基于无单元声波叠加的自辐射近似解析表达研究

摘要

Fictitious acoustic sources have to be placed inside a structure apart from its surface in the conventional wave superposition method.Otherwise,the singularity of Green's function for self-radiation terms will arise in the corresponding algorithm,leading to worse sound field calculation.To solve this problem,a meshless acoustic wave superposition method based on discretized radiating surface of a vibrating structure was studied.The singularity problems of Green's function when a sound source and a receiver point coincided were overcome by removing the singular point, replacing part integration regions and using invariant-embedded,respectively.Non-singular expressions for self-radiation terms ineluding acoustic pressure and velocity were obtained.Then the source strength and sound pressure could be determined with velocity boundary conditions.The self-radiation terms inclading acoustic pressure and velocity were correctly calculated with the approximate analytical expressions,they were validated with an example of pulsating sphere. Thus,the prediction of sound field could be realized.%传统波叠加法中虚拟声源必须设于结构体内离表面一定距离处，否则会使算法中的自辐射项中的格林函数产生奇异性，无法正确计算声场。针对这一问题，研究了针对振动结构辐射表面离散化域形成的无单元空间离散域波叠加计算方法，采用奇异点挖去法、部分积分区域替换法和不变量嵌入法克服当声源点与接收点重合时格林函数的奇异性问题，得到自辐射声压项和速度项的非奇异表达。然后利用速度边界条件确定声源强度和声压。通过具有解析解的脉动球源的例子验证，该近似解析表达式能较好地代表声压和速度自辐射项，从而实现声场的预测。