Flutter prediction using an eigenvector orientation approach

A method for predicting the onset of coupled-mode flutter is presented. A distinguishing characteristic of this method is that it emphasizes eigenvectors rather than eigenvalues. In the popular methods based on eigenvalues, flutter is predicted as instability begins to occur, as evidenced by the movement of one or more eigenvalues from the left-hand to the right-hand side of the s-plane, or the coalescence of eigenvalues. Alternatively, the method of eigenvector orientation being presented has the potential to predict the occurence of instability. Although the eigenvectors of vibrating systems generally satisfy the orthogonality condition, there are certain cases In aeroelasticity in which they are not orthogonal. In a typical case of coupled-mode flutter, the eigenvectors initially may be oriented orthogonally but gradually lose orthogonality as airspeed is varied. The consequence of such a progressive loss of eigenvector orthogonality on structural dynamics is a phenomenon that seems to warrant further investigation. This investigation has applications in areas such as helicopter dynamics, aeroelastic analysis of plate and shell structures, analysis of slightly mistuned bladed disk assemblies, and rotordynamics.