An Implicit Floquet Analysis for Rotorcraft Stability Evaluation

Floquet theory has been extensively used for assessing the. stability characteristics of systems with periodic coefficients. In classical application of the theory, the Floquet transition matrix (FTM) of the system is explicitly computed first, then its eigenvalues are evaluated. Stability of the system depends on the dominant eigenvalue: if this eigenvalue is larger than unity, the system is unstable. The proposed implicit Floquet analysis extracts the dominant eigenvalues of the FTM using the Arnoldi algorithm, without the explicit computation of this matrix. As a result, the proposed method yields stability information at a far lower computational cost than that of classical Floquet analysis, and is ideally suited for stability computations of systems involving a large number of degrees of freedom. Examples of application demonstrate the accuracy and computational efficiency of the proposed method