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

机译：使用描述功能和接收方法限制非线性空气弹性系统中的循环分配

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摘要

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.
机译：可以使用特征值分配处理空气弹性中的颤动抑制问题。因此，可以考虑由RAM和定位器开发的特征值分配的接收方法以进行颤振抑制。而且，非线性颤动的特征在于周期性。因此，描述功能技术适用于非线性空气弹性系统，使得可以采用传统的线性分析方法。在LCO的情况下，特征值分配尤其相关，因此中性稳定，因此在频域中易于分配。本文将考虑结构非线性。近似结构非线性使用描述功能，基于接收方法的非线性主动控制理论将通过延长线性主动控制的良好开发的理论来实现。此外，将导出基于描述函数方法的频域中的新限制循环预测方法和基于描述函数方法的闭环系统的极限循环的新形式的稳定性标准。分别具有三个自由度翼型的二维自由度翼型的数值结果分别示出，以表明，通过新方法可以精确地预测限制循环，并且所提出的非线性主动控制技术可能能够抑制稳定的颤动LCO。

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