Numerical Evaluation of Limit Cycles of Aeroelastic Systems

This paper focuses on the analysis of limit-cycle oscillations of aeroelastic systems with multiple lumped nonlinearities. It aims at a comprehensive investigation capable of identifying limit cycles and their stability. The goal is achieved by using an incremental complexity approach. At the beginning, a solution based on dual-input describing functions is sought, to find both symmetric and asymmetric cycles approximated to their first harmonic. The related stability is investigated afterward by extending the single-input describing function “quasi-static” method. Such an approach is simple and quite similar to well-established existing methods used to evaluate linear flutter conditions directly. If higher harmonics are required, an extended harmonic balance based on a numerical minimization in the frequency domain is adopted and the stability of the computed solutions is then determined by using Floquet theory. The presented approach is applied to several nonlinear aeroelastic examples and validated by comparing stable limit cycles with solutions obtained through direct time marching integrations.