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  

A virtual boundary spectral method with complex radius vector for acoustic radiation problem of 3-Dimension axisymetric cavity

作　　者：陆静[1,2] 向宇[1] 黄玉盈[2] 

机构地区：[1]广西工学院汽车工程系,柳州545006 [2]华中科技大学土木工程与力学学院,武汉430074

出　　处：《声学学报》2011年第3期308-317,共10页Acta Acustica

基　　金：国家自然科学基金资助项目(10662003)

摘　　要：基于虚拟边界积分法(或波叠加法),利用轴旋转空穴的儿何特性,将积分核函数和未知源强密度函数沿周向和子午线方向用Fourier级数展开,导出了轴旋转空穴辐射声压的谱表达式,进而采用复数矢径虚拟边界技术,建立了一种求解轴旋转空穴三维声辐射问题的新方法,可称之为复数矢径虚拟边界谱方法。该方法不仅不存在处理奇异积分问题,而且可在全波数域内有效克服解的非唯一性问题。通过与解析解的计算结果比较以及数值试验的验证表明,本文方法具有较高的计算精度和效率,且适用于较高频率范围的计算。Based on the virtual boundary integral equation method（wave superposition method）,the spectral expression of the radiation sound pressure is derived by expanding the integral kernel function and unknown source density distributed with Fourier series on circumferential and meridian direction according to the geometry characteristic of the axisymetric cavity.Then,a new method for solving the 3-D acoustic radiation problem of the axisymetric cavity is presented by adopting the complex radius vector boundary technology.This method is called virtual boundary spectral method with complex radius vector.The present method can not only avoid the singular integral,but also overcome the non-uniqueness of solution effectively for all wave numbers.The comparisons with the analytical solutions and validation of numerical experiments show that the present method is accurate and efficient,which is suitable for a higher frequency range.

关 键 词：声辐射问题 虚拟边界 谱方法 空穴 旋转 矢径 复数 三维 

分 类 号：O422.6[理学—声学]