The solution of linear flutter equations carries the risk of missing important aeroelastic modes, particularly with large, complex models or control systems. A mathematical technique known as the topological degree of a system of nonlinear equations tells how many roots the equations have within a given region. Using the degree to determine the number of roots of the flutter determinant, regions, such as a velocity-frequency interval, can be tested for missed neutral-stability points. A generalized-bisection technique, together with the topological degree, provides a globally convergent nonlinear-equation solver requiring only function values. Applied to flutter equations, it is a safe way to narrow regions containing neutral-stability points or start points for aeroelastic mode-tracking processes in preparation for more efficient techniques, such as Newton's method.
Topological Degree Applied to Flutter Equations
AIAA journal ; 53 , 3
2015
Aufsatz (Zeitschrift)
Englisch
Topological Degree Applied to Flutter Equations
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