Nonlinear Active Vibration Suppression in Aeroelasticity

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.

The potential of this research is a significant improvement in flight safety, which is achievable because the methodology is based on vibration measurements that may be carried out in flight. Thus, in flight tests (for example of military aircraft with different store configurations) the control system will be able to adapt, not only to the different configurations, but also to unpredicted instabilities. It can be used to improve the speed and safety of flight flutter tests. In addition, the controller will adjust itself to a changing dynamic brought about, for example by damage to the airframe or, in an extreme case, to the loss of an engine.
Active feedback control for aircraft vibration suppression is a science in its infancy. There are examples of feed-forward control for vibration cancellation, mostly in rotorcraft, and some examples of active damping in fixed-wing aircraft. There are academic examples of flutter suppression in wind tunnels, but nonlinear active feedback control has never been applied to a production aircraft to the PI and CIs' knowledge. Therefore the soonest impact of this research, in term of implementation in a production aircraft, is likely to be medium-term. However, commercial (and other) pressures are likely to intensify the demand for more adaptive and safer aircraft so that a time-scale of ten years is considered feasible. The direct industrial beneficiaries of the research will be Airbus UK and Stirling Dynamics. Engineering scientists from both organisations will participate in the project by attending progress meetings at six-monthly intervals. The research will be connected to what is achievable industrially (but not necessarily restricted by it) and to industrial requirements. Task 8 will be defined in collaboration with engineering scientists from Airbus UK using the XFR-1 model (CAD/FE/CFD) of a long-range twin engine wide body aircraft, including the insertion of nonlinearity/damage unknown to the Liverpool researchers. The investigators have an established collaboration with Airbus UK and Stirling Dynamics through an initiative known as DiPaRT - Distributed Partnership in R&T. Provision of the XFR-1 model represents a significant level of confidence in the project by Airbus UK.
Research results will be published in international journals including AIAA Journal, AIAA Journal of Aircraft, Mechanical Systems and Signal Processing and Journal of Sound and Vibration. In addition papers will be presented at major international conferences such as the AIAA Structures, Structural Dynamics, and Materials Conference (SDM), International Forum on Aeroelasticity and Structural Dynamics (IFASD) and the International Conference on Noise and Vibration Engineering (ISMA).
The Impact Plan includes a Project Web Site on the University of Liverpool VOCAL system where results and links to published journal papers will be made generally available. The methodologies developed in the project will feed into other complementary studies involving the PI and CIs, and these included several EU funded collaborative programmes. Other impact will arise via the School of Engineering's Virtual Engineering Centre (VEC) which is a £5.4m (NWDA, ERDF, BAESYSTEMS, Airbus) initiative that is aimed at transferring fundamental scientific research (TRL levels 1 - 3) through to industry (TRL levels 4 - 6). At the end of the project a two-day Workshop will be organised for the further dissemination of research results especially to other industries, including automotive, aero-engines and machine tools where there is further potential for application of the research.
Posters and information packs for school sixth-forms will be developed by undergraduate MEng students with projects linked to this research programme. The MEng students will give presentations in local schools in Merseyside.