method, and analytical method.

Key words: equivalent sound source, axial symmetry, wave superposition, characteristic frequency, acoustic radiation

中图分类号:

TB52
TB53

刘宝, 王小二, 张卫. 轴对称结构声辐射预报的等效面声源与点声源联合算法[J]. 兵工学报, 2025, 46(5): 240317-.

LIU Bao, WANG Xiao’er, ZHANG Wei. A Joint Algorithm of Equivalent Surface Sound Source and Point Sound Source for Predicting the Acoustic Radiation from Axisymmetric Structure[J]. Acta Armamentarii, 2025, 46(5): 240317-.

图/表 10

图1 等效源方法示意图

Fig.1 The sketch map of equivalent sound source method

图2 轴对称结构坐标示意图

Fig.2 Schematic diagram of axisymmetric structural coordinates

图3 θa=0°处声压实部比较图

Fig.3 Real part of acoustic pressure for θa=0°

图4 θa=0°处声压虚部比较图

Fig.4 Imaginary part of acoustic pressure for θa=0°

图5 θa=45°处声压实部比较图

Fig.5 Real part of acoustic pressure for θa=45°

图6 θa=45°处声压虚部比较图

Fig.6 Imaginary part of acoustic pressure for θa=45°

图7 θa=0°处无量纲化声压实部比较图

Fig.7 Real part of dimensionless acoustic pressure for θa=0°

图8 θa=0°处无量纲化声压虚部比较图

Fig.8 Imaginary part of dimensionless acoustic pressure for θa=0°

图9 θa=45°处无量纲化声压实部比较图

Fig.9 Real part of dimensionless acoustic pressure for θa=45°

图10 θa=45°处无量纲化声压虚部比较图

Fig.10 Imaginary part of dimensionless acoustic pressure for θa=45°

参考文献 29

[1]	罗祎, 陈鑫. 水下空气腔角反射器声散射特性[J]. 兵工学报, 2019, 40(10):2129-2135. doi: 10.3969/j.issn.1000-1093.2019.10.019
	LUO Y, CHEN X. Acoustic scattering characteristics of underwater air-filled cavity corner reflector[J]. Acta Armamentarii, 2019, 40(10):2129-2135. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.10.019
[2]	朱寅弢, 吴海军, 孙瑞华, 等. 声学时域边界元法的时间卷积计算方法研究[J]. 声学学报, 2023, 48(6):1218-1226.
	ZHU Y T, WU H J, SUN R H, et al. A convolution quadrature method for acoustic time domain boundary element method[J]. Acta Acustica, 2023, 48(6):1218-1226. (in Chinese)
[3]	LEES K L. Review:the use of equivalent source method in computational acoustics[J]. Journal of Computational Acoustics, 2017, 25(1):1630001.
[4]	谢志南, 郑永路, 章旭斌, 等. 弱形式时域完美匹配层——滞弹性近场波动数值模拟[J]. 地球物理学报, 2019, 62(8):3140-3154. doi: 10.6038/cjg2019M0425
	XIE Z N, ZHENG Y L, ZHANG X B, et al. Weak-form time-domain perfectly matched layer for numerical simulation of viscoelastic wave propagation in infinite-domain[J]. Chinese Journal of Geophysics, 2019, 62(8):3140-3154. (in Chinese)
[5]	SCHODER S, TOTH F, FREIDHAGER C, et al. Revisiting infinite mapping layer for open domain problems[J]. Journal of Computational Physics, 2019, 392:354-367. doi: 10.1016/j.jcp.2019.04.067
[6]	PANAGIOTOPOULOS D, DESMET W, DECKERS E. A fast multi-frequency iterative acoustic boundary element method solver based on a preconditioned accelerated recycling strategy[J]. Journal of Theoretical and Computational Acoustics, 2019, 31(4): 2350019.
[7]	张见明, 肖榕雄, 柴朋飞, 等. 双层插值边界面法研究进展[J]. 力学学报, 2024, 56(5):1-24.
	ZHANG J M, XIAO R X, CHAI P F, et al. Advance on dual interpolation boundary face method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5):1-24. (in Chinese)
[8]	刘宝, 王德石, 周奇郑, 等. 基于Burton-Miller方程的轴对称结构声学边界元方法[J]. 声学学报, 2019, 44(3):303-311.
	LIU B, WANG D S, ZHOU Q Z, et al. Acoustic boundary element method for axisymmetric structures based on Burton-Miller equation[J]. Acta Acustica, 2019, 44(3): 303-311. (in Chinese)
[9]	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 J Y, AN J Y, MA L, 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. (in Chinese)
[10]	MOHSEN A, HESHHAM M. A method for selecting chief points in acoustic scattering[J]. Canadian Acoustics, 2004, 32(1):5-12.
[11]	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(5): 2433-2438.
[12]	FERMANDEZ-GRANDE E, XENAKI A, GERSTOFT P. A sparse equivalent source method for near-field acoustic holography[J]. Journal of the Acoustical Society of America, 2017, 141(1):532-542.
