Nonlinear Multiparameter Eigenvalue Problems in Aeroelasticity

Abstract

In this work, we devise solution algorithms for nonlinear multiparameter eigenvalue problems arising in the analysis of aeroelastic flutter. Two iterative algorithms are devised, as well as a restriction method for simplifying the system behavior away from the desired flutter points. The algorithms are tested on a sectional model and on the Goland wing. Both are found to have fast and reliable convergence properties, yielding flutter point solutions which are validated by the literature. The definition of the eigenvalues is found to have a significant influence on the convergence properties of the algorithm; preferable choices for eigenvalue definitions are noted. The computational costs of the algorithms are tested and discussed; they are found to be favorable relative to other approaches from the literature. Opportunities for extending these methods are also tested and discussed.