Computational stability analysis of dynamical systems

Ph.D.Olivier A. Baucha

Aeroelastic stability analysis using reduced order aerodynamic models

The stability of linear systems defined by ordinary differential equations with constant or periodic coefficients can be assessed from the spectral radius of their transition matrix. In classical applications of this theory, the transition matrix is explicitly computed first, then its eigenvalues are evaluated; if the norm of the largest eigenvalue is larger than unity, the system is unstable. The proposed implicit transition matrix approach extracts the dominant eigenvalues of the transition matrix using the Arnoldi algorithm, without the explicit computation of this matrix. As a result, the proposed implicit method yields stability information at a far lower computational cost than that of the classical approach, and is ideally suited for stability computations of systems involving a large number of degrees of freedom. Examples of application of the proposed methodology are presented that demonstrate its accuracy and computational efficiency

Implicit Floquet analysis for rotorcraft stability evaluation

Floquet theory has been extensively used for assessing stability of periodic systems. In the classical application of the theory, the transition matrix of the system is explicitly computed first, then its eigenvalues are evaluated. The 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 transition matrix 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 the classical Floquet analysis. The proposed implicit Floquet analysis is ideally suited for stability computations of systems involving a large number of degrees of freedom. Examples of application of the proposed methodology are presented that demonstrate its accuracy and computational efficiency