弹性飞机两种颤振分析方法的比较

本文在颤振分析图解法基础上研究了目前广泛采用的模拟非定常气动力Roger型有理近似建立起来的解析方法的近似性问题，并以某超音速飞机单独机冀为例讨论了在不同速度及不同模态因不同的Roger型有理式所表现出的近似速度，所得结论对于工程设计有一定的参考价值。

Comparison of Two Flutter Analysis Methods for Elastic Aircraft

Analytical method of flutter analysis of Liebst et al1] is an approximate one. Its degree of approximation has not yet been reported in the open literature, perhaps because an exact method was not available. The second author made use of the research results of Zhang7] and obtained an exact method, called graphical method 3]. The authors use the second au- thor's graphical method to determine the degree of approximation of the analytical method for the first five modes of a single wing of a supersonic aircraft. The following findings are obtained: 1) In general, the difference between solutions given by above two methods increases with increasing flight speed. But for mode two, the difference is somewhat greater at middle flight speed than at low or high flight speed. 2) The above difference is greatest for mode one and less for higher modes. 3) Flutter speeds obtained for three different Roger approximations (three-fraction, four-fraction, five-fraction) are almost the same and greater than that given by the graphical method by less than 10 m/s. 4) For modes two to five, the root loci obtained for the above three Roger approxima- tions are similar. But for mode one, the root loci for four-fraction approximation can fit better those obtained with the graphical method. Engineers are usually interested in amount of damping and frequency in flutter analy- sis. The calculations for the wing of a certain supersonic aircraft show that, in general, the error of amount of damping is 4-8%, and that of frequency is 1%. But under certain con- ditions, rather large errors can occur. When one uses three-fraction or five-fraction Roger approximations for the case of large damping and low frequency, the errors for amount of damping and frequency may be as high as 30% and 32% respectively.