The influence of unsymmetrical bending and torsion on elastic and viscoelastic wing flutter

The analysis in this paper considers the effects of in-plane bending, i.e. about the vertical axis, on torsional and plunging bending as well as utter instabilities in any one or more bending modes (DOFs) present. The inclusion of the in-plane bending displacements and in particular their associated velocities changes the problem from a linear one to a nonlinear one for slow flying vehicles such as UAVs and MAVs. In both instances the spatial dependences of the five governing relations are eliminated by Galerkin's method. The resulting nonlinear elastic ODEs are solved by using the Runge-Kutta numerical approach. The equivalent viscoelastic relations are nonlinear integral ordinary differential equations (IODEs) with variable coefficients, which unfortunately also can only be solved numerically thus making general parametric solutions, studies and conclusions unreachable. A number of illustrative problem examples with results are presented and discussed. The character and stability (utter) of the solutions are examined.