大规模结构-声学耦合问题的高精度快速计算方法研究

It is inevitable to develop a coupling method for an accurate analysis of such structural-acoustic problems that the interactions between vibration of structure and exterior acoustics cannot be neglected. Due to limitations of computational efficiency and accuracy as well as the coupling theory, the available methods cannot meet the demand of large scale structural-acoustic problems for high-precision and fast computational algorithms. The project is aim to developing a set of coupling theory and high-precision fast algorithms which have clear physics explanations and are robust for large scale structural-acoustic problems. A theory of acoustic radiation modes with coupling effects considered in is proposed. The theory is then applied to investigate the characteristics of radiated sound from structural-acoustic models, and build a fast coupling algorithm, which has semi-analytical expression of exterior acoustics, in conjunction of finite element method (FEM) for structural-acoustic problems. On another hand, a fast inverse algorithm for large scale sparse matrix is developed for the smoothed FEM. Adaptive expansion method and fast translation algorithm of the fast multipole boundary element method (FMBEM) are proposed. An accurate coupling algorithm of FEM and BEM for the structural-acoustic problems is developed based on high order element. In addition, an efficient preconditioning technique is proposed for the coupling algorithm to speed the convergence and improve the accuracy. Those contributions compose of a fast and high-precision algorithm based on smoothed FEM and FMBEM for structural-acoustic problems. Finally, the proposed coupling theory and fast algorithms are validated by an experimental study. Outcomes of the project can supply a set of high-precision and fast computational algorithms for the coupling analysis of structural-acoustic problems in the acoustic design of large scale equipment.

当结构振动和外部声场的相互影响不容忽视时，需要建立耦合分析的方法才能精确计算此类结构-声学问题。但现有方法由于耦合理论及求解效率和精度的限制，无法满足大规模复杂结构-声学耦合问题对快速精确计算的要求。本课题拟建立一套理论清晰、算法稳健高效的大规模结构-声学耦合分析理论和高精度快速计算方法。首先发展考虑耦合效应的声辐射模态理论，研究结构-声学的耦合声辐射特性，建立一种具有半解析声学表达式的结构-声学快速耦合计算方法；另一方面，发展光滑有限元法的稀疏矩阵快速求逆技术，研究自适应展开法和多极子快速传递算法，以及基于高阶单元的精确耦合算法，发展基于声辐射模态的高效预处理技术，从而建立基于光滑有限元法和快速多极子边界元法的结构-声学高精度快速计算方法。最后，进行实验测量，验证所发展的耦合理论和计算方法的正确性。本课题研究成果可为重大装备设计中的结构-声学耦合分析提供高精度的快速计算方法。

大型设备如潜艇和飞机舱壁等的壳体结构振动会向周围流体辐射声波,反之流体声场的动压力也作用于结构，影响结构振动。因此，结构振动与媒质中声场之间的耦合不容忽视。解析方法对于这些大型复杂设备的噪声定量预测是无能为力的，实验分析则成本高周期长，数值计算是分析大型复杂结构-声学耦合问题的不二选择。. 本项目发展了结构和声学的等几何理论和计算方法，减少模型的离散误差，提高结构和声学单独分析的计算精度；针对边界元方法系数矩阵数值计算时，内存大和效率低的缺点，发展了基于多层矩阵压缩技术的快速边界元方法，提出将多极子理论和矩阵压缩技术有机结合的新型高效快速边界元方法；在流固耦合分析上，正在开展有限元方法与非奇异线性边界元方法的耦合理论及计算方法研究，提高耦合面上不同介质物理量插值精度。.（1）建立了模型设计和分析的统一的几何描述方法，即等几何分析方法，开发了基于B-Spline和NURBS等几何分析的c++程序库。.（2）发展了的二维、三维弹性静力学、动力学和声学分析的等几何有限元方法，完成了高精度有限元法、边界元法理论和算法的开发。.（3）将全频段快速多极子边界元方法推广到多联通声学问题的求解，如多孔吸声材料的设计、水下结构声学探测及生物组织中声学特性模拟等，实现了基于边界元方法的耦合声学问题求解框架，建立了结构-声学耦合问题（有限元法/边界元法）的分析框架。. 所建立的有限元和快速边界元耦合算法及映射声辐射模态理论，解决了传统分析方法在计算精度、效率上的缺陷，被成功用于某企业商用压缩机壳体加筋位置和某型号潜艇阻尼布局的声学优化。压缩机壳体的成功拓扑声学优化，提高了产品的竞争力，实现了良好的经济效益。潜艇阻尼布局声学优化、燃气轮机辐射噪声预报及双体船水下结构声固耦合分析的成功尝试，充分显示了所建立的计算理论和方法的重大意义和广阔应用前景。