The non-uniqueness of sound field solution at corresponding structural internal characteristic frequencies and the high sensitivity of the solution to the point sound source positions exist in virtual point sound source method. A method is proposed to utilize the surface sound sources and point sound sources to model the sound field, thus achieving the uniqueness of solution and the high calculation accuracy in the whole wavenumber domain. According to wave superposition principle, the virtual surface sound sources and point sound sources are simultaneously arranged inside the structure to disperse the sound fields. The surface sound sources are located on a surface conformal to the structural boundary in order to match the sound pressure and vibration velocity of the structural surface. The point sound sources are located inside the virtual surface.A sound radiation impedance matrix was constructed using the linearized Euler equation, and the acoustic parameters of the structure, such as surface sound pressure and vibration velocity, were obtained. Taking pulsating spherical source and transverse vibration spherical source as examples, on the basis of comparing the calculation accuracies of using surface sources and point sources, the accuracy and uniqueness of the proposed method are illustrated by comparing the results with the analytical solutions.
LIU Bao, HU Jinhua, CHENG Guangli.
A Surface and Point Sound Sources Combined Method for Calculating Radiated Noise. Acta Armamentarii. 2021, 42(2): 370-378 https://doi.org/10.3969/j.issn.1000-1093.2021.02.014
[1]SUNF X, LIU C, CHEN Y M. An improved interpolating element-free Galerkin method based on nonsingular weight functions[J]. Mathematical Problems in Engineering, 2014(8):249-269. [2]夏百战,于德介,姚凌云. 二维多流体域耦合声场的光滑有限元解法[J]. 声学学报,2012,37(6):601-609. XIA B Z,YU D J,YAO L Y. A smoothed finite element method for two-dimensional coupling acoustic fields in multi-fluid domain[J]. Chinese Journal of Acoustics,2012,37(6):601-609. (in Chinese) [3]LIU J Y, RUDOLPHI T J. New identities for fundamental solutions and their applications to non-singular boundary element formulations[J]. Computational Mechanics,1999,24(4):286-292. [4]ATALLAN,BEMHARD R J.Review of numerical solutions for low-frequency structural-acoustic problems[J].Applied Acoustics,1994,43(3):271-294. [5]COYETTE J P,FYFE K R.An improved formulation for acoustic eigenmode extraction from boundary element methods[J].Journal of Vibration and Acoustics,1990,112(3):392-397. [6]BURTON A J,MILLER G F.The application of integral equation methods to the numerical solution of some exterior boundary-value problems[J].Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences ,1971,323(1553):201-210. [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]SONG L,KOOPMANN G H,FAHNLINEJ B.Numerical errors associated with the method of superposition for computing acoustic fields[J].Journal of the Acoustical Society of America,1991,89(6): 2625-2633. [9]KOOPMANN G H,BELEGUNDU A D.Tuning a wine glass via material tailoring an application of a method for optimal acoustic design[J].Journal of Sound and Vibration,2001,239 (4):665-678. [10]KOOPMANNG H,FAHNLINE J B.Designing quiet structures: a sound power minimization approach [M].San Diego, CA ,US: Academic Press, 1997. [11]BENTHIEN G W,SCHENCK H A.Nonexistence and nonuniqueness problems associated with integral equation methods in acoustic[J].Computers & Structures,1997,65(3):295-305. [12]JEANS R A,MATHEWS I C.The wave superposition method as a robust technique for computing acoustic fields[J].Journal of the Acoustical Society of America,1992,92(2):1156-1166. [13]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. [14]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. [15]向宇,黄玉盈,马小强.求解二维结构—声耦合问题的一种直接方法[J].振动与冲击,2003,22(4):40-44,31. XIANG Y,HUANG Y Y,MA X Q.Direct solution to 2-D sound-structure interaction problems[J].Journal of Vibration and Shock,2003,22(4):40-44,31.(in Chinese) [16]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[J].Journal of Ship Mechanics,2015,19(1/2):206-214.(in Chinese) [17]夏雪宝,向阳.基于附加源波叠加法的声辐射计算研究[J].振动与冲击,2015,34(1):104-109. XIA X B,XIANG Y.Acoustic radiation calculation based on additional sources wave superposition method[J].Journal of Vibration and Shock,2015,34(1):104-109.(in Chinese) [18]向宇, 黄玉盈. 伸缩虚拟边界元法解二维Helmholtz外问题[J]. 力学学报,2003,35(3):272-279. XIANG Y,HUANG Y Y.The expanding-contracting virtual boundary element method for 2D-Helmholtz exterior problems[J].Acta Mechanica Sinica,2003,35(3):272-279.(in Chinese) [19]GOLUB G H,VAN LOAN C F.Matrix computations[M].Baltimore, MD, US: Johns Hopkins University Press,1983:11-29. [20]BORGIOTTI G V,SARKISSIAN A,Williams E G,et al.Conformal generalized near-field acoustic holography for axisymmetric geometries[J].Journal of the Acoustical Society of America,1990,88(1):199-209. [21]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. [22]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 Acoustical Society of America ,1991,90(2):167-180. [23]GOUNOTY 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. [24]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. [25]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]. Chinese Journal of Acoustics,2013,38(2):137-146. (in Chinese) [26]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. [27]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)