结构声学灵敏度分析的有限元法/宽频快速奇异边界法研究

Vibration noise is the primary source of the traffic noise pollution. It is of great significance to analyze the vibro-acoustic design sensitivity in the vibro–acoustic optimum design and noise control. It is still a challenging task to efficiently and effectively calculate vibro-acoustic sensitivity analysis for large-scale structure in a broad frequency range in both science and engineering communities. In this project, a highly efficient numerical technique for the wideband structural-acoustic sensitivity analysis will be established based on the adaptive cross approximation method (ACA), singular boundary method (SBM), chain-ruled derivatives and adjoint variable method. In order to simplify the formulation of the SBM, an analytical formula of the origin source intensity should be deduced. After that, a fast SBM will be developed in conjunction with the ACA to overcome the prohibitive memory consumption and numerical inefficiency of the traditional numerical methods in dealing with high frequency acoustic problems. By coupling the fast SBM and finite element method (FEM), a efficient numerical method is presented for structural acoustics problems. In the final, a global acoustic design sensitivity analysis will be proposed with the fast SBM/FEM, chain-ruled derivatives and adjoint variable method, which provides the direction and amount of design change needed for optimal design. The achievements of this project will serve as powerful numerical tools for vibro-acoustic design sensitivity analysis for large-scale wideband problems in automobile, aerospace and marine science.

振动噪声是交通噪声污染的主要来源，结构声振灵敏度分析对交通工具的声学性能优化设计以及噪声控制有着重要意义。快速高效地计算大规模复杂结构的宽频声振耦合设计灵敏度是计算科学和工程科学中一项挑战性研究。本项目基于自适应交叉近似法、奇异边界法、链式微分法则和伴随变量法等技术发展结构声学灵敏度分析的数值方法。将研究消除基本解源点奇异性的解析技术，简化奇异边界法；基于自适应交叉近似法，发展快速奇异边界法模拟声场问题，解决传统高频声波分析数值方法中计算量和存储量巨大、求解效率低等问题；耦合奇异边界法和有限元法用于结构声振耦合特性分析，为声振耦合问题提供可靠的数值模拟技术；结合有限元法/奇异边界法、链式微分法则、伴随变量法等发展全局声学设计灵敏度分析的数值算法，为优化设计提供优化方向和量化依据。本项目的目标是建立一套高效准确的大型复杂结构全局声学灵敏度分析技术，为汽车、航空、船舶等工业领域提供计算依据。

声学灵敏度分析是噪声声源优化控制的关键，快速高效地求解结构的振动声学问题，实现结构声学优化灵敏度分析对汽车、航空、船舶等工业领域有重要的意义。. 针对结构声学灵敏度问题，本项目依次研究了奇异边界法、自适应交叉近似法、链式微分法则等，以实现声学灵敏度的快速分析。具体包括：建立了二维、三维以及2.5维奇异边界法用于模拟声波的辐射和散射，基于已有的基本解推导了各类问题的源点强度因子；将奇异边界法用于分析固体结构振动分析，分别分析了三维弹性波，正交各向异性弹性波，非饱和固体振动，板振动，功能梯度板振动，建立了对应的分析格式；建立了结构声振耦合的强耦合和弱耦合分析格式，包括有限元-奇异边界法的耦合和奇异边界法-奇异边界法耦合；引入自适应交叉近似法，克服奇异边界法稠密矩阵的计算量和存储量巨大、求解效率低的问题，实现了几十万到百万自由度的计算模拟；基于链式微分法则建立了结构声学灵敏度分析格式，简化了传统灵敏度分析的过程。. 通过编程实现上述内容，模拟了结构声学的相关问题，并发表了14篇论文，2个软件著作权，并举办了2次计算力学会议。.