基于间接边界元法的薄壁结构声学灵敏度分析及形状优化设计

声屏障等非封闭型薄壁结构被广泛应用于交通噪声控制等工程领域,然而结构的特殊性给其散射和辐射声场的仿真分析带来了困难。为此,文章基于间接边界元法提出一种适用于薄壁结构声学灵敏度分析及形状优化设计的方法。为准确高效地计算奇异积分,基于常值单元离散推导出无奇异的声学灵敏度间接边界积分方程;为避免外声场分析时解的非唯一性问题,通过单层势和双层势组合形成基于混合势的灵敏度分析方法,并对组合参数的最优取值进行探讨;在此基础上引入最优化方法,构建薄壁结构的形状优化设计方法,为声屏障降噪性能的提升提供了有效手段。数值算例验证了文章所提方法的有效性和准确性,并证实了其在薄壁结构优化设计中的应用潜力。

The open thin-body structures, such as noise barriers, have been widely used in traffic noise control and other engineering fields. However, the structural particularity of thin-body structures brings difficulties to the numerical simulation of their scattered and radiated sound fields. Therefore, an effective method for the acoustic sensitivity analysis and shape optimization of thin-body structures is proposed based on the indirect boundary element method (IBEM) in this paper. Firstly, to calculate the singular integrals accurately and efficiently, the non-singular indirect boundary integral equations for acoustic sensitivity is derived based on the constant element discretization. Then, the non-uniqueness difficulty which may be encountered when solving the external field problem is avoided by combining the single-layer and double-layer potentials to obtain a mixed potential-based sensitivity analysis method, and its optimal coupling parameter is also discussed. Additionally, the shape optimization method of thin-body structures is constructed to provide an effective means for improving the noise reduction performance of noise barriers. Numerical examples demonstrate the effectiveness and accuracy of the method proposed in this paper and its potential in the shape optimization of thin-body structures.