[13]	ZOU M S, WU Y S, LIU H X. A three-dimensional sono-elastic method of ships in flnite depth water with experimental validation[J]. Ocean Engineering, 2018, 164:238-247.
[14]	黄河, 邹明松, 蒋令闻. 海洋波导中目标声辐射场的计算方法[J]. 声学学报, 2019, 44(6):1027-1035.
	HUANG H, ZOU M S, JIANG L W. Computing method of sound radiation of target in ocean acoustic environment[J]. Acta Acustica, 2019, 44(6):1027-1035. (in Chinese)
[15]	ZOU M S, LIU S X, JIANG L W, et al. A mixed analytical-numerical method for the acoustic radiation of a spherical double shell in the ocean-acoustic environment[J]. Ocean Engineering, 2020, 199:107040.
[16]	商德江, 钱治文, 何元安, 等. 基于联合波叠加法的浅海信道下圆柱壳声辐射研究[J]. 物理学报, 2018, 67(8):125-138.
	SHANG D J, QIAN Z W, HE Y A, et al. Sound radiation of cylinder in shallow water investigated by combined wave superposition method[J]. Acta Physica Sinica, 2018, 67(8):125-138. (in Chinese)
[17]	钱治文, 商德江, 孙启航, 等. 三维浅海下弹性结构声辐射预报的有限元-抛物方程法[J]. 物理学报, 2019, 68(2):145-158.
	QIAN Z W, SHANG D J, SUN Q H, et al. Acoustic radiation from a cylinder in shallow water by finite element-parabolic equation method[J]. Acta Physica Sinica, 2019, 68(2):145-158. (in Chinese)
[18]	WU S W, XIANG Y, QIN T. A novel hybrid superposition method for predicting ship seismic wave in shallow sea[J]. Ocean Engineering, 2022, 259:111948.
[19]	WILTON D T, MATHEWS I C, JEANS R A. A clarification of nonexistence problems with superposition method[J]. Journal of the Acoustical Society of America, 1993, 94(3): 1676-1680.
[20]	XIANG Y, LU J, HUANG Y Y. A fast wave superposition spectral method with complex radius vector combined with two-dimensional fast Fourier transform algorithm for acoustic radiation of axisymmetric bodies[J]. Journal of Sound & Vibration, 2012, 331(6):1441-1454.
[21]	陆静, 向宇, 黄玉盈. 求解轴旋转空穴三维声辐射问题的复数矢径虚拟边界谱方法[J]. 声学学报, 2011, 36(3): 308-317.
	LU J, XIANG Y, HUANG Y Y. A virtual boundary spectral method with complex radius vector for acoustic radiation problem of 3-Dimension axisymmetric cavity[J]. Acta Acustica, 2011, 36(3): 308-317. (in Chinese)
[22]	夏雪宝, 向阳, 王校青, 等. 基于波叠加法的声辐射阻计算研究[J]. 船舶力学, 2015, 19(1/2):206-214.
	XIA X B, XIANG Y, WANG X Q, et al. Research on the acoustic radiation resistance calculation based on wave superposition method[J]. Journal of Ship Mechanics, 2015, 19(1/2): 206-214. (in Chinese)
[23]	ZELLERS B C. An acoustic superposition method for computing structural radiation in spatially digitized domains[D]. State College,PA, US: The Pennsylvania State University, 2006.
[24]	HWANG J Y, CHANG S C. A retracted boundary integral equation for exterior acoustic problem with unique solution for all wave numbers[J]. Journal of the Physical Society of Japan, 1991, 15(1): 1167-1180.
[25]	GOUNOT Y J R, MUSAFIR R E. Genetic algorithms:a global search tool to find optimal equivalent source sets[J]. Journal of Sound & Vibration, 2009, 322(1/2):282-298.
[26]	PAVIC G. A technique for the computation of sound radiation by vibrating bodies using multipole substitute sources[J]. Acta Acustica United with Acustica, 2009, 92(1): 112-126.
[27]	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 H Y, SHANG D J, LI Q, et al. Sound radiation prediction for underwater structure by field-matching wave superposition method[J]. Acta Acustica, 2013, 38(2):137-146. (in Chinese)
[28]	WU S W, XIANG Y. Location optimization of monopole equivalent sources in wave superposition method[J]. International Journal of Acoustics and Vibration, 2018, 23(2):254-263.
[29]	刘宝, 胡金华, 程广利. 计算辐射噪声的面声源和点声源结合方法[J]. 兵工学报, 2021, 42(2):370-378. doi: 10.3969/j.issn.1000-1093.2021.02.014
	LIU B, HU J H, CHENG G L. A surface and point sound sources combined method for calculating radiated noise[J]. Acta Armamentarii, 2021, 42(2):370-378. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.02.014