In this paper, a novel Burton-Miller-type singular boundary method (BM-SBM) formulation is proposed for the acoustic design sensitivity analysis, with the help of the direct differentiation method. The Burton-Miller formulation is employed to overcome the fictitious frequency problem in the numerical solutions of exterior acoustic problems. The simple empirical formulas are used to estimate the origin intensity factors in the BM-SBM. Compared with the traditional methods, the present scheme is an accurate and semi-analytical approach with the merits of truly meshless, integration-free, mathematical simplicity, and easy-to-program. As a boundary-type method based on the fundamental solution, furthermore, the BM-SBM is straightforward for addressing the exterior Helmholtz problems encountered in the acoustic design sensitivity analysis. Numerical experiments, including 2D and 3D geometries with Neumann boundary conditions, indicate that the proposed methodology is an accurate, stable, and convergent numerical approach for the acoustic design sensitivity analysis.

本文提出了一种新的 Burton-Miller 型奇异边界法 (BM-SBM) 公式，用于声学设计灵敏度分析，并借助直接微分法。Burton-Miller 公式用于克服外部声学问题数值解中的虚拟频率问题。简单的经验公式用于估计 BM-SBM 中的起源强度因子。与传统方法相比，本方案是一种精确的半解析方法，具有真正无网格、免积分、数学简单和易于编程的优点。此外，BM-SBM 作为一种基于基本解的边界型方法，可以直接解决声学设计灵敏度分析中遇到的外部亥姆霍兹问题。