Flying animals possess flexible wings that deform during flight. The chordwise flexibility alters the wing shape, affecting the effective angle of attack and hence the surrounding aerodynamics. However, the effects of spanwise flexibility on the locomotion are inadequately understood. Here, we present a two-way coupled aeroelastic model of a plunging spanwise flexible wing. The aerodynamics is modelled with a two-dimensional, unsteady, incompressible potential flow model, evaluated at each spanwise location of the wing. The two-way coupling is realized by considering the transverse displacement as the effective plunge under the dynamic balance of wing inertia, elastic restoring force and aerodynamic force. The thrust is a result of the competition between the enhancement due to wing deformation and induced drag. The results for a purely plunging spanwise flexible wing agree well with experimental and high-fidelity numerical results from the literature. Our analysis suggests that the wing aspect ratio of the abstracted passerine and goose models corresponds to the optimal aeroelastic response, generating the highest thrust while minimizing the power required to flap the wings. At these optimal aspect ratios, the flapping frequency is near the first spanwise natural frequency of the wing, suggesting that these birds may benefit from the resonance to generate thrust.

This paper presents a novel analytical model that predicts the two-way coupled aeroelastic response of a linear elastic plate in axial potential flow, including the effects of plate curvature. The plate deforms in dynamic balance of the inertia, elastic, and aerodynamic forces. Analytical solutions are obtained by deriving the generalized aerodynamic force with respect to the beam eigenfunctions, which are expressed in a Chebyshev polynomial expansion. Exact expressions are derived for the generated lift, thrust and required input power. The derived solution agrees well with the results reported in the literature for plate flutter and flapping wings.

We explore the triggering mechanism of aeroelastic instability due to freeplay in a 2-dimensional rigid airfoil with a control surface. This 3-DOF aeroelastic model is mounted on a cubic nonlinear stiffness in heave and pitch, with the freeplay being piecewise linear (i.e., nonsmooth); and the quasisteady aerodynamic theory is considered. Similar to the 2-DOF aeroelastic model, the LCO triggering consists of a series of resonance captures and escapes from resonances. Furthermore, the nonlinear modal interactions become more complicated for full LCO development due to nonsmooth dynamics introduced when the angular displacement of the control surface reaches the clearance limit. Understanding such LCO triggering, we apply a nonlinear energy sink (NES) such that the NES can interact primarily with the heave mode to prevent its initial triggering from being developed further, and also that it can engage in attenuating the pitch mode response. Three distinct suppression mechanisms by means of targeted energy transfers can be identified: recurrent burstouts and suppressions, partial suppression and complete elimination of aeroelastic instability. We explore the respective mechanisms extensively by numerical methods such as a numerical continuation method and wavelet transform spectra.

No abstract