正交球面波源的近场声全息射线波函数波叠加法  

Wave superposition method with ray wave functions for near‑field acoustic holography based on orthogonal spherical wave sources

作　　者：石梓玉 向宇[1,2] 陆静[1,2] 王玉江[1,2] SHI Zi‑yu;XIANG Yu;LU Jing;WANG Yu‑jiang(Guangxi Key Laboratory of Automobile Components and Vehicle Technology,Guangxi University of Science and Technology,Liuzhou 545006,China;School of Mechanical and Automotive Engineering,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]广西科技大学广西汽车零部件与整车技术重点实验室,广西柳州545006 [2]广西科技大学机械与汽车工程学院,广西柳州545006

出　　处：《振动工程学报》2023年第2期534-544,共11页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51775121)。

摘　　要：在基于传统波叠加法的近场声全息技术中,多采用辐射球面波的单极子作为等效源,易导致传递矩阵病态,利用射线波函数替换球面波函数可有效改善传递矩阵病态性。然而,以往的射线波函数法采用格林函数的方向导数作为波函数,其解析表达式复杂,计算效率低。此外,以往方法的波函数指向设置对节点分布方式要求较高,限制了其应用的灵活性。针对上述问题,采用(n, 0)阶的球面波源重新构造了一系列射线波函数,该射线波函数可利用球Hankel函数和Legendre多项式的递推形式方便地计算出其任意阶的表达式,大幅提高了效率。通过改进射线波函数的主指向设置,使其在实际使用中更加灵活,提出一种基于正交球面波源的射线波函数波叠加法。利用正四面体辐射体、两端带球帽的圆柱辐射体和简支矩形钢板声源3个数值仿真,对比验证了传统方法和所提方法在声场重建中的效果。仿真结果表明:在声场细节信息较为丰富的高频下,即便采用正则化方法求解,传统波叠加法由于传递矩阵病态严重,在3个仿真中均难以保证重建精度,误差为20%左右;而建立的射线波函数法则有效降低了传递矩阵的条件数,改善了系统病态性,获得了更高的重建精度,误差在5%~10%之间,说明了所提方法更具优越性。In the near-field acoustic holography based on the traditional wave superposition method,the monopole radiating the spherical wave is often used as the equivalent source,which is easy to cause the ill conditioned transfer matrix.Replacing the spheri⁃cal wave function with the ray wave function can effectively improve the ill conditioned transfer matrix.However,the previous ray wave function method uses the directional derivative of Green′s function as the wave function,which has complex analytical expres⁃sion and low computational efficiency.In addition,the wave function direction setting of the previous methods has high require⁃ments for the node distribution,which limits the flexibility of its application.In order to solve the above problems,a series of ray wave functions are reconstructed by using(n,0)order spherical wave source,this ray wave function can be easily calculated to any order by using the recursive form of spherical Hankel function and Legendre polynomial,and the efficiency is greatly improved.By improving the main direction setting of ray wave function to make it more flexible in practical use,a ray wave function wave super⁃position method based on orthogonal spherical wave source is proposed.Three numerical simulations,i.e.,radiator of regular tetra⁃hedral,radiator of cylinder with two spherical caps and simply supported rectangular steel plate acoustic source,are performed to verify the sound field reconstruction effect in both traditional method and proposed method.The simulation results show that in the high frequency with abundant sound field details,due to the serious ill conditioned transfer matrix,the traditional wave superposi⁃tion method cannot guarantee the reconstruction accuracy in the three simulations even with the help of regularization method,and the error is about 20%.The established ray wave function method effectively reduces the condition number of the transfer matrix and improves the ill condition of the system.Therefore,higher reconstruction accuracy is obtain

关 键 词：近场声全息 波叠加法 正交球面波源 射线波函数 

分 类 号：O422.2[理学—声学] TB53[理学—物理]