Dynamic model of an ornithopter with elastic high-aspect-ratio flapping wings

A simple computational model is proposed for investigating the dynamic behavior of an ornithopter with elastic flapping wings of high aspect ratio. The wings are modeled as an elongated, orthotropic composite plate of a rod-like type. It is assumed that the orthotropy axes of the plate material do not coincide with the axes of the chosen Cartesian coordinate system for the wing, which allows for the description of its coupled bending-torsional vibrations. The ornithopter's body core is modeled as an absolutely rigid solid body. The developed deformation model for the wing is based on the relations of the refined shear model of S.P. Timoshenko, formulated for rods in a geometrically nonlinear approximation, neglecting compression in the transverse directions. The kinematic coupling conditions between the wings and the body core are formulated. Using these conditions and based on the variational D'Alembert-Lagrange principle, the corresponding equilibrium (motion) equations and boundary conditions are derived for the considered ornithopter elements. The force coupling conditions at the wing-body junction are also obtained, which essentially represent the equations of perturbed motion for the body core.