Abstract: The general requests of finite-dimension approaching interpolating shape functions are presented, the method and procedure of construction of the meshless interpolating shape function using moving least square method are introduced. The point collocation method was adopted to discretize the Kirchhoff-Helmholtz boundary integral equations into linear equation groups that constrained by boundary conditions. Constrained equation groups were solved by matrix-division method, and then the discrete numeric expression of acoustic radiating and transferring model was obtained. In the example, acoustic field was calculated by the acoustic radiating and transferring model that obtained through both BMLM and BEM, and the comparison between the results of numerical computation and that of analysis shows that the interpolating functions of boundary meshless method self-constructed are more flexible and of higher accuracy of interpolation and calculation.

Key words: acoustics , computational acoustic field , acoustic radiating and transferring model , boundary meshless method , interpolating function , weighted residual

摘要： 研究函数有限维逼近插值形函数的一般要求，介绍采用移动最小二乘构建无网格插值形函数的方法与步骤；通过配点法将Kirchhoff-Helmholtz边界积分方程离散为受边界条件约束的线性方程组；最后通过分块矩阵法求解约束方程组，得到离散后的声辐射传输模型数值表达式。在计算实例中，分别用边界无网格法和边界元法建立声辐射传输模型进行声场计算，计算声场值与解析值相对比的结果表明，由于边界无网格法插值形函数根据求解情况自行构建，因此更灵活，具有更高的插值和计算精度。

关键词: 声学, 计算声场, 声辐射传输模型, 边界无网格法, 插值形函数, 加权余量