Nonlinear Dynamics of High-Aspect-Ratio Wings
: Using Numerical Continuation

  • Andrew Eaton

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


High-aspect-ratio wings are of interest to civil aircraft manufacturers, due to the aerodynamic benefit they provide; however, the flexibility of these wings means that nonlinear dynamical phenomena, such as limit cycle oscillations (LCOs), may exist, which cannot be captured by classical tools for aeroelastic flutter prediction. This thesis makes novel contributions by investigating the nonlinear dynamics of high-aspect-ratio wings using numerical continuation techniques, which are path-following methods well-suited for the study of parameter dependancy in nonlinear dynamical systems without using time histories. A fully nonlinear, low-order beam formulation is combined with strip theory aerodynamics, and it is shown that the geometric nonlinearity inherent in high-aspect-ratio wings can be a fundamental driver of undesirable dynamical phenomena, without need for aerodynamic nonlinearity.
A 2 degree-of-freedom (DoF) binary flutter wing is first used as the basis for an analytical and physical discussion, and it is shown that the criticality of the flutter point (i.e. the supercritical or subcritical nature of the Hopf bifurcation) can be changed depending on how the frequencies of the linearised system vary with airspeed. A high altitude, long endurance (HALE) wing is then investigated, and the one-parameter continuation of equilibria and LCOs reveals that complex dynamics exist in this system; the two-parameter continuation of Hopf and periodic fold bifurcations reveals the sensitivity of these dynamics to variations in bending and torsional stiffness. Observations from the 2 DoF wing, relating to Hopf criticality, are investigated in the HALE wing. Finally, the dynamics of a ‘free-free’ HALE aircraft are investigated; while the continuation of LCOs reveals the flutter point to be relatively benign, detrimental nonlinear phenomena are found to affect the rigid-body flight dynamics due to the presence of periodic fold bifurcations. These undesirable phenomena are shown to be removed by varying torsional stiffness.
Date of Award23 Jan 2020
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorSimon A Neild (Supervisor) & Mark H Lowenberg (Supervisor)


  • Flutter
  • Nonlinear
  • Bifurcations
  • LCO
  • High-aspect-ratio
  • Numerical continuation

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