Analytical model and stability analysis of the leading edge spar of a passively morphing ornithopter wing

Abstract

This paper presents the stability analysis of the leading edge spar of a flapping wing unmanned air vehicle with a compliant spine inserted in it. The compliant spine is a mechanism that was designed to be flexible during the upstroke and stiff during the downstroke. Inserting a variable stiffness mechanism into the leading edge spar affects its structural stability. The model for the spar-spine system was formulated in terms of the well-known Mathieu's equation, in which the compliant spine was modeled as a torsional spring with a sinusoidal stiffness function. Experimental data was used to validate the model and results show agreement within 11%. The structural stability of the leading edge spar-spine system was determined analytically and graphically using a phase plane plot and Strutt diagrams. Lastly, a torsional viscous damper was added to the leading edge spar-spine model to investigate the effect of damping on stability. Results show that for the un-damped case, the leading edge spar-spine response was stable and bounded; however, there were areas of instability that appear for a range of spine upstroke and downstroke stiffnesses. Results also show that there exist a damping ratio between 0.2 and 0.5, for which the leading edge spar-spine system was stable for all values of spine upstroke and downstroke stiffnesses.

Tuning of a Rigid-Body Dynamics Model of a Flapping Wing Structure With Compliant Joints

“…This focus of the current paper is on experimentally validating the structural components of the model, i.e., structural stiffness and structural damping. Previous benchtop experiments performed with the leading edge spar of the test ornithopter flapping in vacuum and ambient conditions showed very little aerodynamic effects on the spar kinematics without the wing membrane attached [32,37]. Thus, it is assumed that in the experiment, the aerodynamic forces acting on the spar and CCM without the wing membrane attached are small due to low Reynold's number, and therefore the tuned model parameters using ambient data would be very similar to using vacuum data.…”

Aeroelastic model and analysis of an active camber morphing wing

“…Smart materials have been used as actuators to control wing panels [10,11], spanwise deflection [12] and trailing-edge flaps [13,14]. Many morphing wing structures are designed as compliant mechanisms to allow the desired deformation [15][16][17][18][19][20][21]. A morphing leading-edge model was designed as a monolithic aluminium internal compliant mechanism to provide droop-nose morphing [18].…”

Towards reconfigurable and flexible multirotors

“…The major source of design inspiration for novel reconfigurable UAVs can be traced to nature, where birds demonstrate flights through narrow gaps/cluttered spaces and excellent use of beaks/claws (Schiffner et al 2014;Von Bayern et al 2009). Consequently, designs based on flexible wings have been explored to achieve foldable UAVs (Grant et al 2010;Wissa et al 2015;Di Luca et al 2017). However, in order to pursue the many advantages of multirotor UAVs over their fixed-wing counterparts such as simple chassis, manoeuvrability, hovering and vertical takeoff/landing, we limit our survey on the state-of-the-art research on reconfigurable multirotor UAVs.…”