航天器声固耦合振动问题的快速边界元-有限元方法研究

Space structures are exposed to complex vibration noise environment during the whole flight, and the noise is not only a great challenge to the safety and reliability of the space structure itself, but also could cause serious damage to the astronauts' health. So it is very meaningful to develope an effective numerical method for structural-acoustic coupling vibration problems of space structures both in theory and practice. According to the speciality of space structures and corresponding noise environment, the present proposal develope a fast BEM-FEM coupling method to solve low frequency structural-acoustic coupling vibration problems of space structures. The BEM(boundary element method) is employed to perform the acoustic field analysis, and the FEM(finite element method) is used to perform the structural dynamic analysis. Then the structural-acoustic coupling analysis is implemented based on the continuity condition of the acoustic pressure on the interface of the structural and acoustic field. In order to improve the computational efficiency and satisfy the computational requirements of complex space structures, the adaptive cross approximation (ACA) method and fast multipole method (FMM) are also used in the present proposal. Based on the previous work, a structural-acoustic coupling vibration analysis software with proprietary intellectual property rights will be developed, and it will be very useful in both acoustic environment prediction and evaluation and dynamic load design and analysis.

航天器在飞行过程中的各个阶段都处于复杂的振动噪声环境中，它不仅对航天结构本身的安全性和可靠性带来挑战，同时也会对航天员的健康造成严重影响。因此发展有效的数值方法研究航天器的声固耦合振动问题在理论和实践上都具有重要意义。本课题将根据航天器结构及相应噪声环境的特点，建立一种快速边界元与有限元耦合方法来研究航天结构的低频声固耦合振动问题。其中声场分析采用边界元方法建立计算格式，结构动力学分析采用有限元方法建立计算格式，然后根据结构与声场交界面上的声压连续条件，实现声固耦合动力学分析。为了最大程度地提高计算效率，满足航天器复杂结构的大规模计算要求，我们将采用快速算法，即自适应交叉逼近算法ACA和快速多极算法FMM进行求解。在此基础上进一步开发具有自主知识产权的声固耦合分析软件，为航天器的噪声环境预测与评估、动态载荷设计与分析提供研究方法和分析手段。

本项目所取得的主要研究成果总结如下：（1）建立了一种边界元与有限元耦合方法来研究航天结构的低频声固耦合振动问题；（2）为了最大程度地提高计算效率、满足航天器复杂结构的计算要求，我们采用自适应交叉逼近算法（ACA）来进行边界元方程组求解；（3）针对声场分析问题，建立了三种类型新的二次高精度边界单元和相应的误差指示；（4）为了处理在三维声场分析中所遇到的曲面上的超奇异积分计算问题，对两种高精度数值积分技术进行了对比研究；（5）此外，本项目还提出并且探索了一种高精度边界元方法体系以适应大规模问题的计算精度要求。以上这些工作对航天器的噪声环境预测与动态载荷设计具有重要的应用价值。