Nichkawde, Chetan (2003-05). Nonlinear aeroelastic analysis of high aspect-ratio wings using the method of numerical continuation. Master's Thesis.
Thesis
This research explores the impact of kinematic structural nonlinearities on the dynamics of a highly deformable cantilevered wing. Two different theoretical formulations are presented and analysed for nonlinear behavior. The first formulation, which is more conventional, assumes zero equilibrias and structural nonlinearities occur as terms up to third order in the Taylor series expansion of structural nonlinearities. In the second approach, no prior assumption about equilibria states of the wing is made. Kinematic nonlinearities due to curvature and inertia were retained in their exact form. Thus, the former becomes a special case of the latter. This nonlinear formulation permits the analysis of dynamics about nonzero trims. Nonzero trim states are computed as a system parameter is varied using a continuation software tool. The stability characteristics of these trim states are also ascertained. Various bifurcation points of the system are determined. Limit-cycle oscillations are also investigated for and are characterized in terms of amplitude of vibration. The research in particular examines the impact of in-plane degree of freedom on the stability of nonzero trim states. The effect of variation of system parameters such as stiffness ratio, aspect ratio and root angle of attack is also studied. The method of direct eigenanalysis of nonzero equilibria is novel and new for an aeroelastic system.
