基于无单元声波叠加的自辐射近似解析表达研究

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。

Research on the approximate analytical expressions of self-radiation terms based on element free acoustic superposition

Fictitious acoustic sources have to be placed inside a structure apart from the surface in conventional wave superposition method. Otherwise, the singularity of Green’s function for self-terms would arise in the algorithm, leading to worse sound field calculation. To solve this problem, a meshless acoustic superposition method based on discretized radiating surface of vibrating structure is studied. The singularity problems of Green's function when the source and receiver point coincide are overcome by removing singular point, replacing part integration region and invariant imbedding separately. Non-singular expressions for the pressure and velocity self-terms are obtained. Then the source strength and pressure could be determined according to velocity boundary conditions. The pressure and velocity self-terms can be correctly calculated by the approximate analytical expressions, validated by an example of pulsating sphere. Thus the prediction of sound field could be realized.