针对大型线弹性结构谐响应分析的计算效率与计算存储的问题,提出了一种基于减基法的快速算法.这种算法把简谐外载荷的频率作为参数,并且对频域进行预采样.把预采样空间对应的解集做成一个训练空间,采用贪婪算法进行减基空间基向量的自适应选取,进而由Galerkin映射得到减缩系统.最后,通过求解减缩系统频域方程来达到结构谐响应快速分析的目的.根据谐响应分析的特点,整个计算过程可以分成离线和在线两个阶段,从而进一步提高减基近似的效率.采用了一个简化机翼模型的谐响应分析来验证该方法的高效性和精确性.%An efficient algorithm was proposed to real-timely perform harmonic response analysis of large-scale structures based on a reduced-basis method (RBM). In this algorithm, the frequency of external harmonic loading was considered as the parameter, and a pre-sampling technique was adopted. The training space was constructed using the so- lutions corresponding to the frequencies in the pre-sampling space. A greedy algorithm was adopted to construct the re- duced basis space adaptively. The reduced system was obtained by using Galerkin mapping. The resultant reduced equa- tion in frequency domain could be solved more effectively than the original equation. To further enhance the efficiency of RBM approximation, the calculation procedure was separated into off-line and on-line stages according to the feature of harmonic response analysis. Eventually, a simplified wing model was used to validate the accuracy and efficiency of the proposed algorithm.
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