基于声波叠加法的基阵声场计算和波束合成

Array Radiation Sound Field Calculation and Beam-Synthesis Based on Wave Superposition Method

水声换能器基阵的辐射声场计算,特别是辐射波束合成对于水下声系统设计十分重要,一直是水声领域研究的热点问题。现有的方法,如边界积分法不仅计算量很大,而且在特征频率处存在解的不唯一性和奇异性等缺点。而声波叠加法由于积分运算在辐射体内部完成,从而避免了边界积分法的缺点。文中基于声波叠加法建立了水声换能器基阵声辐射计算和波束合成的数学模型,推导出基阵辐射声场的声波叠加法计算公式,以及基阵辐射波束合成时阵元法向振速的求解公式,并给出了求解的两种方法——最小二乘法(LS)和奇异值分解法(SVD)。针对安装在硬质半球表面的14元圆弧阵进行了计算机仿真实验以及水池实验,实验结果验证了所建模型的正确性。因此,该模型可用于实际水声系统的设计和性能预估。

The radiation sound field calculation, especially the beam synthesis of the underwater acoustic transducer array are of great importance in the design of underwater systems, therefore, much attention is paid to this item. However, the current methods, the boundary integral method for example, fail to provide an unique solution for the characteristic frequency, and even become singular. On the contrary, due to completing its integral calculation in the interior part of the radiator, wave superposition method does not have the defects as the boundary integral methods do. In this paper, a mathematical model for the radiation sound field calculation as well as the beam synthesis based on the wave superposition method （WSM） is presented, and the corresponding formulas are provided. Furthermore, two methods for solving the formula equations least squared （LS） method and singular value decomposition （SVD） method are presented as well. Computer simulations and water - tank experiments are carried out for a 14 - element circular array mounted on a half - spherical rigid baffle. The results verify the correctness of the proposed model. In conclusion, the proposed model is helpful for the design of underwater acoustic systems and performance predications.