| Summary: | Helicopter ground resonance is a highly non-linear dynamic problem involving complex interactions between the various parts of a helicopter and constituting a major design consideration. Linearised models of the problem are often utilised as the conventional tool of analysis and design. These models, however, portray only the local dynamics of the problem. Therefore, a more useful capability would be to obtain a global picture of the behaviour when system non-linearities are included and for that purpose, novel tools of analysis and design are sought in this research. Dynamic systems theory provides the basis for the continuation and bifurcation methods of analysing non-linear systems of ordinary differential equations. A significant strength of these methods is the gained insight into the phenomena that affect the global behaviour of a non-linear model. The combination of these methods with conventional simulation, provides an unmatched tool for studying non-linear dynamic problems and is therefore an ideal choice for this research. This thesis demonstrates the application of non-linear continuation and bifurcation theory to helicopter ground resonance. The classical model of the problem is reduced into the non-rotating frame and the methods are implemented to obtain the boundaries of instability and to study their variation following helicopter parameter changes. The resulting process is found to be far more efficient than current methods, thus demonstrating the ability of the continuation and bifurcation method to become a powerful and practical design tool. Using these methods, the effects of fuselage stiffness and damping non-linearities on ground resonance are investigated by computing the type, amplitude and frequency of the limit cycles after the onset of instability. Some of these non- linearities are found to be beneficial by producing a boundary of stable limit cycles which surrounds the unstable range of critical rotor speeds. In other instances, however, the potential rise of catastrophic scenarios was noted when unstable limit cycles exist in regions where linear theory predicts a stable behaviour. The determination of the stability boundaries in the rotating frame is also achieved for the first time. This allowed the study of the effects of a non-linear lag damper on the response and valuable insight into how the damper parameters affect this response are gained. Multi-body dynamics formulations are then used to model the ground resonance problem and the procedure required to couple the continuation and bifurcation tools used throughout this research to this model is outlined.
|
|---|
