Abstract: In this paper, the discontinuous element is employed for separating the Helmholtz boundary integral equation. The polar coordinate transformation in discontinuous element is employed to eliminate the singularity in the integrals. Meanwhile, the CHIEF method in addition to the Lagrange multiplier is applied to deal with the non-uniqueness at the characteristic frequencyies. On this basis, the expressions for acoustic radiation power and radiation efficiency are derived by the discontinuous element. Taking the spherical radiation and cubical radiation as numerical examples, the radiation power, radiation efficiency, radiation modes and modal radiation efficiency are computed. The results are compared with those of the existing solutions based on linear continuous element. Both simulation results are in good consistency.

Key words: acoustics, discontinuous element, radiation power, radiation efficiency, radiation modes, continuous element

摘要： 利用非协调单元离散声学Helmholtz边界积分方程，采用极坐标变换法消除积分奇异性，通过CHIEF方法加Lagrange乘子法处理特征频率处解的不唯一性。在此基础上，应用非协调单元推导结构的声辐射功率和声辐射效率的表达式。以脉动球和辐射立方体为例，计算结构的声辐射功率、辐射效率、辐射模态、辐射模态效率等物理量，并与协调单元的计算结果做比较，取得较好的一致性。

关键词: 声学, 非协调单元, 声辐射功率, 声辐射效率, 声辐射模态, 协调单元