振动体声学灵敏度分析的边界元法

振动结构关于设计变量的声学灵敏度分析可以为机械系统的低噪声设计提供量化依据，为结构的优化设计提供方向。采用边界元法，推导了辐射声压关于频率、表面振速等设计变量的声学灵敏度公式。在对系数矩阵求导时，没有采用传统的有限差分法，而是直接求导，并利用不连续单元替换点法处理边界元法中的奇异积分问题。将数值解与理论值比较，证明了计算公式的准确性和有效性。该灵敏度计算方法为机械系统的低噪声设计打下了基础。

Boundary Element Method for Acoustic Sensitivity Analysis of Vibrating Structures

The determination of the acoustic sensitivity characteristics with respect to the variation of the design parameters can provide a method for low-noise design of mechanical structure objectively and quantitatively. Based on the boundary element method, the expressions of sensitivities of the acoustic pressure with respect to changes in frequency and surface vibration velocity are presented. The sensitivities of coefficient matrix are computed by differentiation directly, instead of finite difference approximation. Using displaced points method, the singular integral can be obtained fast and correctly. Numerical sensitivity results obtained by the boundary element method are compared to analytical solutions, and the validation and availability of the present method are proved. These acoustic sensitivity analysis methods can lay a solid foundation for the low-noise design of mechanical structure.