Analysis of non-linear aeroelastic systems using numerical continuation
Non-linearities within structures often present difficulties when developing algorithms to analyse
their dynamic properties. Developing a combined aerodynamic and structural- aeroelastic
- code is an example where non-linearities can induce particular characteristics as the presence
of aerodynamic non-linearities can compound the complexity of the analysis. Furthermore,
when non-linearities occur within actuation devices the impact of coupling control systems
with the aeroelastic algorithms - aeroservoelastic - must also be considered.
In this work, new methods of analysing aero(servo)elastic systems containing various structural
non-linearities are studied. The first technique is used to analyse piecewise linear systems.
In this method, aeroelastic equations are recast in a form where the independent variable
is the time at which the system reaches a discontinuity, sets of these equations are then combined
to form an algebraic set of equations describing a Limit-Cycle Oscillation (LCO). The
second technique is applied to more general non-linearities by approximating any discrete
non-linearities with trigonometric functions, creating a set of continuous Ordinary Differential
Equations (ODEs). For both methods, computational efficiency is achieved by applying
numerical continuation to track solution branches.
The models analysed in this work are two and three degree-of-freedom aerofoil sections containing
non-linearities in their heave, pitch and/or flap freedoms. Four different aerodynamic
representations are used, two incompressible codes establish the accuracy of the new methods.
The other codes are used to study transonic flows and show good agreement with work based
on aeroelastic systems with both linear and non-linear structures.
Three different control laws - fixed gain, optimal and adaptive - are also investigated to assess
their ability to delay flutter onset and suppress LCOs. Optimal control showed the best overall
ability to achieve these aims, although it was found that care must be taken not to destabilise
areas below the flutter boundary.
Finally, a method of analysing fatigue due to structural non-linearities is investigated. The
analysis combines the numerical continuation techniques with the Rainflow method to quantify
damage due to simple acceleration-deceleration profiles.