Nonlinear Active Vibration Suppression in Aeroelasticity

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All systems in nature are inherently nonlinear - therefore the modelling and performance of systems can be improved by applying nonlinear analysis methods. It is convenient, and often very useful, to treat them as linear within a certain range of operation. Outside the range of linear approximation it can be useful to apply perturbation methods, which have mostly been applied to problems of mild nonlinearity but have been developed more recently for problems where the nonlinearity is strong. Frequency domain approaches are applicable whenever the nonlinear vibration is periodic, which includes flutter and LCO in aircraft. New methods will be developed so that the dynamic of a nonlinear aeroelastic system will be assigned in terms of its nonlinear natural frequencies and damping values. The research will be based on two techniques: (1) neutralising the inherrent nonlinearity by a process of feedback linearisation and (2) suppressing flutter into LCOs. This will involve the formulation of new theory and its implementation in experiments.The method is based on a result from the linear algebra, the Sherman-Morrison formula, developed into a new technique for linear active vibration suppression by the PI and his colleagues. This approach, known as the receptance method, has many advantages over conventional matrix modelling and is based entirely on data from vibration tests, i.e. there is no need for the M, C, K matrices or for the aeroelastic damping and stiffness matrices often determined from aeroelastic influence coefficients obtained from various proprietary codes. It is particulary significant that the absence of an an analytical (mathematical) model of the open-loop system extends to any structural or flowfield nonlinearity that might be present. Potentially, the receptance method can be used to control the nonlinear vibration of aircraft by using in-flight test results.A new frequency-domain method for feedback linearisation is proposed by making use of a property of the receptance matrix, i.e. that it is invariant under the Hilbert transform. Conventional linear control techniques may then be applied. Eigenvalue assignment is especially relevant in the case of LCOs, which are neutrally stable and therefore are readily assignable in the frequency domain. Techniques will be developed that include the assignment of stable LCOs, so that the system is dissipative if perturbation leads to an increase in amplitude and absorbs energy from the airflow if the amplitude is reduced, until returning to the original amplitude and frequency before the disturbance. Guaranteed stable LCO behaviour over a considerable velocity range will allow the extension of an aircraft flight envelope.The controller nonlinearity will be represented using describing functions (DFs), including recently developed higher-order DFs that admit nonlinear effects not available from the conventional zero-th order DF.The research will include an experimental programme using the low-speed wind tunnel as well as the development and application of CFD code in the transonic range. The latter will include a study of the XFR-1 (a long-range twin engine wide body aircraft) with nonlinearity/structural damage inserted by engineering scientists from Airbus UK, unknown to the Liverpool researchers.