摘要
本文提出一种颤振分析新方法-正交搜索法,其基本思想是利用复变函数中解析函数保角映射的特性,沿复变量s=σ+iω的实部和虚部交替搜索,逐步达到所求复方程的根。该算法能在计算机上实现,精确,直观,简便,实用。
Graphical method of flutter analysis was mentioned as a possibility by Zhang in 1985 [4]. The possibility was turned into reality by Liu in 1986 [5]. Liu's method is difficult to execute on a computer. To overcome this difficulty, the author improves on the graphical. method and proposes a new method-orthogonal search method. The author's mam contributions are: 1) The orthogonal search method is easily executed on computer. Liu's method performs artificial contracting of mesh function curves so as to capture eigenvalues of flutter equation. As these curves arc complicated, it is almost impossible to capture eigenvalues with computer. Like Liu's method, the orthogonal search method starts from conformal mapping of analytic function, but its searching process alternates between real and imaginary axes and is easy to execute on computer. The author's FORTRAN program contains only 60 easily executed sentences. 2) The orthogonal search method is applicable irrespective of the amount of damping. The classical V-g method is only applicable to calculating ater point which corresponds to zero damping[1]. 3) The orthogonal search method always gives accurate results. Analytical method, which is still widely used, possesses good accuracy only when damping is small; its accuracy deteriorates when damping is not small; and especially for large damping and low vibration frequency, it may give big error[7]. Incidentally, it is perhaps worthwhile to emphasize that the orthogonal search method is also applicable to a large category of mathematical problems involving the finding of zero points of analytic function irrespective of whether the function is polynomial or transcendental.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
1992年第4期462-466,共5页
Journal of Northwestern Polytechnical University
关键词
颤振
图解法
正交搜索
弹性
飞机
flutter analysis
graphical method
conformal mapping
orthogonal search
