Unified flutter solution technique using matrix singularity indicators

Conventional linear flutter analysis using the k or p-k method is based on eigenvalue solution of the flutter equation, which needs to track the eigenmodes to give a proper flutter point, but sometimes the procedure may fail. As a step toward a flutter solution method with more automation and robustness, a discussion is made for the uniqueness of the flutter matrix singularity at and inside the flutter boundary, and proper clearance procedure against nonuniqueness is provided. Four indicators of matrix singularity are introduced: that is, the determinant module, minimum module eigenvalue, minimum singular value, and inverse condition number of the flutter matrix. Finally, a unified algorithm is developed for flutter solution with these indicators. Numerical examples demonstrated that the results by the present method coincide well with the p-k and k methods but need no mode tracking. It is also shown that the coupled flutter-mode information can be extracted qualitatively from frequency diagrams of these indicators at different velocities and quantitatively from the eigenvector corresponding to the minimum module eigenvalue of the flutter matrix at the critical flutter point.