Limit Cycle Assignment in Nonlinear Aeroelastic Systems Using Describing Functions and the Receptance Method

The problem of flutter suppression in aeroelasticity may be treated using eigenvalue assignment. Thus the receptance method of eigenvalue assignment developed by Ram and Mottershead may be considered for flutter suppression. Also, nonlinear flutter is characterized by periodicity. Therefore, the describing function technique is applicable to quasi-linearise the nonlinear aeroelastic system such that traditional linear methods of analysis can be employed. Eigenvalue assignment is especially relevant in the case of LCOs, which are neutrally stable and therefore are readily assignable in the frequency domain. In this paper, structural nonlinearities will be considered. Approximating structural nonlinearities using describing functions, the theory of the nonlinear active control based on the receptance method will be achieved by extending the well-developed theory of linear active control. Also, a new limit cycle prediction method in the frequency domain and a new form of stability criterion of limit cycles for closed-loop systems based on the describing function method will be derived. Numerical results from two two-degree-of-freedom airfoils with cubic and piecewise nonlinear pitching stiffnesses respectively are presented to show that limit cycles can be predicted precisely by the new method and the proposed nonlinear active control technique might be able to suppress flutter into stable LCO.

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