Abstract:

There have been, in mathematics, several numerical methods of solving nonlinear equation W(s) =0. However, most of them become ineffective when they are used to determine the complex zero points of the above equation. This fact forces engineers to adopt some approximate methods. Graphical method for solving this problem was mentioned as a possibility by Zhang. The possibility was turned into reality by Liu. But Liu's method is difficult to execute on a computer. To overcome this difficulty, the authors improve on the graphical method and proposes a new method ——orthogonal searching technique. The authors' main contributions are:(1) The orthogonal searching technique is easily executed on a computer. Liu's method performs artificial contracting of mesh function curves so as to capture the roots of W(s) =0. As these curves are complicated, it is almost impossible to capture these roots with the computer. Like Liu's method, the orthogonal searching technique starts from conformal mapping of analytic functions, but its searching process alternates between real and imaginary axes and is easy to execute on computer. The FORTRAN program by the first author contains only 60 easily executed sentences.(2) The orthogonal searching technique always gives accurate results and its searching processes have good property of convergence. The methods given in Ref.for solving nonlinear equations frequently cause occurrence of a limit ring so that accurate roots of W(s) =0 can not be obtained. The orthogonal searching technique makes sure that its iterative searching process is able to approach gradually the true roots. The authors utilized the orthogonal searching technique to make flutter analysis of the single wing of a supersonic aircraft and obtained successful results.

Key words: nonlinear equation, graph icalmethod, flutter analysis, orthogonal searching tech nique (OST )